\hypertarget{namespacemom__meke}{}\section{mom\+\_\+meke Module Reference} \label{namespacemom__meke}\index{mom\+\_\+meke@{mom\+\_\+meke}} \subsection{Detailed Description} Implements the Mesoscale Eddy Kinetic Energy framework with topographic beta effect included in computing beta in Rhines scale. \hypertarget{namespacemom__meke_section_MEKE}{}\subsection{The Mesoscale Eddy Kinetic Energy (\+M\+E\+K\+E) framework}\label{namespacemom__meke_section_MEKE} The M\+E\+KE framework accounts for the mean potential energy removed by the first order closures used to parameterize mesoscale eddies. It requires closure at the second order, namely dissipation and transport of eddy energy. Monitoring the sub-\/grid scale eddy energy budget provides a means to predict a sub-\/grid eddy-\/velocity scale which can be used in the lower order closures.\hypertarget{namespacemom__meke_section_MEKE_equations}{}\subsubsection{M\+E\+K\+E equations}\label{namespacemom__meke_section_MEKE_equations} The eddy kinetic energy equation is\+: \[ \partial_{\tilde{t}} E = \overbrace{ \dot{E}_b + \gamma_\eta \dot{E}_\eta + \gamma_v \dot{E}_v }^\text{sources} - \overbrace{ ( \lambda + C_d | U_d | \gamma_b^2 ) E }^\text{local dissipation} + \overbrace{ \nabla \cdot ( ( \kappa_E + \gamma_M \kappa_M ) \nabla E - \kappa_4 \nabla^3 E ) }^\text{smoothing} \] where $ E $ is the eddy kinetic energy (variable {\ttfamily M\+E\+KE}) with units of m\textsuperscript{2}s\textsuperscript{-\/2}, and $\tilde{t} = a t$ is a scaled time. The non-\/dimensional factor $ a\geq 1 $ is used to accelerate towards equilibrium. The M\+E\+KE equation is two-\/dimensional and obtained by depth averaging the the three-\/dimensional eddy energy equation. In the following expressions $ \left< \phi \right> = \frac{1}{H} \int^\eta_{-D} \phi \, dz $ maps three dimensional terms into the two-\/dimensional quantities needed.\hypertarget{namespacemom__meke_section_MEKE_source_terms}{}\paragraph{M\+E\+K\+E source terms}\label{namespacemom__meke_section_MEKE_source_terms} The source term $ \dot{E}_b $ is a constant background source of energy intended to avoid the limit $E\rightarrow 0$. The \char`\"{}\+G\+M\char`\"{} source term \[ \dot{E}_\eta = - \left< \overline{w^\prime b^\prime} \right> = \left< \kappa_h N^2S^2 \right> \approx \left< \kappa_h g\prime |\nabla_\sigma \eta|^2 \right>\] equals the mean potential energy removed by the Gent-\/\+Mc\+Williams closure, and is excluded/included in the M\+E\+KE budget by the efficiency parameter $ \gamma_\eta \in [0,1] $. The \char`\"{}frictional\char`\"{} source term \[ \dot{E}_{v} = \left< \partial_i u_j \tau_{ij} \right> \] equals the mean kinetic energy removed by lateral viscous fluxes, and is excluded/included in the M\+E\+KE budget by the efficiency parameter $ \gamma_v \in [0,1] $.\hypertarget{namespacemom__meke_section_MEKE_dissipation_terms}{}\paragraph{M\+E\+K\+E dissipation terms}\label{namespacemom__meke_section_MEKE_dissipation_terms} The local dissipation of $ E $ is parameterized through a linear damping, $\lambda$, and bottom drag, $ C_d | U_d | \gamma_b^2 $. The $ \gamma_b $ accounts for the weak projection of the column-\/mean eddy velocty to the bottom. In other words, the bottom velocity is estimated as $ \gamma_b U_e $. The bottom drag coefficient, $ C_d $ is the same as that used in the bottom friction in the mean model equations. The bottom drag velocity scale, $ U_d $, has contributions from the resolved state and $ E $\+: \[ U_d = \sqrt{ U_b^2 + |u|^2_{z=-D} + |\gamma_b U_e|^2 } .\] where the eddy velocity scale, $ U_e $, is given by\+: \[ U_e = \sqrt{ 2 E } .\] $ U_b $ is a constant background bottom velocity scale and is typically not used (i.\+e. set to zero). Following Jansen et al., 2015, the projection of eddy energy on to the bottom is given by the ratio of bottom energy to column mean energy\+: \[ \gamma_b^2 = \frac{E_b}{E} = \gamma_{d0} + \left( 1 + c_{b} \frac{L_d}{L_f} \right)^{-\frac{4}{5}} , \] \[ \gamma_b^2 \leftarrow \max{\left( \gamma_b^2, \gamma_{min}^2 \right)} . \]\hypertarget{namespacemom__meke_section_MEKE_smoothing}{}\subsubsection{M\+E\+K\+E smoothing terms}\label{namespacemom__meke_section_MEKE_smoothing} $ E $ is laterally diffused by a diffusivity $ \kappa_E + \gamma_M \kappa_M $ where $ \kappa_E $ is a constant diffusivity and the term $ \gamma_M \kappa_M $ is a \char`\"{}self diffusion\char`\"{} using the diffusivity calculated in the section \hyperlink{namespacemom__meke_section_MEKE_diffusivity}{Diffusivity derived from M\+E\+KE}. $ \kappa_4 $ is a constant bi-\/harmonic diffusivity.\hypertarget{namespacemom__meke_section_MEKE_diffusivity}{}\subsubsection{Diffusivity derived from M\+E\+KE}\label{namespacemom__meke_section_MEKE_diffusivity} The predicted eddy velocity scale, $ U_e $, can be combined with a mixing length scale to form a diffusivity. The primary use of a M\+E\+KE derived diffusivity is for use in thickness diffusion (module \hyperlink{namespacemom__thickness__diffuse}{mom\+\_\+thickness\+\_\+diffuse}) and optionally in along isopycnal mixing of tracers (module \hyperlink{namespacemom__tracer__hor__diff}{mom\+\_\+tracer\+\_\+hor\+\_\+diff}). The original form used (enabled with M\+E\+K\+E\+\_\+\+O\+L\+D\+\_\+\+L\+S\+C\+A\+LE=True)\+: \[ \kappa_M = \gamma_\kappa \sqrt{ \gamma_t^2 U_e^2 A_\Delta } \] where $ A_\Delta $ is the area of the grid cell. Following Jansen et al., 2015, we now use \[ \kappa_M = \gamma_\kappa l_M \sqrt{ \gamma_t^2 U_e^2 } \] where $ \gamma_\kappa \in [0,1] $ is a non-\/dimensional factor and, following Jansen et al., 2015, $\gamma_t^2$ is the ratio of barotropic eddy energy to column mean eddy energy given by \[ \gamma_t^2 = \frac{E_t}{E} = \left( 1 + c_{t} \frac{L_d}{L_f} \right)^{-\frac{1}{4}} , \] \[ \gamma_t^2 \leftarrow \max{\left( \gamma_t^2, \gamma_{min}^2 \right)} . \] The length-\/scale is a configurable combination of multiple length scales\+: \[ l_M = \left( \frac{\alpha_d}{L_d} + \frac{\alpha_f}{L_f} + \frac{\alpha_R}{L_R} + \frac{\alpha_e}{L_e} + \frac{\alpha_\Delta}{L_\Delta} + \frac{\delta[L_c]}{L_c} \right)^{-1} \] where \begin{eqnarray*} L_d & = & \sqrt{\frac{c_g^2}{f^2+2\beta c_g}} \sim \frac{ c_g }{f} \\\\ L_R & = & \sqrt{\frac{U_e}{\beta^*}} \\\\ L_e & = & \frac{U_e}{|S| N} \\\\ L_f & = & \frac{H}{c_d} \\\\ L_\Delta & = & \sqrt{A_\Delta} . \end{eqnarray*} $L_c$ is a constant and $\delta[L_c]$ is the impulse function so that the term $\frac{\delta[L_c]}{L_c}$ evaluates to $\frac{1}{L_c}$ when $L_c$ is non-\/zero but is dropped if $L_c=0$. $\beta^*$ is the effective $\beta$ that combines both the planetary vorticity gradient (i.\+e. $\beta=\nabla f$) and the topographic $\beta$ effect, with the latter weighed by a weighting constant, $c_\beta$, that varies from 0 to 1, so that $c_\beta=0$ means the topographic $\beta$ effect is ignored, while $c_\beta=1$ means it is fully considered. The new $\beta^*$ therefore takes the form of \[ \beta^* = \sqrt{( \partial_xf - c_\beta\frac{f}{D}\partial_xD )^2 + ( \partial_yf - c_\beta\frac{f}{D}\partial_yD )^2} \] where $D$ is water column depth at T points.\hypertarget{namespacemom__meke_section_MEKE_viscosity}{}\subsubsection{Viscosity derived from M\+E\+KE}\label{namespacemom__meke_section_MEKE_viscosity} As for $ \kappa_M $, the predicted eddy velocity scale can be used to form a harmonic eddy viscosity, \[ \kappa_u = \gamma_u \sqrt{ U_e^2 A_\Delta } \] as well as a biharmonic eddy viscosity, \[ \kappa_4 = \gamma_4 \sqrt{ U_e^2 A_\Delta^3 } \]\hypertarget{namespacemom__meke_section_MEKE_limit_case}{}\subsubsection{Limit cases for local source-\/dissipative balance}\label{namespacemom__meke_section_MEKE_limit_case} Note that in steady-\/state (or when $ a>>1 $) and there is no diffusion of $ E $ then \[ \overline{E} \approx \frac{ \dot{E}_b + \gamma_\eta \dot{E}_\eta + \gamma_v \dot{E}_v }{ \lambda + C_d|U_d|\gamma_b^2 } . \] In the linear drag limit, where $ U_e << \min(U_b, |u|_{z=-D}, C_d^{-1}\lambda) $, the equilibrium becomes $ \overline{E} \approx \frac{ \dot{E}_b + \gamma_\eta \dot{E}_\eta + \gamma_v \dot{E}_v }{ \lambda + C_d \sqrt{ U_b^2 + |u|^2_{z=-D} } } $. In the nonlinear drag limit, where $ U_e >> \max(U_b, |u|_{z=-D}, C_d^{-1}\lambda) $, the equilibrium becomes $ \overline{E} \approx \left( \frac{ \dot{E}_b + \gamma_\eta \dot{E}_\eta + \gamma_v \dot{E}_v }{ \sqrt{2} C_d \gamma_b^3 } \right)^\frac{2}{3} $.\hypertarget{namespacemom__meke_section_MEKE_module_parameters}{}\paragraph{M\+E\+K\+E module parameters}\label{namespacemom__meke_section_MEKE_module_parameters} \tabulinesep=1mm \begin{longtabu} spread 0pt [c]{*{2}{|X[-1]}|} \hline \rowcolor{\tableheadbgcolor}\textbf{ Symbol }&\textbf{ Module parameter }\\\cline{1-2} \endfirsthead \hline \endfoot \hline \rowcolor{\tableheadbgcolor}\textbf{ Symbol }&\textbf{ Module parameter }\\\cline{1-2} \endhead -\/ &{\ttfamily U\+S\+E\+\_\+\+M\+E\+KE} \\\cline{1-2} $ a $ &{\ttfamily M\+E\+K\+E\+\_\+\+D\+T\+S\+C\+A\+LE} \\\cline{1-2} $ \dot{E}_b $ &{\ttfamily M\+E\+K\+E\+\_\+\+B\+G\+S\+RC} \\\cline{1-2} $ \gamma_\eta $ &{\ttfamily M\+E\+K\+E\+\_\+\+G\+M\+C\+O\+E\+FF} \\\cline{1-2} $ \gamma_v $ &{\ttfamily M\+E\+K\+E\+\_\+\+Fr\+C\+O\+E\+FF} \\\cline{1-2} $ \lambda $ &{\ttfamily M\+E\+K\+E\+\_\+\+D\+A\+M\+P\+I\+NG} \\\cline{1-2} $ U_b $ &{\ttfamily M\+E\+K\+E\+\_\+\+U\+S\+C\+A\+LE} \\\cline{1-2} $ \gamma_{d0} $ &{\ttfamily M\+E\+K\+E\+\_\+\+C\+D\+\_\+\+S\+C\+A\+LE} \\\cline{1-2} $ c_{b} $ &{\ttfamily M\+E\+K\+E\+\_\+\+CB} \\\cline{1-2} $ c_{t} $ &{\ttfamily M\+E\+K\+E\+\_\+\+CT} \\\cline{1-2} $ \kappa_E $ &{\ttfamily M\+E\+K\+E\+\_\+\+KH} \\\cline{1-2} $ \kappa_4 $ &{\ttfamily M\+E\+K\+E\+\_\+\+K4} \\\cline{1-2} $ \gamma_\kappa $ &{\ttfamily M\+E\+K\+E\+\_\+\+K\+H\+C\+O\+E\+FF} \\\cline{1-2} $ \gamma_M $ &{\ttfamily M\+E\+K\+E\+\_\+\+K\+H\+M\+E\+K\+E\+\_\+\+F\+AC} \\\cline{1-2} $ \gamma_u $ &{\ttfamily M\+E\+K\+E\+\_\+\+V\+I\+S\+C\+O\+S\+I\+T\+Y\+\_\+\+C\+O\+E\+F\+F\+\_\+\+KU} \\\cline{1-2} $ \gamma_4 $ &{\ttfamily M\+E\+K\+E\+\_\+\+V\+I\+S\+C\+O\+S\+I\+T\+Y\+\_\+\+C\+O\+E\+F\+F\+\_\+\+AU} \\\cline{1-2} $ \gamma_{min}^2 $&{\ttfamily M\+E\+K\+E\+\_\+\+M\+I\+N\+\_\+\+G\+A\+M\+M\+A2} \\\cline{1-2} $ \alpha_d $ &{\ttfamily M\+E\+K\+E\+\_\+\+A\+L\+P\+H\+A\+\_\+\+D\+E\+F\+O\+RM} \\\cline{1-2} $ \alpha_f $ &{\ttfamily M\+E\+K\+E\+\_\+\+A\+L\+P\+H\+A\+\_\+\+F\+R\+I\+CT} \\\cline{1-2} $ \alpha_R $ &{\ttfamily M\+E\+K\+E\+\_\+\+A\+L\+P\+H\+A\+\_\+\+R\+H\+I\+N\+ES} \\\cline{1-2} $ \alpha_e $ &{\ttfamily M\+E\+K\+E\+\_\+\+A\+L\+P\+H\+A\+\_\+\+E\+A\+DY} \\\cline{1-2} $ \alpha_\Delta $ &{\ttfamily M\+E\+K\+E\+\_\+\+A\+L\+P\+H\+A\+\_\+\+G\+R\+ID} \\\cline{1-2} $ L_c $ &{\ttfamily M\+E\+K\+E\+\_\+\+F\+I\+X\+E\+D\+\_\+\+M\+I\+X\+I\+N\+G\+\_\+\+L\+E\+N\+G\+TH} \\\cline{1-2} $ c_\beta $ &{\ttfamily M\+E\+K\+E\+\_\+\+T\+O\+P\+O\+G\+R\+A\+P\+H\+I\+C\+\_\+\+B\+E\+TA} \\\cline{1-2} -\/ &{\ttfamily M\+E\+K\+E\+\_\+\+K\+H\+T\+H\+\_\+\+F\+AC} \\\cline{1-2} -\/ &{\ttfamily M\+E\+K\+E\+\_\+\+K\+H\+T\+R\+\_\+\+F\+AC} \\\cline{1-2} \end{longtabu} \tabulinesep=1mm \begin{longtabu} spread 0pt [c]{*{2}{|X[-1]}|} \hline \rowcolor{\tableheadbgcolor}\textbf{ Symbol }&\textbf{ Model parameter }\\\cline{1-2} \endfirsthead \hline \endfoot \hline \rowcolor{\tableheadbgcolor}\textbf{ Symbol }&\textbf{ Model parameter }\\\cline{1-2} \endhead $ C_d $ &{\ttfamily C\+D\+R\+AG} \\\cline{1-2} \end{longtabu} \hypertarget{namespacemom__meke_section_MEKE_references}{}\subsubsection{References}\label{namespacemom__meke_section_MEKE_references} Jansen, M. F., A. J. Adcroft, R. Hallberg, and I. M. Held, 2015\+: Parameterization of eddy fluxes based on a mesoscale energy budget. Ocean Modelling, 92, 28--41, \href{http://doi.org/10.1016/j.ocemod.2015.05.007}{\tt http\+://doi.\+org/10.\+1016/j.\+ocemod.\+2015.\+05.\+007} . Marshall, D. P., and A. J. Adcroft, 2010\+: Parameterization of ocean eddies\+: Potential vorticity mixing, energetics and Arnold first stability theorem. Ocean Modelling, 32, 188--204, \href{http://doi.org/10.1016/j.ocemod.2010.02.001}{\tt http\+://doi.\+org/10.\+1016/j.\+ocemod.\+2010.\+02.\+001} . \subsection*{Data Types} \begin{DoxyCompactItemize} \item type \hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs} \begin{DoxyCompactList}\small\item\em Control structure that contains M\+E\+KE parameters and diagnostics handles. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \hyperlink{namespacemom__meke_a5f752f097ddeba7071e1703110e51bc2}{step\+\_\+forward\+\_\+meke} (M\+E\+KE, h, S\+N\+\_\+u, S\+N\+\_\+v, visc, dt, G, GV, US, CS, hu, hv) \begin{DoxyCompactList}\small\item\em Integrates forward-\/in-\/time the M\+E\+KE eddy energy equation. See \hyperlink{namespacemom__meke_section_MEKE_equations}{M\+E\+KE equations}. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__meke_a0ef9a8bcdf705b544db9b8c28a5e6a56}{meke\+\_\+equilibrium} (CS, M\+E\+KE, G, GV, US, S\+N\+\_\+u, S\+N\+\_\+v, drag\+\_\+rate\+\_\+visc, I\+\_\+mass) \begin{DoxyCompactList}\small\item\em Calculates the equilibrium solutino where the source depends only on M\+E\+KE diffusivity and there is no lateral diffusion of M\+E\+KE. Results is in M\+E\+KEM\+E\+KE. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__meke_a843244b0cc72a08489920dcda464b063}{meke\+\_\+equilibrium\+\_\+restoring} (CS, G, US, S\+N\+\_\+u, S\+N\+\_\+v) \item subroutine \hyperlink{namespacemom__meke_a8180d5d0cacf48bcbdffead9e6a06efd}{meke\+\_\+lengthscales} (CS, M\+E\+KE, G, GV, US, S\+N\+\_\+u, S\+N\+\_\+v, E\+KE, bottom\+Fac2, barotr\+Fac2, Lmix\+Scale) \begin{DoxyCompactList}\small\item\em Calculates the eddy mixing length scale and $\gamma_b$ and $\gamma_t$ functions that are ratios of either bottom or barotropic eddy energy to the column eddy energy, respectively. See \hyperlink{namespacemom__meke_section_MEKE_equations}{M\+E\+KE equations}. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__meke_aed5885cde342caa59b2b9cde72a3e1e7}{meke\+\_\+lengthscales\+\_\+0d} (CS, US, area, beta, depth, Rd\+\_\+dx, SN, E\+KE, bottom\+Fac2, barotr\+Fac2, Lmix\+Scale, Lrhines, Leady) \begin{DoxyCompactList}\small\item\em Calculates the eddy mixing length scale and $\gamma_b$ and $\gamma_t$ functions that are ratios of either bottom or barotropic eddy energy to the column eddy energy, respectively. See \hyperlink{namespacemom__meke_section_MEKE_equations}{M\+E\+KE equations}. \end{DoxyCompactList}\item logical function, public \hyperlink{namespacemom__meke_a099f1cfad37430ef1bd60972a92b1be4}{meke\+\_\+init} (Time, G, US, param\+\_\+file, diag, CS, M\+E\+KE, restart\+\_\+\+CS) \begin{DoxyCompactList}\small\item\em Initializes the M\+O\+M\+\_\+\+M\+E\+KE module and reads parameters. Returns True if module is to be used, otherwise returns False. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespacemom__meke_a1900316331157e48f1a6029bac63fbd0}{meke\+\_\+alloc\+\_\+register\+\_\+restart} (HI, param\+\_\+file, M\+E\+KE, restart\+\_\+\+CS) \begin{DoxyCompactList}\small\item\em Allocates memory and register restart fields for the M\+O\+M\+\_\+\+M\+E\+KE module. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespacemom__meke_acc007bf1aa24263f699b059d3e9cc6eb}{meke\+\_\+end} (M\+E\+KE, CS) \begin{DoxyCompactList}\small\item\em Deallocates any variables allocated in M\+E\+K\+E\+\_\+init or M\+E\+K\+E\+\_\+alloc\+\_\+register\+\_\+restart. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespacemom__meke_a1900316331157e48f1a6029bac63fbd0}\label{namespacemom__meke_a1900316331157e48f1a6029bac63fbd0}} \index{mom\+\_\+meke@{mom\+\_\+meke}!meke\+\_\+alloc\+\_\+register\+\_\+restart@{meke\+\_\+alloc\+\_\+register\+\_\+restart}} \index{meke\+\_\+alloc\+\_\+register\+\_\+restart@{meke\+\_\+alloc\+\_\+register\+\_\+restart}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{meke\+\_\+alloc\+\_\+register\+\_\+restart()}{meke\_alloc\_register\_restart()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+meke\+::meke\+\_\+alloc\+\_\+register\+\_\+restart (\begin{DoxyParamCaption}\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(param\+\_\+file\+\_\+type), intent(in)}]{param\+\_\+file, }\item[{type(meke\+\_\+type), pointer}]{M\+E\+KE, }\item[{type(mom\+\_\+restart\+\_\+cs), pointer}]{restart\+\_\+\+CS }\end{DoxyParamCaption})} Allocates memory and register restart fields for the M\+O\+M\+\_\+\+M\+E\+KE module. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em hi} & Horizontal index structure\\ \hline \mbox{\tt in} & {\em param\+\_\+file} & Parameter file parser structure.\\ \hline & {\em meke} & A structure with M\+E\+K\+E-\/related fields.\\ \hline & {\em restart\+\_\+cs} & Restart control structure for M\+O\+M\+\_\+\+M\+E\+KE. \\ \hline \end{DoxyParams} Definition at line 1347 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 1347 \textcolor{comment}{! Arguments} 1348 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: hi\textcolor{comment}{ !< Horizontal index structure} 1349 \textcolor{keywordtype}{type}(param\_file\_type), \textcolor{keywordtype}{intent(in)} :: param\_file\textcolor{comment}{ !< Parameter file parser structure.} 1350 \textcolor{keywordtype}{type}(meke\_type), \textcolor{keywordtype}{pointer} :: meke\textcolor{comment}{ !< A structure with MEKE-related fields.} 1351 \textcolor{keywordtype}{type}(mom\_restart\_cs), \textcolor{keywordtype}{pointer} :: restart\_cs\textcolor{comment}{ !< Restart control structure for MOM\_MEKE.} 1352 \textcolor{comment}{! Local variables} 1353 \textcolor{keywordtype}{type}(vardesc) :: vd 1354 \textcolor{keywordtype}{real} :: meke\_gmcoeff, meke\_frcoeff, meke\_gmecoeff, meke\_khcoeff, meke\_visccoeff\_ku, meke\_visccoeff\_au 1355 \textcolor{keywordtype}{logical} :: use\_kh\_in\_meke 1356 \textcolor{keywordtype}{logical} :: usemeke 1357 \textcolor{keywordtype}{integer} :: isd, ied, jsd, jed 1358 1359 \textcolor{comment}{! Determine whether this module will be used} 1360 usemeke = .false.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"USE\_MEKE"},usemeke) 1361 1362 \textcolor{comment}{! Read these parameters to determine what should be in the restarts} 1363 meke\_gmcoeff =-1.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"MEKE\_GMCOEFF"},meke\_gmcoeff) 1364 meke\_frcoeff =-1.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"MEKE\_FRCOEFF"},meke\_frcoeff) 1365 meke\_gmecoeff =-1.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"MEKE\_GMECOEFF"},meke\_gmecoeff) 1366 meke\_khcoeff =1.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"MEKE\_KHCOEFF"},meke\_khcoeff) 1367 meke\_visccoeff\_ku =0.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"MEKE\_VISCOSITY\_COEFF\_KU"},meke\_visccoeff\_ku) 1368 meke\_visccoeff\_au =0.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"MEKE\_VISCOSITY\_COEFF\_AU"},meke\_visccoeff\_au) 1369 use\_kh\_in\_meke = .false.; \textcolor{keyword}{call }read\_param(param\_file,\textcolor{stringliteral}{"USE\_KH\_IN\_MEKE"}, use\_kh\_in\_meke) 1370 \textcolor{comment}{! Allocate control structure} 1371 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke)) \textcolor{keywordflow}{then} 1372 \textcolor{keyword}{call }mom\_error(warning, \textcolor{stringliteral}{"MEKE\_alloc\_register\_restart called with an associated "}// & 1373 \textcolor{stringliteral}{"MEKE type."}) 1374 \textcolor{keywordflow}{return} 1375 else; \textcolor{keyword}{allocate}(meke);\textcolor{keywordflow}{ endif} 1376 1377 \textcolor{keywordflow}{if} (.not. usemeke) \textcolor{keywordflow}{return} 1378 1379 \textcolor{comment}{! Allocate memory} 1380 \textcolor{keyword}{call }mom\_mesg(\textcolor{stringliteral}{"MEKE\_alloc\_register\_restart: allocating and registering"}, 5) 1381 isd = hi%isd ; ied = hi%ied ; jsd = hi%jsd ; jed = hi%jed 1382 \textcolor{keyword}{allocate}(meke%MEKE(isd:ied,jsd:jed)) ; meke%MEKE(:,:) = 0.0 1383 vd = var\_desc(\textcolor{stringliteral}{"MEKE"}, \textcolor{stringliteral}{"m2 s-2"}, hor\_grid=\textcolor{stringliteral}{'h'}, z\_grid=\textcolor{stringliteral}{'1'}, & 1384 longname=\textcolor{stringliteral}{"Mesoscale Eddy Kinetic Energy"}) 1385 \textcolor{keyword}{call }register\_restart\_field(meke%MEKE, vd, .false., restart\_cs) 1386 \textcolor{keywordflow}{if} (meke\_gmcoeff>=0.) \textcolor{keywordflow}{then} 1387 \textcolor{keyword}{allocate}(meke%GM\_src(isd:ied,jsd:jed)) ; meke%GM\_src(:,:) = 0.0 1388 \textcolor{keywordflow}{ endif} 1389 \textcolor{keywordflow}{if} (meke\_frcoeff>=0. .or. meke\_gmecoeff>=0.) \textcolor{keywordflow}{then} 1390 \textcolor{keyword}{allocate}(meke%mom\_src(isd:ied,jsd:jed)) ; meke%mom\_src(:,:) = 0.0 1391 \textcolor{keywordflow}{ endif} 1392 \textcolor{keywordflow}{if} (meke\_gmecoeff>=0.) \textcolor{keywordflow}{then} 1393 \textcolor{keyword}{allocate}(meke%GME\_snk(isd:ied,jsd:jed)) ; meke%GME\_snk(:,:) = 0.0 1394 \textcolor{keywordflow}{ endif} 1395 \textcolor{keywordflow}{if} (meke\_khcoeff>=0.) \textcolor{keywordflow}{then} 1396 \textcolor{keyword}{allocate}(meke%Kh(isd:ied,jsd:jed)) ; meke%Kh(:,:) = 0.0 1397 vd = var\_desc(\textcolor{stringliteral}{"MEKE\_Kh"}, \textcolor{stringliteral}{"m2 s-1"}, hor\_grid=\textcolor{stringliteral}{'h'}, z\_grid=\textcolor{stringliteral}{'1'}, & 1398 longname=\textcolor{stringliteral}{"Lateral diffusivity from Mesoscale Eddy Kinetic Energy"}) 1399 \textcolor{keyword}{call }register\_restart\_field(meke%Kh, vd, .false., restart\_cs) 1400 \textcolor{keywordflow}{ endif} 1401 \textcolor{keyword}{allocate}(meke%Rd\_dx\_h(isd:ied,jsd:jed)) ; meke%Rd\_dx\_h(:,:) = 0.0 1402 \textcolor{keywordflow}{if} (meke\_visccoeff\_ku/=0.) \textcolor{keywordflow}{then} 1403 \textcolor{keyword}{allocate}(meke%Ku(isd:ied,jsd:jed)) ; meke%Ku(:,:) = 0.0 1404 vd = var\_desc(\textcolor{stringliteral}{"MEKE\_Ku"}, \textcolor{stringliteral}{"m2 s-1"}, hor\_grid=\textcolor{stringliteral}{'h'}, z\_grid=\textcolor{stringliteral}{'1'}, & 1405 longname=\textcolor{stringliteral}{"Lateral viscosity from Mesoscale Eddy Kinetic Energy"}) 1406 \textcolor{keyword}{call }register\_restart\_field(meke%Ku, vd, .false., restart\_cs) 1407 \textcolor{keywordflow}{ endif} 1408 \textcolor{keywordflow}{if} (use\_kh\_in\_meke) \textcolor{keywordflow}{then} 1409 \textcolor{keyword}{allocate}(meke%Kh\_diff(isd:ied,jsd:jed)) ; meke%Kh\_diff(:,:) = 0.0 1410 vd = var\_desc(\textcolor{stringliteral}{"MEKE\_Kh\_diff"}, \textcolor{stringliteral}{"m2 s-1"},hor\_grid=\textcolor{stringliteral}{'h'},z\_grid=\textcolor{stringliteral}{'1'}, & 1411 longname=\textcolor{stringliteral}{"Copy of thickness diffusivity for diffusing MEKE"}) 1412 \textcolor{keyword}{call }register\_restart\_field(meke%Kh\_diff, vd, .false., restart\_cs) 1413 \textcolor{keywordflow}{ endif} 1414 1415 \textcolor{keywordflow}{if} (meke\_visccoeff\_au/=0.) \textcolor{keywordflow}{then} 1416 \textcolor{keyword}{allocate}(meke%Au(isd:ied,jsd:jed)) ; meke%Au(:,:) = 0.0 1417 vd = var\_desc(\textcolor{stringliteral}{"MEKE\_Au"}, \textcolor{stringliteral}{"m4 s-1"}, hor\_grid=\textcolor{stringliteral}{'h'}, z\_grid=\textcolor{stringliteral}{'1'}, & 1418 longname=\textcolor{stringliteral}{"Lateral biharmonic viscosity from Mesoscale Eddy Kinetic Energy"}) 1419 \textcolor{keyword}{call }register\_restart\_field(meke%Au, vd, .false., restart\_cs) 1420 \textcolor{keywordflow}{ endif} 1421 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__meke_acc007bf1aa24263f699b059d3e9cc6eb}\label{namespacemom__meke_acc007bf1aa24263f699b059d3e9cc6eb}} \index{mom\+\_\+meke@{mom\+\_\+meke}!meke\+\_\+end@{meke\+\_\+end}} \index{meke\+\_\+end@{meke\+\_\+end}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{meke\+\_\+end()}{meke\_end()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+meke\+::meke\+\_\+end (\begin{DoxyParamCaption}\item[{type(meke\+\_\+type), pointer}]{M\+E\+KE, }\item[{type(\hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs}), pointer}]{CS }\end{DoxyParamCaption})} Deallocates any variables allocated in M\+E\+K\+E\+\_\+init or M\+E\+K\+E\+\_\+alloc\+\_\+register\+\_\+restart. \begin{DoxyParams}{Parameters} {\em meke} & A structure with M\+E\+K\+E-\/related fields.\\ \hline {\em cs} & The control structure for M\+O\+M\+\_\+\+M\+E\+KE. \\ \hline \end{DoxyParams} Definition at line 1427 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 1427 \textcolor{keywordtype}{type}(meke\_type), \textcolor{keywordtype}{pointer} :: meke\textcolor{comment}{ !< A structure with MEKE-related fields.} 1428 \textcolor{keywordtype}{type}(meke\_cs), \textcolor{keywordtype}{pointer} :: cs\textcolor{comment}{ !< The control structure for MOM\_MEKE.} 1429 1430 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(cs)) \textcolor{keyword}{deallocate}(cs) 1431 1432 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{associated}(meke)) \textcolor{keywordflow}{return} 1433 1434 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%MEKE)) \textcolor{keyword}{deallocate}(meke%MEKE) 1435 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%GM\_src)) \textcolor{keyword}{deallocate}(meke%GM\_src) 1436 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%mom\_src)) \textcolor{keyword}{deallocate}(meke%mom\_src) 1437 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%GME\_snk)) \textcolor{keyword}{deallocate}(meke%GME\_snk) 1438 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh)) \textcolor{keyword}{deallocate}(meke%Kh) 1439 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh\_diff)) \textcolor{keyword}{deallocate}(meke%Kh\_diff) 1440 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Ku)) \textcolor{keyword}{deallocate}(meke%Ku) 1441 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Au)) \textcolor{keyword}{deallocate}(meke%Au) 1442 \textcolor{keyword}{deallocate}(meke) 1443 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__meke_a0ef9a8bcdf705b544db9b8c28a5e6a56}\label{namespacemom__meke_a0ef9a8bcdf705b544db9b8c28a5e6a56}} \index{mom\+\_\+meke@{mom\+\_\+meke}!meke\+\_\+equilibrium@{meke\+\_\+equilibrium}} \index{meke\+\_\+equilibrium@{meke\+\_\+equilibrium}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{meke\+\_\+equilibrium()}{meke\_equilibrium()}} {\footnotesize\ttfamily subroutine mom\+\_\+meke\+::meke\+\_\+equilibrium (\begin{DoxyParamCaption}\item[{type(\hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs}), pointer}]{CS, }\item[{type(meke\+\_\+type), pointer}]{M\+E\+KE, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(inout)}]{G, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension( g \%isdb\+: g \%iedb, g \%jsd\+: g \%jed), intent(in)}]{S\+N\+\_\+u, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsdb\+: g \%jedb), intent(in)}]{S\+N\+\_\+v, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed), intent(in)}]{drag\+\_\+rate\+\_\+visc, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed), intent(in)}]{I\+\_\+mass }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Calculates the equilibrium solutino where the source depends only on M\+E\+KE diffusivity and there is no lateral diffusion of M\+E\+KE. Results is in M\+E\+KEM\+E\+KE. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in,out} & {\em g} & Ocean grid.\\ \hline \mbox{\tt in} & {\em gv} & Ocean vertical grid structure.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline & {\em cs} & M\+E\+KE control structure.\\ \hline & {\em meke} & A structure with M\+E\+KE data.\\ \hline \mbox{\tt in} & {\em sn\+\_\+u} & Eady growth rate at u-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em sn\+\_\+v} & Eady growth rate at v-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drag\+\_\+rate\+\_\+visc} & Mean flow velocity contribution to the M\+E\+KE drag rate \mbox{[}L T-\/1 $\sim$$>$ m s-\/1\mbox{]}\\ \hline \mbox{\tt in} & {\em i\+\_\+mass} & Inverse of column mass \mbox{[}R-\/1 Z-\/1 $\sim$$>$ m2 kg-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 644 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 644 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(inout)} :: g\textcolor{comment}{ !< Ocean grid.} 645 \textcolor{keywordtype}{type}(verticalgrid\_type), \textcolor{keywordtype}{intent(in)} :: gv\textcolor{comment}{ !< Ocean vertical grid structure.} 646 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: us\textcolor{comment}{ !< A dimensional unit scaling type} 647 \textcolor{keywordtype}{type}(meke\_cs), \textcolor{keywordtype}{pointer} :: cs\textcolor{comment}{ !< MEKE control structure.} 648 \textcolor{keywordtype}{type}(meke\_type), \textcolor{keywordtype}{pointer} :: meke\textcolor{comment}{ !< A structure with MEKE data.} 649 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZIB\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_u\textcolor{comment}{ !< Eady growth rate at u-points [T-1 ~> s-1].} 650 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJB\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_v\textcolor{comment}{ !< Eady growth rate at v-points [T-1 ~> s-1].} 651 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(in)} :: drag\_rate\_visc\textcolor{comment}{ !< Mean flow velocity contribution} 652 \textcolor{comment}{ !! to the MEKE drag rate [L T-1 ~> m s-1]} 653 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(in)} :: i\_mass\textcolor{comment}{ !< Inverse of column mass [R-1 Z-1 ~> m2 kg-1].} 654 \textcolor{comment}{! Local variables} 655 \textcolor{keywordtype}{real} :: beta \textcolor{comment}{! Combined topograpic and planetary vorticity gradient [T-1 L-1 ~> s-1 m-1]} 656 \textcolor{keywordtype}{real} :: sn \textcolor{comment}{! The local Eady growth rate [T-1 ~> s-1]} 657 \textcolor{keywordtype}{real} :: bottomfac2, barotrfac2 \textcolor{comment}{! Vertical structure factors [nondim]} 658 \textcolor{keywordtype}{real} :: lmixscale, lrhines, leady \textcolor{comment}{! Various mixing length scales [L ~> m]} 659 \textcolor{keywordtype}{real} :: i\_h, khcoeff 660 \textcolor{keywordtype}{real} :: kh \textcolor{comment}{! A lateral diffusivity [L2 T-1 ~> m2 s-1]} 661 \textcolor{keywordtype}{real} :: ubg2 \textcolor{comment}{! Background (tidal?) velocity squared [L2 T-2 ~> m2 s-2]} 662 \textcolor{keywordtype}{real} :: cd2 663 \textcolor{keywordtype}{real} :: drag\_rate \textcolor{comment}{! The MEKE spindown timescale due to bottom drag [T-1 ~> s-1].} 664 \textcolor{keywordtype}{real} :: src \textcolor{comment}{! The sum of MEKE sources [L2 T-3 ~> W kg-1]} 665 \textcolor{keywordtype}{real} :: ldamping \textcolor{comment}{! The MEKE damping rate [T-1 ~> s-1].} 666 \textcolor{keywordtype}{real} :: eke, ekemin, ekemax, ekeerr \textcolor{comment}{! [L2 T-2 ~> m2 s-2]} 667 \textcolor{keywordtype}{real} :: resid, resmin, resmax \textcolor{comment}{! Residuals [L2 T-3 ~> W kg-1]} 668 \textcolor{keywordtype}{real} :: fath \textcolor{comment}{! Coriolis parameter at h points; to compute topographic beta [T-1 ~> s-1]} 669 \textcolor{keywordtype}{real} :: beta\_topo\_x, beta\_topo\_y \textcolor{comment}{! Topographic PV gradients in x and y [T-1 L-1 ~> s-1 m-1]} 670 \textcolor{keywordtype}{integer} :: i, j, is, ie, js, je, n1, n2 671 \textcolor{keywordtype}{real} :: tolerance \textcolor{comment}{! Width of EKE bracket [L2 T-2 ~> m2 s-2].} 672 \textcolor{keywordtype}{logical} :: usesecant, debugiteration 673 674 \textcolor{keywordtype}{real} :: lgrid, ldeform, lfrict 675 676 is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec 677 678 debugiteration = .false. 679 khcoeff = cs%MEKE\_KhCoeff 680 ubg2 = cs%MEKE\_Uscale**2 681 cd2 = cs%cdrag**2 682 tolerance = 1.0e-12*us%m\_s\_to\_L\_T**2 683 684 \textcolor{comment}{!$OMP do} 685 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 686 \textcolor{comment}{! SN = 0.25*max( (SN\_u(I,j) + SN\_u(I-1,j)) + (SN\_v(i,J) + SN\_v(i,J-1)), 0.)} 687 \textcolor{comment}{! This avoids extremes values in equilibrium solution due to bad values in SN\_u, SN\_v} 688 sn = min(sn\_u(i,j), sn\_u(i-1,j), sn\_v(i,j), sn\_v(i,j-1)) 689 690 \textcolor{keywordflow}{if} (cs%MEKE\_equilibrium\_alt) \textcolor{keywordflow}{then} 691 meke%MEKE(i,j) = (cs%MEKE\_GEOMETRIC\_alpha * sn * us%Z\_to\_m*g%bathyT(i,j))**2 / cd2 692 \textcolor{keywordflow}{else} 693 fath = 0.25*((g%CoriolisBu(i,j) + g%CoriolisBu(i-1,j-1)) + & 694 (g%CoriolisBu(i-1,j) + g%CoriolisBu(i,j-1))) \textcolor{comment}{! Coriolis parameter at h points} 695 696 \textcolor{comment}{! Since zero-bathymetry cells are masked, this avoids calculations on land} 697 \textcolor{keywordflow}{if} (cs%MEKE\_topographic\_beta == 0. .or. g%bathyT(i,j) == 0.) \textcolor{keywordflow}{then} 698 beta\_topo\_x = 0. ; beta\_topo\_y = 0. 699 \textcolor{keywordflow}{else} 700 \textcolor{comment}{!### Consider different combinations of these estimates of topographic beta, and the use} 701 \textcolor{comment}{! of the water column thickness instead of the bathymetric depth.} 702 beta\_topo\_x = -cs%MEKE\_topographic\_beta * fath * 0.5 * ( & 703 (g%bathyT(i+1,j)-g%bathyT(i,j)) * g%IdxCu(i,j) & 704 / max(g%bathyT(i+1,j),g%bathyT(i,j), gv%H\_subroundoff) & 705 + (g%bathyT(i,j)-g%bathyT(i-1,j)) * g%IdxCu(i-1,j) & 706 / max(g%bathyT(i,j),g%bathyT(i-1,j), gv%H\_subroundoff) ) 707 beta\_topo\_y = -cs%MEKE\_topographic\_beta * fath * 0.5 * ( & 708 (g%bathyT(i,j+1)-g%bathyT(i,j)) * g%IdyCv(i,j) & 709 / max(g%bathyT(i,j+1),g%bathyT(i,j), gv%H\_subroundoff) + & 710 (g%bathyT(i,j)-g%bathyT(i,j-1)) * g%IdyCv(i,j-1) & 711 / max(g%bathyT(i,j),g%bathyT(i,j-1), gv%H\_subroundoff) ) 712 \textcolor{keywordflow}{ endif} 713 beta = sqrt((g%dF\_dx(i,j) + beta\_topo\_x)**2 + & 714 (g%dF\_dy(i,j) + beta\_topo\_y)**2 ) 715 716 i\_h = us%L\_to\_Z*gv%Rho0 * i\_mass(i,j) 717 718 \textcolor{keywordflow}{if} (khcoeff*sn*i\_h>0.) \textcolor{keywordflow}{then} 719 \textcolor{comment}{! Solve resid(E) = 0, where resid = Kh(E) * (SN)^2 - damp\_rate(E) E} 720 ekemin = 0. \textcolor{comment}{! Use the trivial root as the left bracket} 721 resmin = 0. \textcolor{comment}{! Need to detect direction of left residual} 722 ekemax = 0.01*us%m\_s\_to\_L\_T**2 \textcolor{comment}{! First guess at right bracket} 723 usesecant = .false. \textcolor{comment}{! Start using a bisection method} 724 725 \textcolor{comment}{! First find right bracket for which resid<0} 726 resid = 1.0*us%m\_to\_L**2*us%T\_to\_s**3 ; n1 = 0 727 \textcolor{keywordflow}{do} \textcolor{keywordflow}{while} (resid>0.) 728 n1 = n1 + 1 729 eke = ekemax 730 \textcolor{keyword}{call }meke\_lengthscales\_0d(cs, us, g%areaT(i,j), beta, g%bathyT(i,j), & 731 meke%Rd\_dx\_h(i,j), sn, eke, & 732 bottomfac2, barotrfac2, lmixscale, lrhines, leady) 733 \textcolor{comment}{! TODO: Should include resolution function in Kh} 734 kh = (khcoeff * sqrt(2.*barotrfac2*eke) * lmixscale) 735 src = kh * (sn * sn) 736 drag\_rate = i\_h * sqrt(drag\_rate\_visc(i,j)**2 + cd2 * ( 2.0*bottomfac2*eke + ubg2 ) ) 737 ldamping = cs%MEKE\_damping + drag\_rate * bottomfac2 738 resid = src - ldamping * eke 739 \textcolor{comment}{! if (debugIteration) then} 740 \textcolor{comment}{! write(0,*) n1, 'EKE=',EKE,'resid=',resid} 741 \textcolor{comment}{! write(0,*) 'EKEmin=',EKEmin,'ResMin=',ResMin} 742 \textcolor{comment}{! write(0,*) 'src=',src,'ldamping=',ldamping} 743 \textcolor{comment}{! write(0,*) 'gamma-b=',bottomFac2,'gamma-t=',barotrFac2} 744 \textcolor{comment}{! write(0,*) 'drag\_visc=',drag\_rate\_visc(i,j),'Ubg2=',Ubg2} 745 \textcolor{comment}{! endif} 746 \textcolor{keywordflow}{if} (resid>0.) \textcolor{keywordflow}{then} \textcolor{comment}{! EKE is to the left of the root} 747 ekemin = eke \textcolor{comment}{! so we move the left bracket here} 748 ekemax = 10. * eke \textcolor{comment}{! and guess again for the right bracket} 749 \textcolor{keywordflow}{if} (resid 2.e17*us%m\_s\_to\_L\_T**2) \textcolor{keywordflow}{then} 752 \textcolor{keywordflow}{if} (debugiteration) stop \textcolor{stringliteral}{'Something has gone very wrong'} 753 debugiteration = .true. 754 resid = 1. ; n1 = 0 755 ekemin = 0. ; resmin = 0. 756 ekemax = 0.01*us%m\_s\_to\_L\_T**2 757 usesecant = .false. 758 \textcolor{keywordflow}{ endif} 759 \textcolor{keywordflow}{ endif} 760 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! while(resid>0.) searching for right bracket} 761 resmax = resid 762 763 \textcolor{comment}{! Bisect the bracket} 764 n2 = 0 ; ekeerr = ekemax - ekemin 765 \textcolor{keywordflow}{do} \textcolor{keywordflow}{while} (ekeerr > tolerance) 766 n2 = n2 + 1 767 \textcolor{keywordflow}{if} (usesecant) \textcolor{keywordflow}{then} 768 eke = ekemin + (ekemax - ekemin) * (resmin / (resmin - resmax)) 769 \textcolor{keywordflow}{else} 770 eke = 0.5 * (ekemin + ekemax) 771 \textcolor{keywordflow}{ endif} 772 ekeerr = min( eke-ekemin, ekemax-eke ) 773 \textcolor{comment}{! TODO: Should include resolution function in Kh} 774 kh = (khcoeff * sqrt(2.*barotrfac2*eke) * lmixscale) 775 src = kh * (sn * sn) 776 drag\_rate = i\_h * sqrt( drag\_rate\_visc(i,j)**2 + cd2 * ( 2.0*bottomfac2*eke + ubg2 ) ) 777 ldamping = cs%MEKE\_damping + drag\_rate * bottomfac2 778 resid = src - ldamping * eke 779 \textcolor{keywordflow}{if} (usesecant .and. resid>resmin) usesecant = .false. 780 \textcolor{keywordflow}{if} (resid>0.) \textcolor{keywordflow}{then} \textcolor{comment}{! EKE is to the left of the root} 781 ekemin = eke \textcolor{comment}{! so we move the left bracket here} 782 \textcolor{keywordflow}{if} (resid EKE is exactly at the root} 789 \textcolor{keywordflow}{ endif} 790 \textcolor{keywordflow}{if} (n2>200) stop \textcolor{stringliteral}{'Failing to converge?'} 791 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! while(EKEmax-EKEmin>tolerance)} 792 793 \textcolor{keywordflow}{else} 794 eke = 0. 795 \textcolor{keywordflow}{ endif} 796 meke%MEKE(i,j) = eke 797 \textcolor{keywordflow}{ endif} 798 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 799 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__meke_a843244b0cc72a08489920dcda464b063}\label{namespacemom__meke_a843244b0cc72a08489920dcda464b063}} \index{mom\+\_\+meke@{mom\+\_\+meke}!meke\+\_\+equilibrium\+\_\+restoring@{meke\+\_\+equilibrium\+\_\+restoring}} \index{meke\+\_\+equilibrium\+\_\+restoring@{meke\+\_\+equilibrium\+\_\+restoring}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{meke\+\_\+equilibrium\+\_\+restoring()}{meke\_equilibrium\_restoring()}} {\footnotesize\ttfamily subroutine mom\+\_\+meke\+::meke\+\_\+equilibrium\+\_\+restoring (\begin{DoxyParamCaption}\item[{type(\hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs}), pointer}]{CS, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(inout)}]{G, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension( g \%isdb\+: g \%iedb, g \%jsd\+: g \%jed), intent(in)}]{S\+N\+\_\+u, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsdb\+: g \%jedb), intent(in)}]{S\+N\+\_\+v }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} \begin{DoxyParams}[1]{Parameters} \mbox{\tt in,out} & {\em g} & Ocean grid.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type.\\ \hline & {\em cs} & M\+E\+KE control structure.\\ \hline \mbox{\tt in} & {\em sn\+\_\+u} & Eady growth rate at u-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em sn\+\_\+v} & Eady growth rate at v-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 806 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 806 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(inout)} :: g\textcolor{comment}{ !< Ocean grid.} 807 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: us\textcolor{comment}{ !< A dimensional unit scaling type.} 808 \textcolor{keywordtype}{type}(meke\_cs), \textcolor{keywordtype}{pointer} :: cs\textcolor{comment}{ !< MEKE control structure.} 809 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZIB\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_u\textcolor{comment}{ !< Eady growth rate at u-points [T-1 ~> s-1].} 810 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJB\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_v\textcolor{comment}{ !< Eady growth rate at v-points [T-1 ~> s-1].} 811 \textcolor{comment}{! Local variables} 812 \textcolor{keywordtype}{real} :: sn \textcolor{comment}{! The local Eady growth rate [T-1 ~> s-1]} 813 \textcolor{keywordtype}{integer} :: i, j, is, ie, js, je \textcolor{comment}{! local indices} 814 \textcolor{keywordtype}{real} :: cd2 \textcolor{comment}{! bottom drag} 815 816 is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec 817 cd2 = cs%cdrag**2 818 819 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(cs%equilibrium\_value)) \textcolor{keyword}{allocate}(cs%equilibrium\_value(szi\_(g),szj\_(g))) 820 cs%equilibrium\_value(:,:) = 0.0 821 822 \textcolor{comment}{!$OMP do} 823 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 824 \textcolor{comment}{! SN = 0.25*max( (SN\_u(I,j) + SN\_u(I-1,j)) + (SN\_v(i,J) + SN\_v(i,J-1)), 0.)} 825 \textcolor{comment}{! This avoids extremes values in equilibrium solution due to bad values in SN\_u, SN\_v} 826 sn = min(sn\_u(i,j), sn\_u(i-1,j), sn\_v(i,j), sn\_v(i,j-1)) 827 cs%equilibrium\_value(i,j) = (cs%MEKE\_GEOMETRIC\_alpha * sn * us%Z\_to\_m*g%bathyT(i,j))**2 / cd2 828 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 829 830 \textcolor{keywordflow}{if} (cs%id\_MEKE\_equilibrium>0) \textcolor{keyword}{call }post\_data(cs%id\_MEKE\_equilibrium, cs%equilibrium\_value, cs%diag) 831 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__meke_a099f1cfad37430ef1bd60972a92b1be4}\label{namespacemom__meke_a099f1cfad37430ef1bd60972a92b1be4}} \index{mom\+\_\+meke@{mom\+\_\+meke}!meke\+\_\+init@{meke\+\_\+init}} \index{meke\+\_\+init@{meke\+\_\+init}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{meke\+\_\+init()}{meke\_init()}} {\footnotesize\ttfamily logical function, public mom\+\_\+meke\+::meke\+\_\+init (\begin{DoxyParamCaption}\item[{type(time\+\_\+type), intent(in)}]{Time, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(inout)}]{G, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{type(param\+\_\+file\+\_\+type), intent(in)}]{param\+\_\+file, }\item[{type(diag\+\_\+ctrl), intent(inout), target}]{diag, }\item[{type(\hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs}), pointer}]{CS, }\item[{type(meke\+\_\+type), pointer}]{M\+E\+KE, }\item[{type(mom\+\_\+restart\+\_\+cs), pointer}]{restart\+\_\+\+CS }\end{DoxyParamCaption})} Initializes the M\+O\+M\+\_\+\+M\+E\+KE module and reads parameters. Returns True if module is to be used, otherwise returns False. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em time} & The current model time.\\ \hline \mbox{\tt in,out} & {\em g} & The ocean\textquotesingle{}s grid structure.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline \mbox{\tt in} & {\em param\+\_\+file} & Parameter file parser structure.\\ \hline \mbox{\tt in,out} & {\em diag} & Diagnostics structure.\\ \hline & {\em cs} & M\+E\+KE control structure.\\ \hline & {\em meke} & M\+E\+K\+E-\/related fields.\\ \hline & {\em restart\+\_\+cs} & Restart control structure for M\+O\+M\+\_\+\+M\+E\+KE. \\ \hline \end{DoxyParams} Definition at line 984 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 984 \textcolor{keywordtype}{type}(time\_type), \textcolor{keywordtype}{intent(in)} :: time\textcolor{comment}{ !< The current model time.} 985 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(inout)} :: g\textcolor{comment}{ !< The ocean's grid structure.} 986 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: us\textcolor{comment}{ !< A dimensional unit scaling type} 987 \textcolor{keywordtype}{type}(param\_file\_type), \textcolor{keywordtype}{intent(in)} :: param\_file\textcolor{comment}{ !< Parameter file parser structure.} 988 \textcolor{keywordtype}{type}(diag\_ctrl), \textcolor{keywordtype}{target}, \textcolor{keywordtype}{intent(inout)} :: diag\textcolor{comment}{ !< Diagnostics structure.} 989 \textcolor{keywordtype}{type}(meke\_cs), \textcolor{keywordtype}{pointer} :: cs\textcolor{comment}{ !< MEKE control structure.} 990 \textcolor{keywordtype}{type}(meke\_type), \textcolor{keywordtype}{pointer} :: meke\textcolor{comment}{ !< MEKE-related fields.} 991 \textcolor{keywordtype}{type}(mom\_restart\_cs), \textcolor{keywordtype}{pointer} :: restart\_cs\textcolor{comment}{ !< Restart control structure for MOM\_MEKE.} 992 993 \textcolor{comment}{! Local variables} 994 \textcolor{keywordtype}{real} :: i\_t\_rescale \textcolor{comment}{! A rescaling factor for time from the internal representation in this} 995 \textcolor{comment}{! run to the representation in a restart file.} 996 \textcolor{keywordtype}{real} :: l\_rescale \textcolor{comment}{! A rescaling factor for length from the internal representation in this} 997 \textcolor{comment}{! run to the representation in a restart file.} 998 \textcolor{keywordtype}{real} :: meke\_restoring\_timescale \textcolor{comment}{! The timescale used to nudge MEKE toward its equilibrium value.} 999 \textcolor{keywordtype}{real} :: cdrag \textcolor{comment}{! The default bottom drag coefficient [nondim].} 1000 \textcolor{keywordtype}{integer} :: i, j, is, ie, js, je, isd, ied, jsd, jed 1001 \textcolor{keywordtype}{logical} :: laplacian, biharmonic, usevarmix, coldstart 1002 \textcolor{comment}{! This include declares and sets the variable "version".} 1003 \textcolor{preprocessor}{# include "version\_variable.h"} 1004 \textcolor{preprocessor}{} \textcolor{keywordtype}{character(len=40)} :: mdl = \textcolor{stringliteral}{"MOM\_MEKE"} \textcolor{comment}{! This module's name.} 1005 1006 is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec 1007 isd = g%isd ; ied = g%ied ; jsd = g%jsd ; jed = g%jed 1008 1009 \textcolor{comment}{! Determine whether this module will be used} 1010 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"USE\_MEKE"}, meke\_init, default=.false., do\_not\_log=.true.) 1011 \textcolor{keyword}{call }log\_version(param\_file, mdl, version, \textcolor{stringliteral}{""}, all\_default=.not.meke\_init) 1012 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"USE\_MEKE"}, meke\_init, & 1013 \textcolor{stringliteral}{"If true, turns on the MEKE scheme which calculates "}// & 1014 \textcolor{stringliteral}{"a sub-grid mesoscale eddy kinetic energy budget."}, & 1015 default=.false.) 1016 \textcolor{keywordflow}{if} (.not. meke\_init) \textcolor{keywordflow}{return} 1017 1018 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke)) \textcolor{keywordflow}{then} 1019 \textcolor{comment}{! The MEKE structure should have been allocated in MEKE\_alloc\_register\_restart()} 1020 \textcolor{keyword}{call }mom\_error(warning, \textcolor{stringliteral}{"MEKE\_init called with NO associated "}// & 1021 \textcolor{stringliteral}{"MEKE-type structure."}) 1022 \textcolor{keywordflow}{return} 1023 \textcolor{keywordflow}{ endif} 1024 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(cs)) \textcolor{keywordflow}{then} 1025 \textcolor{keyword}{call }mom\_error(warning, & 1026 \textcolor{stringliteral}{"MEKE\_init called with an associated control structure."}) 1027 \textcolor{keywordflow}{return} 1028 \textcolor{keywordflow}{else} ; \textcolor{keyword}{allocate}(cs) ;\textcolor{keywordflow}{ endif} 1029 1030 \textcolor{keyword}{call }mom\_mesg(\textcolor{stringliteral}{"MEKE\_init: reading parameters "}, 5) 1031 1032 \textcolor{comment}{! Read all relevant parameters and write them to the model log.} 1033 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_DAMPING"}, cs%MEKE\_damping, & 1034 \textcolor{stringliteral}{"The local depth-independent MEKE dissipation rate."}, & 1035 units=\textcolor{stringliteral}{"s-1"}, default=0.0, scale=us%T\_to\_s) 1036 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_CD\_SCALE"}, cs%MEKE\_Cd\_scale, & 1037 \textcolor{stringliteral}{"The ratio of the bottom eddy velocity to the column mean "}//& 1038 \textcolor{stringliteral}{"eddy velocity, i.e. sqrt(2*MEKE). This should be less than 1 "}//& 1039 \textcolor{stringliteral}{"to account for the surface intensification of MEKE."}, & 1040 units=\textcolor{stringliteral}{"nondim"}, default=0.) 1041 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_CB"}, cs%MEKE\_Cb, & 1042 \textcolor{stringliteral}{"A coefficient in the expression for the ratio of bottom projected "}//& 1043 \textcolor{stringliteral}{"eddy energy and mean column energy (see Jansen et al. 2015)."},& 1044 units=\textcolor{stringliteral}{"nondim"}, default=25.) 1045 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_MIN\_GAMMA2"}, cs%MEKE\_min\_gamma, & 1046 \textcolor{stringliteral}{"The minimum allowed value of gamma\_b^2."},& 1047 units=\textcolor{stringliteral}{"nondim"}, default=0.0001) 1048 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_CT"}, cs%MEKE\_Ct, & 1049 \textcolor{stringliteral}{"A coefficient in the expression for the ratio of barotropic "}//& 1050 \textcolor{stringliteral}{"eddy energy and mean column energy (see Jansen et al. 2015)."},& 1051 units=\textcolor{stringliteral}{"nondim"}, default=50.) 1052 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_GMCOEFF"}, cs%MEKE\_GMcoeff, & 1053 \textcolor{stringliteral}{"The efficiency of the conversion of potential energy "}//& 1054 \textcolor{stringliteral}{"into MEKE by the thickness mixing parameterization. "}//& 1055 \textcolor{stringliteral}{"If MEKE\_GMCOEFF is negative, this conversion is not "}//& 1056 \textcolor{stringliteral}{"used or calculated."}, units=\textcolor{stringliteral}{"nondim"}, default=-1.0) 1057 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_GEOMETRIC"}, cs%MEKE\_GEOMETRIC, & 1058 \textcolor{stringliteral}{"If MEKE\_GEOMETRIC is true, uses the GM coefficient formulation "}//& 1059 \textcolor{stringliteral}{"from the GEOMETRIC framework (Marshall et al., 2012)."}, default=.false.) 1060 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_GEOMETRIC\_ALPHA"}, cs%MEKE\_GEOMETRIC\_alpha, & 1061 \textcolor{stringliteral}{"The nondimensional coefficient governing the efficiency of the GEOMETRIC \(\backslash\)n"}//& 1062 \textcolor{stringliteral}{"thickness diffusion."}, units=\textcolor{stringliteral}{"nondim"}, default=0.05) 1063 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_EQUILIBRIUM\_ALT"}, cs%MEKE\_equilibrium\_alt, & 1064 \textcolor{stringliteral}{"If true, use an alternative formula for computing the (equilibrium)"}//& 1065 \textcolor{stringliteral}{"initial value of MEKE."}, default=.false.) 1066 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_EQUILIBRIUM\_RESTORING"}, cs%MEKE\_equilibrium\_restoring, & 1067 \textcolor{stringliteral}{"If true, restore MEKE back to its equilibrium value, which is calculated at "}//& 1068 \textcolor{stringliteral}{"each time step."}, default=.false.) 1069 \textcolor{keywordflow}{if} (cs%MEKE\_equilibrium\_restoring) \textcolor{keywordflow}{then} 1070 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_RESTORING\_TIMESCALE"}, meke\_restoring\_timescale, & 1071 \textcolor{stringliteral}{"The timescale used to nudge MEKE toward its equilibrium value."}, units=\textcolor{stringliteral}{"s"}, & 1072 default=1e6, scale=us%T\_to\_s) 1073 cs%MEKE\_restoring\_rate = 1.0 / meke\_restoring\_timescale 1074 \textcolor{keywordflow}{ endif} 1075 1076 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_FRCOEFF"}, cs%MEKE\_FrCoeff, & 1077 \textcolor{stringliteral}{"The efficiency of the conversion of mean energy into "}//& 1078 \textcolor{stringliteral}{"MEKE. If MEKE\_FRCOEFF is negative, this conversion "}//& 1079 \textcolor{stringliteral}{"is not used or calculated."}, units=\textcolor{stringliteral}{"nondim"}, default=-1.0) 1080 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_GMECOEFF"}, cs%MEKE\_GMECoeff, & 1081 \textcolor{stringliteral}{"The efficiency of the conversion of MEKE into mean energy "}//& 1082 \textcolor{stringliteral}{"by GME. If MEKE\_GMECOEFF is negative, this conversion "}//& 1083 \textcolor{stringliteral}{"is not used or calculated."}, units=\textcolor{stringliteral}{"nondim"}, default=-1.0) 1084 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_BGSRC"}, cs%MEKE\_BGsrc, & 1085 \textcolor{stringliteral}{"A background energy source for MEKE."}, units=\textcolor{stringliteral}{"W kg-1"}, & 1086 default=0.0, scale=us%m\_to\_L**2*us%T\_to\_s**3) 1087 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_KH"}, cs%MEKE\_Kh, & 1088 \textcolor{stringliteral}{"A background lateral diffusivity of MEKE. "}//& 1089 \textcolor{stringliteral}{"Use a negative value to not apply lateral diffusion to MEKE."}, & 1090 units=\textcolor{stringliteral}{"m2 s-1"}, default=-1.0, scale=us%m\_to\_L**2*us%T\_to\_s) 1091 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_K4"}, cs%MEKE\_K4, & 1092 \textcolor{stringliteral}{"A lateral bi-harmonic diffusivity of MEKE. "}//& 1093 \textcolor{stringliteral}{"Use a negative value to not apply bi-harmonic diffusion to MEKE."}, & 1094 units=\textcolor{stringliteral}{"m4 s-1"}, default=-1.0, scale=us%m\_to\_L**4*us%T\_to\_s) 1095 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_DTSCALE"}, cs%MEKE\_dtScale, & 1096 \textcolor{stringliteral}{"A scaling factor to accelerate the time evolution of MEKE."}, & 1097 units=\textcolor{stringliteral}{"nondim"}, default=1.0) 1098 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_KHCOEFF"}, cs%MEKE\_KhCoeff, & 1099 \textcolor{stringliteral}{"A scaling factor in the expression for eddy diffusivity "}//& 1100 \textcolor{stringliteral}{"which is otherwise proportional to the MEKE velocity- "}//& 1101 \textcolor{stringliteral}{"scale times an eddy mixing-length. This factor "}//& 1102 \textcolor{stringliteral}{"must be >0 for MEKE to contribute to the thickness/ "}//& 1103 \textcolor{stringliteral}{"and tracer diffusivity in the rest of the model."}, & 1104 units=\textcolor{stringliteral}{"nondim"}, default=1.0) 1105 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_USCALE"}, cs%MEKE\_Uscale, & 1106 \textcolor{stringliteral}{"The background velocity that is combined with MEKE to "}//& 1107 \textcolor{stringliteral}{"calculate the bottom drag."}, units=\textcolor{stringliteral}{"m s-1"}, default=0.0, scale=us%m\_s\_to\_L\_T) 1108 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_GM\_SRC\_ALT"}, cs%GM\_src\_alt, & 1109 \textcolor{stringliteral}{"If true, use the GM energy conversion form S^2*N^2*kappa rather "}//& 1110 \textcolor{stringliteral}{"than the streamfunction for the MEKE GM source term."}, default=.false.) 1111 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_VISC\_DRAG"}, cs%visc\_drag, & 1112 \textcolor{stringliteral}{"If true, use the vertvisc\_type to calculate the bottom "}//& 1113 \textcolor{stringliteral}{"drag acting on MEKE."}, default=.true.) 1114 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_KHTH\_FAC"}, meke%KhTh\_fac, & 1115 \textcolor{stringliteral}{"A factor that maps MEKE%Kh to KhTh."}, units=\textcolor{stringliteral}{"nondim"}, & 1116 default=0.0) 1117 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_KHTR\_FAC"}, meke%KhTr\_fac, & 1118 \textcolor{stringliteral}{"A factor that maps MEKE%Kh to KhTr."}, units=\textcolor{stringliteral}{"nondim"}, & 1119 default=0.0) 1120 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_KHMEKE\_FAC"}, cs%KhMEKE\_Fac, & 1121 \textcolor{stringliteral}{"A factor that maps MEKE%Kh to Kh for MEKE itself."}, & 1122 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1123 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_OLD\_LSCALE"}, cs%use\_old\_lscale, & 1124 \textcolor{stringliteral}{"If true, use the old formula for length scale which is "}//& 1125 \textcolor{stringliteral}{"a function of grid spacing and deformation radius."}, & 1126 default=.false.) 1127 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_MIN\_LSCALE"}, cs%use\_min\_lscale, & 1128 \textcolor{stringliteral}{"If true, use a strict minimum of provided length scales "}//& 1129 \textcolor{stringliteral}{"rather than harmonic mean."}, & 1130 default=.false.) 1131 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_RD\_MAX\_SCALE"}, cs%Rd\_as\_max\_scale, & 1132 \textcolor{stringliteral}{"If true, the length scale used by MEKE is the minimum of "}//& 1133 \textcolor{stringliteral}{"the deformation radius or grid-spacing. Only used if "}//& 1134 \textcolor{stringliteral}{"MEKE\_OLD\_LSCALE=True"}, units=\textcolor{stringliteral}{"nondim"}, default=.false.) 1135 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_VISCOSITY\_COEFF\_KU"}, cs%viscosity\_coeff\_Ku, & 1136 \textcolor{stringliteral}{"If non-zero, is the scaling coefficient in the expression for"}//& 1137 \textcolor{stringliteral}{"viscosity used to parameterize harmonic lateral momentum mixing by"}//& 1138 \textcolor{stringliteral}{"unresolved eddies represented by MEKE. Can be negative to"}//& 1139 \textcolor{stringliteral}{"represent backscatter from the unresolved eddies."}, & 1140 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1141 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_VISCOSITY\_COEFF\_AU"}, cs%viscosity\_coeff\_Au, & 1142 \textcolor{stringliteral}{"If non-zero, is the scaling coefficient in the expression for"}//& 1143 \textcolor{stringliteral}{"viscosity used to parameterize biharmonic lateral momentum mixing by"}//& 1144 \textcolor{stringliteral}{"unresolved eddies represented by MEKE. Can be negative to"}//& 1145 \textcolor{stringliteral}{"represent backscatter from the unresolved eddies."}, & 1146 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1147 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_FIXED\_MIXING\_LENGTH"}, cs%Lfixed, & 1148 \textcolor{stringliteral}{"If positive, is a fixed length contribution to the expression "}//& 1149 \textcolor{stringliteral}{"for mixing length used in MEKE-derived diffusivity."}, & 1150 units=\textcolor{stringliteral}{"m"}, default=0.0, scale=us%m\_to\_L) 1151 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_ALPHA\_DEFORM"}, cs%aDeform, & 1152 \textcolor{stringliteral}{"If positive, is a coefficient weighting the deformation scale "}//& 1153 \textcolor{stringliteral}{"in the expression for mixing length used in MEKE-derived diffusivity."}, & 1154 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1155 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_ALPHA\_RHINES"}, cs%aRhines, & 1156 \textcolor{stringliteral}{"If positive, is a coefficient weighting the Rhines scale "}//& 1157 \textcolor{stringliteral}{"in the expression for mixing length used in MEKE-derived diffusivity."}, & 1158 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1159 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_ALPHA\_EADY"}, cs%aEady, & 1160 \textcolor{stringliteral}{"If positive, is a coefficient weighting the Eady length scale "}//& 1161 \textcolor{stringliteral}{"in the expression for mixing length used in MEKE-derived diffusivity."}, & 1162 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1163 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_ALPHA\_FRICT"}, cs%aFrict, & 1164 \textcolor{stringliteral}{"If positive, is a coefficient weighting the frictional arrest scale "}//& 1165 \textcolor{stringliteral}{"in the expression for mixing length used in MEKE-derived diffusivity."}, & 1166 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1167 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_ALPHA\_GRID"}, cs%aGrid, & 1168 \textcolor{stringliteral}{"If positive, is a coefficient weighting the grid-spacing as a scale "}//& 1169 \textcolor{stringliteral}{"in the expression for mixing length used in MEKE-derived diffusivity."}, & 1170 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1171 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_COLD\_START"}, coldstart, & 1172 \textcolor{stringliteral}{"If true, initialize EKE to zero. Otherwise a local equilibrium solution "}//& 1173 \textcolor{stringliteral}{"is used as an initial condition for EKE."}, default=.false.) 1174 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_BACKSCAT\_RO\_C"}, meke%backscatter\_Ro\_c, & 1175 \textcolor{stringliteral}{"The coefficient in the Rossby number function for scaling the biharmonic "}//& 1176 \textcolor{stringliteral}{"frictional energy source. Setting to non-zero enables the Rossby number function."}, & 1177 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1178 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_BACKSCAT\_RO\_POW"}, meke%backscatter\_Ro\_pow, & 1179 \textcolor{stringliteral}{"The power in the Rossby number function for scaling the biharmonic "}//& 1180 \textcolor{stringliteral}{"frictional energy source."}, units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1181 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_ADVECTION\_FACTOR"}, cs%MEKE\_advection\_factor, & 1182 \textcolor{stringliteral}{"A scale factor in front of advection of eddy energy. Zero turns advection off. "}//& 1183 \textcolor{stringliteral}{"Using unity would be normal but other values could accommodate a mismatch "}//& 1184 \textcolor{stringliteral}{"between the advecting barotropic flow and the vertical structure of MEKE."}, & 1185 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1186 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_TOPOGRAPHIC\_BETA"}, cs%MEKE\_topographic\_beta, & 1187 \textcolor{stringliteral}{"A scale factor to determine how much topographic beta is weighed in "} //& 1188 \textcolor{stringliteral}{"computing beta in the expression of Rhines scale. Use 1 if full "}//& 1189 \textcolor{stringliteral}{"topographic beta effect is considered; use 0 if it's completely ignored."}, & 1190 units=\textcolor{stringliteral}{"nondim"}, default=0.0) 1191 1192 \textcolor{comment}{! Nonlocal module parameters} 1193 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"CDRAG"}, cdrag, & 1194 \textcolor{stringliteral}{"CDRAG is the drag coefficient relating the magnitude of "}//& 1195 \textcolor{stringliteral}{"the velocity field to the bottom stress."}, units=\textcolor{stringliteral}{"nondim"}, & 1196 default=0.003) 1197 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"MEKE\_CDRAG"}, cs%cdrag, & 1198 \textcolor{stringliteral}{"Drag coefficient relating the magnitude of the velocity "}//& 1199 \textcolor{stringliteral}{"field to the bottom stress in MEKE."}, units=\textcolor{stringliteral}{"nondim"}, & 1200 default=cdrag) 1201 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"LAPLACIAN"}, laplacian, default=.false., do\_not\_log=.true.) 1202 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"BIHARMONIC"}, biharmonic, default=.false., do\_not\_log=.true.) 1203 1204 \textcolor{keywordflow}{if} (cs%viscosity\_coeff\_Ku/=0. .and. .not. laplacian) \textcolor{keyword}{call }mom\_error(fatal, & 1205 \textcolor{stringliteral}{"LAPLACIAN must be true if MEKE\_VISCOSITY\_COEFF\_KU is true."}) 1206 1207 \textcolor{keywordflow}{if} (cs%viscosity\_coeff\_Au/=0. .and. .not. biharmonic) \textcolor{keyword}{call }mom\_error(fatal, & 1208 \textcolor{stringliteral}{"BIHARMONIC must be true if MEKE\_VISCOSITY\_COEFF\_AU is true."}) 1209 1210 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"DEBUG"}, cs%debug, default=.false., do\_not\_log=.true.) 1211 1212 \textcolor{comment}{! Identify if any lateral diffusive processes are active} 1213 cs%kh\_flux\_enabled = .false. 1214 \textcolor{keywordflow}{if} ((cs%MEKE\_KH >= 0.0) .or. (cs%KhMEKE\_FAC > 0.0) .or. (cs%MEKE\_advection\_factor > 0.0)) & 1215 cs%kh\_flux\_enabled = .true. 1216 1217 \textcolor{comment}{! Register fields for output from this module.} 1218 cs%diag => diag 1219 cs%id\_MEKE = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE'}, diag%axesT1, time, & 1220 \textcolor{stringliteral}{'Mesoscale Eddy Kinetic Energy'}, \textcolor{stringliteral}{'m2 s-2'}, conversion=us%L\_T\_to\_m\_s**2) 1221 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%MEKE)) cs%id\_MEKE = -1 1222 cs%id\_Kh = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_KH'}, diag%axesT1, time, & 1223 \textcolor{stringliteral}{'MEKE derived diffusivity'}, \textcolor{stringliteral}{'m2 s-1'}, conversion=us%L\_to\_m**2*us%s\_to\_T) 1224 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%Kh)) cs%id\_Kh = -1 1225 cs%id\_Ku = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_KU'}, diag%axesT1, time, & 1226 \textcolor{stringliteral}{'MEKE derived lateral viscosity'}, \textcolor{stringliteral}{'m2 s-1'}, conversion=us%L\_to\_m**2*us%s\_to\_T) 1227 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%Ku)) cs%id\_Ku = -1 1228 cs%id\_Au = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_AU'}, diag%axesT1, time, & 1229 \textcolor{stringliteral}{'MEKE derived lateral biharmonic viscosity'}, \textcolor{stringliteral}{'m4 s-1'}, conversion=us%L\_to\_m**4*us%s\_to\_T) 1230 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%Au)) cs%id\_Au = -1 1231 cs%id\_Ue = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_Ue'}, diag%axesT1, time, & 1232 \textcolor{stringliteral}{'MEKE derived eddy-velocity scale'}, \textcolor{stringliteral}{'m s-1'}, conversion=us%L\_T\_to\_m\_s) 1233 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%MEKE)) cs%id\_Ue = -1 1234 cs%id\_Ub = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_Ub'}, diag%axesT1, time, & 1235 \textcolor{stringliteral}{'MEKE derived bottom eddy-velocity scale'}, \textcolor{stringliteral}{'m s-1'}, conversion=us%L\_T\_to\_m\_s) 1236 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%MEKE)) cs%id\_Ub = -1 1237 cs%id\_Ut = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_Ut'}, diag%axesT1, time, & 1238 \textcolor{stringliteral}{'MEKE derived barotropic eddy-velocity scale'}, \textcolor{stringliteral}{'m s-1'}, conversion=us%L\_T\_to\_m\_s) 1239 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%MEKE)) cs%id\_Ut = -1 1240 cs%id\_src = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_src'}, diag%axesT1, time, & 1241 \textcolor{stringliteral}{'MEKE energy source'}, \textcolor{stringliteral}{'m2 s-3'}, conversion=(us%L\_T\_to\_m\_s**2)*us%s\_to\_T) 1242 cs%id\_decay = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_decay'}, diag%axesT1, time, & 1243 \textcolor{stringliteral}{'MEKE decay rate'}, \textcolor{stringliteral}{'s-1'}, conversion=us%s\_to\_T) 1244 cs%id\_GM\_src = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_GM\_src'}, diag%axesT1, time, & 1245 \textcolor{stringliteral}{'MEKE energy available from thickness mixing'}, & 1246 \textcolor{stringliteral}{'W m-2'}, conversion=us%RZ3\_T3\_to\_W\_m2*us%L\_to\_Z**2) 1247 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%GM\_src)) cs%id\_GM\_src = -1 1248 cs%id\_mom\_src = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_mom\_src'},diag%axesT1, time, & 1249 \textcolor{stringliteral}{'MEKE energy available from momentum'}, & 1250 \textcolor{stringliteral}{'W m-2'}, conversion=us%RZ3\_T3\_to\_W\_m2*us%L\_to\_Z**2) 1251 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%mom\_src)) cs%id\_mom\_src = -1 1252 cs%id\_GME\_snk = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_GME\_snk'},diag%axesT1, time, & 1253 \textcolor{stringliteral}{'MEKE energy lost to GME backscatter'}, & 1254 \textcolor{stringliteral}{'W m-2'}, conversion=us%RZ3\_T3\_to\_W\_m2*us%L\_to\_Z**2) 1255 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(meke%GME\_snk)) cs%id\_GME\_snk = -1 1256 cs%id\_Le = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_Le'}, diag%axesT1, time, & 1257 \textcolor{stringliteral}{'Eddy mixing length used in the MEKE derived eddy diffusivity'}, \textcolor{stringliteral}{'m'}, conversion=us%L\_to\_m) 1258 cs%id\_Lrhines = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_Lrhines'}, diag%axesT1, time, & 1259 \textcolor{stringliteral}{'Rhines length scale used in the MEKE derived eddy diffusivity'}, \textcolor{stringliteral}{'m'}, conversion=us%L\_to\_m) 1260 cs%id\_Leady = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_Leady'}, diag%axesT1, time, & 1261 \textcolor{stringliteral}{'Eady length scale used in the MEKE derived eddy diffusivity'}, \textcolor{stringliteral}{'m'}, conversion=us%L\_to\_m) 1262 cs%id\_gamma\_b = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_gamma\_b'}, diag%axesT1, time, & 1263 \textcolor{stringliteral}{'Ratio of bottom-projected eddy velocity to column-mean eddy velocity'}, \textcolor{stringliteral}{'nondim'}) 1264 cs%id\_gamma\_t = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_gamma\_t'}, diag%axesT1, time, & 1265 \textcolor{stringliteral}{'Ratio of barotropic eddy velocity to column-mean eddy velocity'}, \textcolor{stringliteral}{'nondim'}) 1266 1267 \textcolor{keywordflow}{if} (cs%kh\_flux\_enabled) \textcolor{keywordflow}{then} 1268 cs%id\_KhMEKE\_u = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'KHMEKE\_u'}, diag%axesCu1, time, & 1269 \textcolor{stringliteral}{'Zonal diffusivity of MEKE'}, \textcolor{stringliteral}{'m2 s-1'}, conversion=us%L\_to\_m**2*us%s\_to\_T) 1270 cs%id\_KhMEKE\_v = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'KHMEKE\_v'}, diag%axesCv1, time, & 1271 \textcolor{stringliteral}{'Meridional diffusivity of MEKE'}, \textcolor{stringliteral}{'m2 s-1'}, conversion=us%L\_to\_m**2*us%s\_to\_T) 1272 \textcolor{keywordflow}{ endif} 1273 1274 \textcolor{keywordflow}{if} (cs%MEKE\_equilibrium\_restoring) \textcolor{keywordflow}{then} 1275 cs%id\_MEKE\_equilibrium = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'MEKE\_equilibrium'}, diag%axesT1, time, & 1276 \textcolor{stringliteral}{'Equilibrated Mesoscale Eddy Kinetic Energy'}, \textcolor{stringliteral}{'m2 s-2'}, conversion=us%L\_T\_to\_m\_s**2) 1277 \textcolor{keywordflow}{ endif} 1278 1279 cs%id\_clock\_pass = cpu\_clock\_id(\textcolor{stringliteral}{'(Ocean continuity halo updates)'}, grain=clock\_routine) 1280 1281 \textcolor{comment}{! Detect whether this instance of MEKE\_init() is at the beginning of a run} 1282 \textcolor{comment}{! or after a restart. If at the beginning, we will initialize MEKE to a local} 1283 \textcolor{comment}{! equilibrium.} 1284 cs%initialize = .not.query\_initialized(meke%MEKE, \textcolor{stringliteral}{"MEKE"}, restart\_cs) 1285 \textcolor{keywordflow}{if} (coldstart) cs%initialize = .false. 1286 \textcolor{keywordflow}{if} (cs%initialize) \textcolor{keyword}{call }mom\_error(warning, & 1287 \textcolor{stringliteral}{"MEKE\_init: Initializing MEKE with a local equilibrium balance."}) 1288 1289 \textcolor{comment}{! Account for possible changes in dimensional scaling for variables that have been} 1290 \textcolor{comment}{! read from a restart file.} 1291 i\_t\_rescale = 1.0 1292 \textcolor{keywordflow}{if} ((us%s\_to\_T\_restart /= 0.0) .and. (us%s\_to\_T\_restart /= us%s\_to\_T)) & 1293 i\_t\_rescale = us%s\_to\_T\_restart / us%s\_to\_T 1294 l\_rescale = 1.0 1295 \textcolor{keywordflow}{if} ((us%m\_to\_L\_restart /= 0.0) .and. (us%m\_to\_L\_restart /= us%m\_to\_L)) & 1296 l\_rescale = us%m\_to\_L / us%m\_to\_L\_restart 1297 1298 \textcolor{keywordflow}{if} (l\_rescale*i\_t\_rescale /= 1.0) \textcolor{keywordflow}{then} 1299 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%MEKE)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (query\_initialized(meke%MEKE, \textcolor{stringliteral}{"MEKE\_MEKE"}, restart\_cs)) \textcolor{keywordflow}{then} 1300 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 1301 meke%MEKE(i,j) = l\_rescale*i\_t\_rescale * meke%MEKE(i,j) 1302 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 1303 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 1304 \textcolor{keywordflow}{ endif} 1305 \textcolor{keywordflow}{if} (l\_rescale**2*i\_t\_rescale /= 1.0) \textcolor{keywordflow}{then} 1306 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (query\_initialized(meke%Kh, \textcolor{stringliteral}{"MEKE\_Kh"}, restart\_cs)) \textcolor{keywordflow}{then} 1307 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 1308 meke%Kh(i,j) = l\_rescale**2*i\_t\_rescale * meke%Kh(i,j) 1309 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 1310 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 1311 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Ku)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (query\_initialized(meke%Ku, \textcolor{stringliteral}{"MEKE\_Ku"}, restart\_cs)) \textcolor{keywordflow}{then} 1312 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 1313 meke%Ku(i,j) = l\_rescale**2*i\_t\_rescale * meke%Ku(i,j) 1314 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 1315 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 1316 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh\_diff)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (query\_initialized(meke%Kh, \textcolor{stringliteral}{"MEKE\_Kh\_diff"}, restart\_cs)) \textcolor{keywordflow}{then} 1317 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 1318 meke%Kh\_diff(i,j) = l\_rescale**2*i\_t\_rescale * meke%Kh\_diff(i,j) 1319 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 1320 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 1321 \textcolor{keywordflow}{ endif} 1322 \textcolor{keywordflow}{if} (l\_rescale**4*i\_t\_rescale /= 1.0) \textcolor{keywordflow}{then} 1323 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Au)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (query\_initialized(meke%Au, \textcolor{stringliteral}{"MEKE\_Au"}, restart\_cs)) \textcolor{keywordflow}{then} 1324 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 1325 meke%Au(i,j) = l\_rescale**4*i\_t\_rescale * meke%Au(i,j) 1326 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 1327 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 1328 \textcolor{keywordflow}{ endif} 1329 1330 \textcolor{comment}{! Set up group passes. In the case of a restart, these fields need a halo update now.} 1331 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%MEKE)) \textcolor{keywordflow}{then} 1332 \textcolor{keyword}{call }create\_group\_pass(cs%pass\_MEKE, meke%MEKE, g%Domain) 1333 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh\_diff)) \textcolor{keyword}{call }create\_group\_pass(cs%pass\_MEKE, meke%Kh\_diff, g%Domain) 1334 \textcolor{keywordflow}{if} (.not.cs%initialize) \textcolor{keyword}{call }do\_group\_pass(cs%pass\_MEKE, g%Domain) 1335 \textcolor{keywordflow}{ endif} 1336 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh)) \textcolor{keyword}{call }create\_group\_pass(cs%pass\_Kh, meke%Kh, g%Domain) 1337 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Ku)) \textcolor{keyword}{call }create\_group\_pass(cs%pass\_Kh, meke%Ku, g%Domain) 1338 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Au)) \textcolor{keyword}{call }create\_group\_pass(cs%pass\_Kh, meke%Au, g%Domain) 1339 1340 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh) .or. \textcolor{keyword}{associated}(meke%Ku) .or. \textcolor{keyword}{associated}(meke%Au)) & 1341 \textcolor{keyword}{call }do\_group\_pass(cs%pass\_Kh, g%Domain) 1342 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__meke_a8180d5d0cacf48bcbdffead9e6a06efd}\label{namespacemom__meke_a8180d5d0cacf48bcbdffead9e6a06efd}} \index{mom\+\_\+meke@{mom\+\_\+meke}!meke\+\_\+lengthscales@{meke\+\_\+lengthscales}} \index{meke\+\_\+lengthscales@{meke\+\_\+lengthscales}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{meke\+\_\+lengthscales()}{meke\_lengthscales()}} {\footnotesize\ttfamily subroutine mom\+\_\+meke\+::meke\+\_\+lengthscales (\begin{DoxyParamCaption}\item[{type(\hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs}), pointer}]{CS, }\item[{type(meke\+\_\+type), pointer}]{M\+E\+KE, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(inout)}]{G, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension( g \%isdb\+: g \%iedb, g \%jsd\+: g \%jed), intent(in)}]{S\+N\+\_\+u, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsdb\+: g \%jedb), intent(in)}]{S\+N\+\_\+v, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed), intent(in)}]{E\+KE, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed), intent(out)}]{bottom\+Fac2, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed), intent(out)}]{barotr\+Fac2, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed), intent(out)}]{Lmix\+Scale }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Calculates the eddy mixing length scale and $\gamma_b$ and $\gamma_t$ functions that are ratios of either bottom or barotropic eddy energy to the column eddy energy, respectively. See \hyperlink{namespacemom__meke_section_MEKE_equations}{M\+E\+KE equations}. \begin{DoxyParams}[1]{Parameters} & {\em cs} & M\+E\+KE control structure.\\ \hline & {\em meke} & M\+E\+KE data.\\ \hline \mbox{\tt in,out} & {\em g} & Ocean grid.\\ \hline \mbox{\tt in} & {\em gv} & Ocean vertical grid structure.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline \mbox{\tt in} & {\em sn\+\_\+u} & Eady growth rate at u-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em sn\+\_\+v} & Eady growth rate at v-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em eke} & Eddy kinetic energy \mbox{[}L2 T-\/2 $\sim$$>$ m2 s-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em bottomfac2} & gamma\+\_\+b$^\wedge$2\\ \hline \mbox{\tt out} & {\em barotrfac2} & gamma\+\_\+t$^\wedge$2\\ \hline \mbox{\tt out} & {\em lmixscale} & Eddy mixing length \mbox{[}L $\sim$$>$ m\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 839 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 839 \textcolor{keywordtype}{type}(meke\_cs), \textcolor{keywordtype}{pointer} :: cs\textcolor{comment}{ !< MEKE control structure.} 840 \textcolor{keywordtype}{type}(meke\_type), \textcolor{keywordtype}{pointer} :: meke\textcolor{comment}{ !< MEKE data.} 841 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(inout)} :: g\textcolor{comment}{ !< Ocean grid.} 842 \textcolor{keywordtype}{type}(verticalgrid\_type), \textcolor{keywordtype}{intent(in)} :: gv\textcolor{comment}{ !< Ocean vertical grid structure.} 843 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: us\textcolor{comment}{ !< A dimensional unit scaling type} 844 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZIB\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_u\textcolor{comment}{ !< Eady growth rate at u-points [T-1 ~> s-1].} 845 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJB\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_v\textcolor{comment}{ !< Eady growth rate at v-points [T-1 ~> s-1].} 846 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(in)} :: eke\textcolor{comment}{ !< Eddy kinetic energy [L2 T-2 ~> m2 s-2].} 847 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(out)} :: bottomfac2\textcolor{comment}{ !< gamma\_b^2} 848 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(out)} :: barotrfac2\textcolor{comment}{ !< gamma\_t^2} 849 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(out)} :: lmixscale\textcolor{comment}{ !< Eddy mixing length [L ~> m].} 850 \textcolor{comment}{! Local variables} 851 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))} :: lrhines, leady \textcolor{comment}{! Possible mixing length scales [L ~> m]} 852 \textcolor{keywordtype}{real} :: beta \textcolor{comment}{! Combined topograpic and planetary vorticity gradient [T-1 L-1 ~> s-1 m-1]} 853 \textcolor{keywordtype}{real} :: sn \textcolor{comment}{! The local Eady growth rate [T-1 ~> s-1]} 854 \textcolor{keywordtype}{real} :: fath \textcolor{comment}{! Coriolis parameter at h points [T-1 ~> s-1]} 855 \textcolor{keywordtype}{real} :: beta\_topo\_x, beta\_topo\_y \textcolor{comment}{! Topographic PV gradients in x and y [T-1 L-1 ~> s-1 m-1]} 856 \textcolor{keywordtype}{integer} :: i, j, is, ie, js, je 857 858 is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec 859 860 \textcolor{comment}{!$OMP do} 861 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 862 \textcolor{keywordflow}{if} (.not.cs%use\_old\_lscale) \textcolor{keywordflow}{then} 863 \textcolor{keywordflow}{if} (cs%aEady > 0.) \textcolor{keywordflow}{then} 864 sn = 0.25 * ( (sn\_u(i,j) + sn\_u(i-1,j)) + (sn\_v(i,j) + sn\_v(i,j-1)) ) 865 \textcolor{keywordflow}{else} 866 sn = 0. 867 \textcolor{keywordflow}{ endif} 868 fath = 0.25* ( ( g%CoriolisBu(i,j) + g%CoriolisBu(i-1,j-1) ) + & 869 ( g%CoriolisBu(i-1,j) + g%CoriolisBu(i,j-1) ) ) \textcolor{comment}{! Coriolis parameter at h points} 870 871 \textcolor{comment}{! If bathyT is zero, then a division by zero FPE will be raised. In this} 872 \textcolor{comment}{! case, we apply Adcroft's rule of reciprocals and set the term to zero.} 873 \textcolor{comment}{! Since zero-bathymetry cells are masked, this should not affect values.} 874 \textcolor{keywordflow}{if} (cs%MEKE\_topographic\_beta == 0. .or. g%bathyT(i,j) == 0.0) \textcolor{keywordflow}{then} 875 beta\_topo\_x = 0. ; beta\_topo\_y = 0. 876 \textcolor{keywordflow}{else} 877 \textcolor{comment}{!### Consider different combinations of these estimates of topographic beta, and the use} 878 \textcolor{comment}{! of the water column thickness instead of the bathymetric depth.} 879 beta\_topo\_x = -cs%MEKE\_topographic\_beta * fath * 0.5 * ( & 880 (g%bathyT(i+1,j)-g%bathyT(i,j)) * g%IdxCu(i,j) & 881 / max(g%bathyT(i+1,j),g%bathyT(i,j), gv%H\_subroundoff) & 882 + (g%bathyT(i,j)-g%bathyT(i-1,j)) * g%IdxCu(i-1,j) & 883 / max(g%bathyT(i,j),g%bathyT(i-1,j), gv%H\_subroundoff) ) 884 beta\_topo\_y = -cs%MEKE\_topographic\_beta * fath * 0.5 * ( & 885 (g%bathyT(i,j+1)-g%bathyT(i,j)) * g%IdyCv(i,j) & 886 / max(g%bathyT(i,j+1),g%bathyT(i,j), gv%H\_subroundoff) + & 887 (g%bathyT(i,j)-g%bathyT(i,j-1)) * g%IdyCv(i,j-1) & 888 / max(g%bathyT(i,j),g%bathyT(i,j-1), gv%H\_subroundoff) ) 889 \textcolor{keywordflow}{ endif} 890 beta = sqrt((g%dF\_dx(i,j) + beta\_topo\_x)**2 + & 891 (g%dF\_dy(i,j) + beta\_topo\_y)**2 ) 892 893 \textcolor{keywordflow}{else} 894 beta = 0. 895 \textcolor{keywordflow}{ endif} 896 \textcolor{comment}{! Returns bottomFac2, barotrFac2 and LmixScale} 897 \textcolor{keyword}{call }meke\_lengthscales\_0d(cs, us, g%areaT(i,j), beta, g%bathyT(i,j), & 898 meke%Rd\_dx\_h(i,j), sn, meke%MEKE(i,j), & 899 bottomfac2(i,j), barotrfac2(i,j), lmixscale(i,j), & 900 lrhines(i,j), leady(i,j)) 901 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 902 \textcolor{keywordflow}{if} (cs%id\_Lrhines>0) \textcolor{keyword}{call }post\_data(cs%id\_LRhines, lrhines, cs%diag) 903 \textcolor{keywordflow}{if} (cs%id\_Leady>0) \textcolor{keyword}{call }post\_data(cs%id\_LEady, leady, cs%diag) 904 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__meke_aed5885cde342caa59b2b9cde72a3e1e7}\label{namespacemom__meke_aed5885cde342caa59b2b9cde72a3e1e7}} \index{mom\+\_\+meke@{mom\+\_\+meke}!meke\+\_\+lengthscales\+\_\+0d@{meke\+\_\+lengthscales\+\_\+0d}} \index{meke\+\_\+lengthscales\+\_\+0d@{meke\+\_\+lengthscales\+\_\+0d}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{meke\+\_\+lengthscales\+\_\+0d()}{meke\_lengthscales\_0d()}} {\footnotesize\ttfamily subroutine mom\+\_\+meke\+::meke\+\_\+lengthscales\+\_\+0d (\begin{DoxyParamCaption}\item[{type(\hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs}), pointer}]{CS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, intent(in)}]{area, }\item[{real, intent(in)}]{beta, }\item[{real, intent(in)}]{depth, }\item[{real, intent(in)}]{Rd\+\_\+dx, }\item[{real, intent(in)}]{SN, }\item[{real, intent(in)}]{E\+KE, }\item[{real, intent(out)}]{bottom\+Fac2, }\item[{real, intent(out)}]{barotr\+Fac2, }\item[{real, intent(out)}]{Lmix\+Scale, }\item[{real, intent(out)}]{Lrhines, }\item[{real, intent(out)}]{Leady }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Calculates the eddy mixing length scale and $\gamma_b$ and $\gamma_t$ functions that are ratios of either bottom or barotropic eddy energy to the column eddy energy, respectively. See \hyperlink{namespacemom__meke_section_MEKE_equations}{M\+E\+KE equations}. \begin{DoxyParams}[1]{Parameters} & {\em cs} & M\+E\+KE control structure.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline \mbox{\tt in} & {\em area} & Grid cell area \mbox{[}L2 $\sim$$>$ m2\mbox{]}\\ \hline \mbox{\tt in} & {\em beta} & Planetary beta = $ \nabla f$ \mbox{[}T-\/1 L-\/1 $\sim$$>$ s-\/1 m-\/1\mbox{]}\\ \hline \mbox{\tt in} & {\em depth} & Ocean depth \mbox{[}Z $\sim$$>$ m\mbox{]}\\ \hline \mbox{\tt in} & {\em rd\+\_\+dx} & Resolution Ld/dx \mbox{[}nondim\mbox{]}.\\ \hline \mbox{\tt in} & {\em sn} & Eady growth rate \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em eke} & Eddy kinetic energy \mbox{[}L2 T-\/2 $\sim$$>$ m2 s-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em bottomfac2} & gamma\+\_\+b$^\wedge$2\\ \hline \mbox{\tt out} & {\em barotrfac2} & gamma\+\_\+t$^\wedge$2\\ \hline \mbox{\tt out} & {\em lmixscale} & Eddy mixing length \mbox{[}L $\sim$$>$ m\mbox{]}.\\ \hline \mbox{\tt out} & {\em lrhines} & Rhines length scale \mbox{[}L $\sim$$>$ m\mbox{]}.\\ \hline \mbox{\tt out} & {\em leady} & Eady length scale \mbox{[}L $\sim$$>$ m\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 912 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 912 \textcolor{keywordtype}{type}(meke\_cs), \textcolor{keywordtype}{pointer} :: cs\textcolor{comment}{ !< MEKE control structure.} 913 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: us\textcolor{comment}{ !< A dimensional unit scaling type} 914 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: area\textcolor{comment}{ !< Grid cell area [L2 ~> m2]} 915 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: beta\textcolor{comment}{ !< Planetary beta = \(\backslash\)f$ \(\backslash\)nabla f\(\backslash\)f$ [T-1 L-1 ~> s-1 m-1]} 916 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: depth\textcolor{comment}{ !< Ocean depth [Z ~> m]} 917 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: rd\_dx\textcolor{comment}{ !< Resolution Ld/dx [nondim].} 918 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: sn\textcolor{comment}{ !< Eady growth rate [T-1 ~> s-1].} 919 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: eke\textcolor{comment}{ !< Eddy kinetic energy [L2 T-2 ~> m2 s-2].} 920 \textcolor{comment}{! real, intent(in) :: Z\_to\_L !< A conversion factor from depth units (Z) to} 921 \textcolor{comment}{! !! the units for lateral distances (L).} 922 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: bottomfac2\textcolor{comment}{ !< gamma\_b^2} 923 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: barotrfac2\textcolor{comment}{ !< gamma\_t^2} 924 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: lmixscale\textcolor{comment}{ !< Eddy mixing length [L ~> m].} 925 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: lrhines\textcolor{comment}{ !< Rhines length scale [L ~> m].} 926 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: leady\textcolor{comment}{ !< Eady length scale [L ~> m].} 927 \textcolor{comment}{! Local variables} 928 \textcolor{keywordtype}{real} :: lgrid, ldeform, lfrict \textcolor{comment}{! Length scales [L ~> m]} 929 \textcolor{keywordtype}{real} :: ue \textcolor{comment}{! An eddy velocity [L T-1 ~> m s-1]} 930 931 \textcolor{comment}{! Length scale for MEKE derived diffusivity} 932 lgrid = sqrt(area) \textcolor{comment}{! Grid scale} 933 ldeform = lgrid * rd\_dx \textcolor{comment}{! Deformation scale} 934 lfrict = (us%Z\_to\_L * depth) / cs%cdrag \textcolor{comment}{! Frictional arrest scale} 935 \textcolor{comment}{! gamma\_b^2 is the ratio of bottom eddy energy to mean column eddy energy} 936 \textcolor{comment}{! used in calculating bottom drag} 937 bottomfac2 = cs%MEKE\_CD\_SCALE**2 938 \textcolor{keywordflow}{if} (lfrict*cs%MEKE\_Cb>0.) bottomfac2 = bottomfac2 + 1./( 1. + cs%MEKE\_Cb*(ldeform/lfrict) )**0.8 939 bottomfac2 = max(bottomfac2, cs%MEKE\_min\_gamma) 940 \textcolor{comment}{! gamma\_t^2 is the ratio of barotropic eddy energy to mean column eddy energy} 941 \textcolor{comment}{! used in the velocity scale for diffusivity} 942 barotrfac2 = 1. 943 \textcolor{keywordflow}{if} (lfrict*cs%MEKE\_Ct>0.) barotrfac2 = 1. / ( 1. + cs%MEKE\_Ct*(ldeform/lfrict) )**0.25 944 barotrfac2 = max(barotrfac2, cs%MEKE\_min\_gamma) 945 \textcolor{keywordflow}{if} (cs%use\_old\_lscale) \textcolor{keywordflow}{then} 946 \textcolor{keywordflow}{if} (cs%Rd\_as\_max\_scale) \textcolor{keywordflow}{then} 947 lmixscale = min(ldeform, lgrid) \textcolor{comment}{! The smaller of Ld or dx} 948 \textcolor{keywordflow}{else} 949 lmixscale = lgrid 950 \textcolor{keywordflow}{ endif} 951 \textcolor{keywordflow}{else} 952 ue = sqrt( 2.0 * max( 0., barotrfac2*eke ) ) \textcolor{comment}{! Barotropic eddy flow scale} 953 lrhines = sqrt( ue / max( beta, 1.e-30*us%T\_to\_s*us%L\_to\_m ) ) \textcolor{comment}{! Rhines scale} 954 \textcolor{keywordflow}{if} (cs%aEady > 0.) \textcolor{keywordflow}{then} 955 leady = ue / max( sn, 1.e-15*us%T\_to\_s ) \textcolor{comment}{! Bound Eady time-scale < 1e15 seconds} 956 \textcolor{keywordflow}{else} 957 leady = 0. 958 \textcolor{keywordflow}{ endif} 959 \textcolor{keywordflow}{if} (cs%use\_min\_lscale) \textcolor{keywordflow}{then} 960 lmixscale = 1.e7 961 \textcolor{keywordflow}{if} (cs%aDeform*ldeform > 0.) lmixscale = min(lmixscale,cs%aDeform*ldeform) 962 \textcolor{keywordflow}{if} (cs%aFrict *lfrict > 0.) lmixscale = min(lmixscale,cs%aFrict *lfrict) 963 \textcolor{keywordflow}{if} (cs%aRhines*lrhines > 0.) lmixscale = min(lmixscale,cs%aRhines*lrhines) 964 \textcolor{keywordflow}{if} (cs%aEady *leady > 0.) lmixscale = min(lmixscale,cs%aEady *leady) 965 \textcolor{keywordflow}{if} (cs%aGrid *lgrid > 0.) lmixscale = min(lmixscale,cs%aGrid *lgrid) 966 \textcolor{keywordflow}{if} (cs%Lfixed > 0.) lmixscale = min(lmixscale,cs%Lfixed) 967 \textcolor{keywordflow}{else} 968 lmixscale = 0. 969 \textcolor{keywordflow}{if} (cs%aDeform*ldeform > 0.) lmixscale = lmixscale + 1./(cs%aDeform*ldeform) 970 \textcolor{keywordflow}{if} (cs%aFrict *lfrict > 0.) lmixscale = lmixscale + 1./(cs%aFrict *lfrict) 971 \textcolor{keywordflow}{if} (cs%aRhines*lrhines > 0.) lmixscale = lmixscale + 1./(cs%aRhines*lrhines) 972 \textcolor{keywordflow}{if} (cs%aEady *leady > 0.) lmixscale = lmixscale + 1./(cs%aEady *leady) 973 \textcolor{keywordflow}{if} (cs%aGrid *lgrid > 0.) lmixscale = lmixscale + 1./(cs%aGrid *lgrid) 974 \textcolor{keywordflow}{if} (cs%Lfixed > 0.) lmixscale = lmixscale + 1./cs%Lfixed 975 \textcolor{keywordflow}{if} (lmixscale > 0.) lmixscale = 1. / lmixscale 976 \textcolor{keywordflow}{ endif} 977 \textcolor{keywordflow}{ endif} 978 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__meke_a5f752f097ddeba7071e1703110e51bc2}\label{namespacemom__meke_a5f752f097ddeba7071e1703110e51bc2}} \index{mom\+\_\+meke@{mom\+\_\+meke}!step\+\_\+forward\+\_\+meke@{step\+\_\+forward\+\_\+meke}} \index{step\+\_\+forward\+\_\+meke@{step\+\_\+forward\+\_\+meke}!mom\+\_\+meke@{mom\+\_\+meke}} \subsubsection{\texorpdfstring{step\+\_\+forward\+\_\+meke()}{step\_forward\_meke()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+meke\+::step\+\_\+forward\+\_\+meke (\begin{DoxyParamCaption}\item[{type(meke\+\_\+type), pointer}]{M\+E\+KE, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(in)}]{h, }\item[{real, dimension( g \%isdb\+: g \%iedb, g \%jsd\+: g \%jed), intent(in)}]{S\+N\+\_\+u, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsdb\+: g \%jedb), intent(in)}]{S\+N\+\_\+v, }\item[{type(vertvisc\+\_\+type), intent(in)}]{visc, }\item[{real, intent(in)}]{dt, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(inout)}]{G, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{type(\hyperlink{structmom__meke_1_1meke__cs}{meke\+\_\+cs}), pointer}]{CS, }\item[{real, dimension( g \%isdb\+: g \%iedb, g \%jsd\+: g \%jed, g \%ke), intent(in)}]{hu, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsdb\+: g \%jedb, g \%ke), intent(in)}]{hv }\end{DoxyParamCaption})} Integrates forward-\/in-\/time the M\+E\+KE eddy energy equation. See \hyperlink{namespacemom__meke_section_MEKE_equations}{M\+E\+KE equations}. \begin{DoxyParams}[1]{Parameters} & {\em meke} & M\+E\+KE data.\\ \hline \mbox{\tt in,out} & {\em g} & Ocean grid.\\ \hline \mbox{\tt in} & {\em gv} & Ocean vertical grid structure.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline \mbox{\tt in} & {\em h} & Layer thickness \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em sn\+\_\+u} & Eady growth rate at u-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em sn\+\_\+v} & Eady growth rate at v-\/points \mbox{[}T-\/1 $\sim$$>$ s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em visc} & The vertical viscosity type.\\ \hline \mbox{\tt in} & {\em dt} & Model(baroclinic) time-\/step \mbox{[}T $\sim$$>$ s\mbox{]}.\\ \hline & {\em cs} & M\+E\+KE control structure.\\ \hline \mbox{\tt in} & {\em hu} & Accumlated zonal mass flux \mbox{[}H L2 $\sim$$>$ m3 or kg\mbox{]}.\\ \hline \mbox{\tt in} & {\em hv} & Accumlated meridional mass flux \mbox{[}H L2 $\sim$$>$ m3 or kg\mbox{]} \\ \hline \end{DoxyParams} Definition at line 112 of file M\+O\+M\+\_\+\+M\+E\+K\+E.\+F90. \begin{DoxyCode} 112 \textcolor{keywordtype}{type}(meke\_type), \textcolor{keywordtype}{pointer} :: meke\textcolor{comment}{ !< MEKE data.} 113 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(inout)} :: g\textcolor{comment}{ !< Ocean grid.} 114 \textcolor{keywordtype}{type}(verticalgrid\_type), \textcolor{keywordtype}{intent(in)} :: gv\textcolor{comment}{ !< Ocean vertical grid structure.} 115 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: us\textcolor{comment}{ !< A dimensional unit scaling type} 116 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< Layer thickness [H ~> m or kg m-2].} 117 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZIB\_(G),SZJ\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_u\textcolor{comment}{ !< Eady growth rate at u-points [T-1 ~> s-1].} 118 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJB\_(G))}, \textcolor{keywordtype}{intent(in)} :: sn\_v\textcolor{comment}{ !< Eady growth rate at v-points [T-1 ~> s-1].} 119 \textcolor{keywordtype}{type}(vertvisc\_type), \textcolor{keywordtype}{intent(in)} :: visc\textcolor{comment}{ !< The vertical viscosity type.} 120 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dt\textcolor{comment}{ !< Model(baroclinic) time-step [T ~> s].} 121 \textcolor{keywordtype}{type}(meke\_cs), \textcolor{keywordtype}{pointer} :: cs\textcolor{comment}{ !< MEKE control structure.} 122 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZIB\_(G),SZJ\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: hu\textcolor{comment}{ !< Accumlated zonal mass flux [H L2 ~> m3 or kg].} 123 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJB\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: hv\textcolor{comment}{ !< Accumlated meridional mass flux [H L2 ~> m3 or kg]} 124 125 \textcolor{comment}{! Local variables} 126 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))} :: & 127 mass, & \textcolor{comment}{! The total mass of the water column [R Z ~> kg m-2].} 128 i\_mass, & \textcolor{comment}{! The inverse of mass [R-1 Z-1 ~> m2 kg-1].} 129 src, & \textcolor{comment}{! The sum of all MEKE sources [L2 T-3 ~> W kg-1] (= m2 s-3).} 130 meke\_decay, & \textcolor{comment}{! A diagnostic of the MEKE decay timescale [T-1 ~> s-1].} 131 drag\_rate\_visc, & \textcolor{comment}{! Near-bottom velocity contribution to bottom dratg [L T-1 ~> m s-1]} 132 drag\_rate, & \textcolor{comment}{! The MEKE spindown timescale due to bottom drag [T-1 ~> s-1].} 133 drag\_rate\_j15, & \textcolor{comment}{! The MEKE spindown timescale due to bottom drag with the Jansen 2015 scheme.} 134 \textcolor{comment}{! Unfortunately, as written the units seem inconsistent. [T-1 ~> s-1].} 135 del2meke, & \textcolor{comment}{! Laplacian of MEKE, used for bi-harmonic diffusion [T-2 ~> s-2].} 136 del4meke, & \textcolor{comment}{! Time-integrated MEKE tendency arising from the biharmonic of MEKE [L2 T-2 ~> m2 s-2].} 137 lmixscale, & \textcolor{comment}{! Eddy mixing length [L ~> m].} 138 barotrfac2, & \textcolor{comment}{! Ratio of EKE\_barotropic / EKE [nondim]} 139 bottomfac2, & \textcolor{comment}{! Ratio of EKE\_bottom / EKE [nondim]} 140 tmp \textcolor{comment}{! Temporary variable for diagnostic computation} 141 142 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZIB\_(G),SZJ\_(G))} :: & 143 meke\_uflux, & \textcolor{comment}{! The zonal advective and diffusive flux of MEKE with units of [R Z L4 T-3 ~> kg m-2 s-3].} 144 \textcolor{comment}{! In one place, MEKE\_uflux is used as temporary work space with units of [L2 T-2 ~> m2 s-2].} 145 kh\_u, & \textcolor{comment}{! The zonal diffusivity that is actually used [L2 T-1 ~> m2 s-1].} 146 barohu, & \textcolor{comment}{! Depth integrated accumulated zonal mass flux [R Z L2 ~> kg].} 147 drag\_vel\_u \textcolor{comment}{! A (vertical) viscosity associated with bottom drag at} 148 \textcolor{comment}{! u-points [Z T-1 ~> m s-1].} 149 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJB\_(G))} :: & 150 meke\_vflux, & \textcolor{comment}{! The meridional advective and diffusive flux of MEKE with units of [R Z L4 T-3 ~> kg m-2 s-3].} 151 \textcolor{comment}{! In one place, MEKE\_vflux is used as temporary work space with units of [L2 T-2 ~> m2 s-2].} 152 kh\_v, & \textcolor{comment}{! The meridional diffusivity that is actually used [L2 T-1 ~> m2 s-1].} 153 barohv, & \textcolor{comment}{! Depth integrated accumulated meridional mass flux [R Z L2 ~> kg].} 154 drag\_vel\_v \textcolor{comment}{! A (vertical) viscosity associated with bottom drag at} 155 \textcolor{comment}{! v-points [Z T-1 ~> m s-1].} 156 \textcolor{keywordtype}{real} :: kh\_here \textcolor{comment}{! The local horizontal viscosity [L2 T-1 ~> m2 s-1]} 157 \textcolor{keywordtype}{real} :: inv\_kh\_max \textcolor{comment}{! The inverse of the local horizontal viscosity [T L-2 ~> s m-2]} 158 \textcolor{keywordtype}{real} :: k4\_here \textcolor{comment}{! The local horizontal biharmonic viscosity [L4 T-1 ~> m4 s-1]} 159 \textcolor{keywordtype}{real} :: inv\_k4\_max \textcolor{comment}{! The inverse of the local horizontal biharmonic viscosity [T L-4 ~> s m-4]} 160 \textcolor{keywordtype}{real} :: cdrag2 161 \textcolor{keywordtype}{real} :: advfac \textcolor{comment}{! The product of the advection scaling factor and 1/dt [T-1 ~> s-1]} 162 \textcolor{keywordtype}{real} :: mass\_neglect \textcolor{comment}{! A negligible mass [R Z ~> kg m-2].} 163 \textcolor{keywordtype}{real} :: ldamping \textcolor{comment}{! The MEKE damping rate [T-1 ~> s-1].} 164 \textcolor{keywordtype}{real} :: rho0 \textcolor{comment}{! A density used to convert mass to distance [R ~> kg m-3].} 165 \textcolor{keywordtype}{real} :: sdt \textcolor{comment}{! dt to use locally [T ~> s] (could be scaled to accelerate)} 166 \textcolor{keywordtype}{real} :: sdt\_damp \textcolor{comment}{! dt for damping [T ~> s] (sdt could be split).} 167 \textcolor{keywordtype}{logical} :: use\_drag\_rate \textcolor{comment}{! Flag to indicate drag\_rate is finite} 168 \textcolor{keywordtype}{integer} :: i, j, k, is, ie, js, je, isq, ieq, jsq, jeq, nz 169 170 is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec ; nz = g%ke 171 isq = g%IscB ; ieq = g%IecB ; jsq = g%JscB ; jeq = g%JecB 172 173 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{associated}(cs)) \textcolor{keyword}{call }mom\_error(fatal, & 174 \textcolor{stringliteral}{"MOM\_MEKE: Module must be initialized before it is used."}) 175 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{associated}(meke)) \textcolor{keyword}{call }mom\_error(fatal, & 176 \textcolor{stringliteral}{"MOM\_MEKE: MEKE must be initialized before it is used."}) 177 178 \textcolor{keywordflow}{if} ((cs%MEKE\_damping > 0.0) .or. (cs%MEKE\_Cd\_scale > 0.0) .or. (cs%MEKE\_Cb>0.) & 179 .or. cs%visc\_drag) \textcolor{keywordflow}{then} 180 use\_drag\_rate = .true. 181 \textcolor{keywordflow}{else} 182 use\_drag\_rate = .false. 183 \textcolor{keywordflow}{ endif} 184 185 \textcolor{comment}{! Only integrate the MEKE equations if MEKE is required.} 186 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{associated}(meke%MEKE)) \textcolor{keywordflow}{then} 187 \textcolor{comment}{! call MOM\_error(FATAL, "MOM\_MEKE: MEKE%MEKE is not associated!")} 188 \textcolor{keywordflow}{return} 189 \textcolor{keywordflow}{ endif} 190 191 \textcolor{keywordflow}{if} (cs%debug) \textcolor{keywordflow}{then} 192 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%mom\_src)) & 193 \textcolor{keyword}{call }hchksum(meke%mom\_src, \textcolor{stringliteral}{'MEKE mom\_src'}, g%HI, scale=us%RZ3\_T3\_to\_W\_m2*us%L\_to\_Z**2) 194 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%GME\_snk)) & 195 \textcolor{keyword}{call }hchksum(meke%GME\_snk, \textcolor{stringliteral}{'MEKE GME\_snk'}, g%HI, scale=us%RZ3\_T3\_to\_W\_m2*us%L\_to\_Z**2) 196 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%GM\_src)) & 197 \textcolor{keyword}{call }hchksum(meke%GM\_src, \textcolor{stringliteral}{'MEKE GM\_src'}, g%HI, scale=us%RZ3\_T3\_to\_W\_m2*us%L\_to\_Z**2) 198 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%MEKE)) \textcolor{keyword}{call }hchksum(meke%MEKE, \textcolor{stringliteral}{'MEKE MEKE'}, g%HI, scale=us%L\_T\_to\_m\_s**2) 199 \textcolor{keyword}{call }uvchksum(\textcolor{stringliteral}{"MEKE SN\_[uv]"}, sn\_u, sn\_v, g%HI, scale=us%s\_to\_T, & 200 scalar\_pair=.true.) 201 \textcolor{keyword}{call }uvchksum(\textcolor{stringliteral}{"MEKE h[uv]"}, hu, hv, g%HI, haloshift=1, & 202 scale=gv%H\_to\_m*(us%L\_to\_m**2)) 203 \textcolor{keywordflow}{ endif} 204 205 sdt = dt*cs%MEKE\_dtScale \textcolor{comment}{! Scaled dt to use for time-stepping} 206 rho0 = gv%Rho0 207 mass\_neglect = gv%H\_to\_RZ * gv%H\_subroundoff 208 cdrag2 = cs%cdrag**2 209 210 \textcolor{comment}{! With a depth-dependent (and possibly strong) damping, it seems} 211 \textcolor{comment}{! advisable to use Strang splitting between the damping and diffusion.} 212 sdt\_damp = sdt ; \textcolor{keywordflow}{if} (cs%MEKE\_KH >= 0.0 .or. cs%MEKE\_K4 >= 0.) sdt\_damp = 0.5*sdt 213 214 \textcolor{comment}{! Calculate depth integrated mass exchange if doing advection [R Z L2 ~> kg]} 215 \textcolor{keywordflow}{if} (cs%MEKE\_advection\_factor>0.) \textcolor{keywordflow}{then} 216 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is-1,ie 217 barohu(i,j) = 0. 218 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 219 \textcolor{keywordflow}{do} k=1,nz 220 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is-1,ie 221 barohu(i,j) = hu(i,j,k) * gv%H\_to\_RZ 222 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 223 \textcolor{keywordflow}{ enddo} 224 \textcolor{keywordflow}{do} j=js-1,je ; \textcolor{keywordflow}{do} i=is,ie 225 barohv(i,j) = 0. 226 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 227 \textcolor{keywordflow}{do} k=1,nz 228 \textcolor{keywordflow}{do} j=js-1,je ; \textcolor{keywordflow}{do} i=is,ie 229 barohv(i,j) = hv(i,j,k) * gv%H\_to\_RZ 230 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 231 \textcolor{keywordflow}{ enddo} 232 \textcolor{keywordflow}{ endif} 233 234 \textcolor{keywordflow}{if} (cs%MEKE\_Cd\_scale == 0.0 .and. .not. cs%visc\_drag) \textcolor{keywordflow}{then} 235 \textcolor{comment}{!$OMP parallel do default(shared) private(ldamping)} 236 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 237 drag\_rate(i,j) = 0. ; drag\_rate\_j15(i,j) = 0. 238 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 239 \textcolor{keywordflow}{ endif} 240 241 \textcolor{comment}{! Calculate drag\_rate\_visc(i,j) which accounts for the model bottom mean flow} 242 \textcolor{keywordflow}{if} (cs%visc\_drag) \textcolor{keywordflow}{then} 243 \textcolor{comment}{!$OMP parallel do default(shared)} 244 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is-1,ie 245 drag\_vel\_u(i,j) = 0.0 246 \textcolor{keywordflow}{if} ((g%mask2dCu(i,j) > 0.0) .and. (visc%bbl\_thick\_u(i,j) > 0.0)) & 247 drag\_vel\_u(i,j) = visc%Kv\_bbl\_u(i,j) / visc%bbl\_thick\_u(i,j) 248 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 249 \textcolor{comment}{!$OMP parallel do default(shared)} 250 \textcolor{keywordflow}{do} j=js-1,je ; \textcolor{keywordflow}{do} i=is,ie 251 drag\_vel\_v(i,j) = 0.0 252 \textcolor{keywordflow}{if} ((g%mask2dCv(i,j) > 0.0) .and. (visc%bbl\_thick\_v(i,j) > 0.0)) & 253 drag\_vel\_v(i,j) = visc%Kv\_bbl\_v(i,j) / visc%bbl\_thick\_v(i,j) 254 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 255 256 \textcolor{comment}{!$OMP parallel do default(shared)} 257 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 258 drag\_rate\_visc(i,j) = (0.25*g%IareaT(i,j) * us%Z\_to\_L * & 259 ((g%areaCu(i-1,j)*drag\_vel\_u(i-1,j) + & 260 g%areaCu(i,j)*drag\_vel\_u(i,j)) + & 261 (g%areaCv(i,j-1)*drag\_vel\_v(i,j-1) + & 262 g%areaCv(i,j)*drag\_vel\_v(i,j)) ) ) 263 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 264 \textcolor{keywordflow}{else} 265 \textcolor{comment}{!$OMP parallel do default(shared)} 266 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 267 drag\_rate\_visc(i,j) = 0. 268 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 269 \textcolor{keywordflow}{ endif} 270 271 \textcolor{comment}{!$OMP parallel do default(shared)} 272 \textcolor{keywordflow}{do} j=js-1,je+1 273 \textcolor{keywordflow}{do} i=is-1,ie+1 ; mass(i,j) = 0.0 ;\textcolor{keywordflow}{ enddo} 274 \textcolor{keywordflow}{do} k=1,nz ; \textcolor{keywordflow}{do} i=is-1,ie+1 275 mass(i,j) = mass(i,j) + g%mask2dT(i,j) * (gv%H\_to\_RZ * h(i,j,k)) \textcolor{comment}{! [R Z ~> kg m-2]} 276 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 277 \textcolor{keywordflow}{do} i=is-1,ie+1 278 i\_mass(i,j) = 0.0 279 \textcolor{keywordflow}{if} (mass(i,j) > 0.0) i\_mass(i,j) = 1.0 / mass(i,j) \textcolor{comment}{! [R-1 Z-1 ~> m2 kg-1]} 280 \textcolor{keywordflow}{ enddo} 281 \textcolor{keywordflow}{ enddo} 282 283 \textcolor{keywordflow}{if} (cs%initialize) \textcolor{keywordflow}{then} 284 \textcolor{keyword}{call }meke\_equilibrium(cs, meke, g, gv, us, sn\_u, sn\_v, drag\_rate\_visc, i\_mass) 285 cs%initialize = .false. 286 \textcolor{keywordflow}{ endif} 287 288 \textcolor{comment}{! Calculates bottomFac2, barotrFac2 and LmixScale} 289 \textcolor{keyword}{call }meke\_lengthscales(cs, meke, g, gv, us, sn\_u, sn\_v, meke%MEKE, bottomfac2, barotrfac2, lmixscale) 290 \textcolor{keywordflow}{if} (cs%debug) \textcolor{keywordflow}{then} 291 \textcolor{keywordflow}{if} (cs%visc\_drag) & 292 \textcolor{keyword}{call }uvchksum(\textcolor{stringliteral}{"MEKE drag\_vel\_[uv]"}, drag\_vel\_u, drag\_vel\_v, g%HI, & 293 scale=us%Z\_to\_m*us%s\_to\_T, scalar\_pair=.true.) 294 \textcolor{keyword}{call }hchksum(mass, \textcolor{stringliteral}{'MEKE mass'},g%HI,haloshift=1, scale=us%RZ\_to\_kg\_m2) 295 \textcolor{keyword}{call }hchksum(drag\_rate\_visc, \textcolor{stringliteral}{'MEKE drag\_rate\_visc'}, g%HI, scale=us%L\_T\_to\_m\_s) 296 \textcolor{keyword}{call }hchksum(bottomfac2, \textcolor{stringliteral}{'MEKE bottomFac2'}, g%HI) 297 \textcolor{keyword}{call }hchksum(barotrfac2, \textcolor{stringliteral}{'MEKE barotrFac2'}, g%HI) 298 \textcolor{keyword}{call }hchksum(lmixscale, \textcolor{stringliteral}{'MEKE LmixScale'}, g%HI,scale=us%L\_to\_m) 299 \textcolor{keywordflow}{ endif} 300 301 \textcolor{comment}{! Aggregate sources of MEKE (background, frictional and GM)} 302 \textcolor{comment}{!$OMP parallel do default(shared)} 303 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 304 src(i,j) = cs%MEKE\_BGsrc 305 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 306 307 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%mom\_src)) \textcolor{keywordflow}{then} 308 \textcolor{comment}{!$OMP parallel do default(shared)} 309 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 310 src(i,j) = src(i,j) - cs%MEKE\_FrCoeff*i\_mass(i,j)*meke%mom\_src(i,j) 311 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 312 \textcolor{keywordflow}{ endif} 313 314 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%GME\_snk)) \textcolor{keywordflow}{then} 315 \textcolor{comment}{!$OMP parallel do default(shared)} 316 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 317 src(i,j) = src(i,j) - cs%MEKE\_GMECoeff*i\_mass(i,j)*meke%GME\_snk(i,j) 318 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 319 \textcolor{keywordflow}{ endif} 320 321 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%GM\_src)) \textcolor{keywordflow}{then} 322 \textcolor{keywordflow}{if} (cs%GM\_src\_alt) \textcolor{keywordflow}{then} 323 \textcolor{comment}{!$OMP parallel do default(shared)} 324 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 325 src(i,j) = src(i,j) - cs%MEKE\_GMcoeff*meke%GM\_src(i,j) / & 326 (gv%Rho0 * max(1.0*us%m\_to\_Z, g%bathyT(i,j))) 327 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 328 \textcolor{keywordflow}{else} 329 \textcolor{comment}{!$OMP parallel do default(shared)} 330 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 331 src(i,j) = src(i,j) - cs%MEKE\_GMcoeff*i\_mass(i,j)*meke%GM\_src(i,j) 332 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 333 \textcolor{keywordflow}{ endif} 334 \textcolor{keywordflow}{ endif} 335 336 \textcolor{keywordflow}{if} (cs%MEKE\_equilibrium\_restoring) \textcolor{keywordflow}{then} 337 \textcolor{keyword}{call }meke\_equilibrium\_restoring(cs, g, us, sn\_u, sn\_v) 338 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 339 src(i,j) = src(i,j) - cs%MEKE\_restoring\_rate*(meke%MEKE(i,j) - cs%equilibrium\_value(i,j)) 340 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 341 \textcolor{keywordflow}{ endif} 342 343 \textcolor{comment}{! Increase EKE by a full time-steps worth of source} 344 \textcolor{comment}{!$OMP parallel do default(shared)} 345 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 346 meke%MEKE(i,j) = (meke%MEKE(i,j) + sdt*src(i,j))*g%mask2dT(i,j) 347 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 348 349 \textcolor{keywordflow}{if} (use\_drag\_rate) \textcolor{keywordflow}{then} 350 \textcolor{comment}{! Calculate a viscous drag rate (includes BBL contributions from mean flow and eddies)} 351 \textcolor{comment}{!$OMP parallel do default(shared)} 352 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 353 drag\_rate(i,j) = (us%L\_to\_Z*rho0 * i\_mass(i,j)) * sqrt( drag\_rate\_visc(i,j)**2 + & 354 cdrag2 * ( max(0.0, 2.0*bottomfac2(i,j)*meke%MEKE(i,j)) + cs%MEKE\_Uscale**2 ) ) 355 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 356 \textcolor{keywordflow}{ endif} 357 358 \textcolor{comment}{! First stage of Strang splitting} 359 \textcolor{comment}{!$OMP parallel do default(shared)} 360 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 361 ldamping = cs%MEKE\_damping + drag\_rate(i,j) * bottomfac2(i,j) 362 \textcolor{keywordflow}{if} (meke%MEKE(i,j) < 0.) ldamping = 0. 363 \textcolor{comment}{! notice that the above line ensures a damping only if MEKE is positive,} 364 \textcolor{comment}{! while leaving MEKE unchanged if it is negative} 365 meke%MEKE(i,j) = meke%MEKE(i,j) / (1.0 + sdt\_damp*ldamping) 366 meke\_decay(i,j) = ldamping*g%mask2dT(i,j) 367 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 368 369 \textcolor{keywordflow}{if} (cs%kh\_flux\_enabled .or. cs%MEKE\_K4 >= 0.0) \textcolor{keywordflow}{then} 370 \textcolor{comment}{! Update MEKE in the halos for lateral or bi-harmonic diffusion} 371 \textcolor{keyword}{call }cpu\_clock\_begin(cs%id\_clock\_pass) 372 \textcolor{keyword}{call }do\_group\_pass(cs%pass\_MEKE, g%Domain) 373 \textcolor{keyword}{call }cpu\_clock\_end(cs%id\_clock\_pass) 374 \textcolor{keywordflow}{ endif} 375 376 \textcolor{keywordflow}{if} (cs%MEKE\_K4 >= 0.0) \textcolor{keywordflow}{then} 377 \textcolor{comment}{! Calculate Laplacian of MEKE using MEKE\_uflux and MEKE\_vflux as temporary work space.} 378 \textcolor{comment}{!$OMP parallel do default(shared)} 379 \textcolor{keywordflow}{do} j=js-1,je+1 ; \textcolor{keywordflow}{do} i=is-2,ie+1 380 \textcolor{comment}{! MEKE\_uflux is used here as workspace with units of [L2 T-2 ~> m2 s-2].} 381 meke\_uflux(i,j) = ((g%dy\_Cu(i,j)*g%IdxCu(i,j)) * g%mask2dCu(i,j)) * & 382 (meke%MEKE(i+1,j) - meke%MEKE(i,j)) 383 \textcolor{comment}{! This would have units of [R Z L2 T-2 ~> kg s-2]} 384 \textcolor{comment}{! MEKE\_uflux(I,j) = ((G%dy\_Cu(I,j)*G%IdxCu(I,j)) * &} 385 \textcolor{comment}{! ((2.0*mass(i,j)*mass(i+1,j)) / ((mass(i,j)+mass(i+1,j)) + mass\_neglect)) ) * &} 386 \textcolor{comment}{! (MEKE%MEKE(i+1,j) - MEKE%MEKE(i,j))} 387 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 388 \textcolor{comment}{!$OMP parallel do default(shared)} 389 \textcolor{keywordflow}{do} j=js-2,je+1 ; \textcolor{keywordflow}{do} i=is-1,ie+1 390 \textcolor{comment}{! MEKE\_vflux is used here as workspace with units of [L2 T-2 ~> m2 s-2].} 391 meke\_vflux(i,j) = ((g%dx\_Cv(i,j)*g%IdyCv(i,j)) * g%mask2dCv(i,j)) * & 392 (meke%MEKE(i,j+1) - meke%MEKE(i,j)) 393 \textcolor{comment}{! This would have units of [R Z L2 T-2 ~> kg s-2]} 394 \textcolor{comment}{! MEKE\_vflux(i,J) = ((G%dx\_Cv(i,J)*G%IdyCv(i,J)) * &} 395 \textcolor{comment}{! ((2.0*mass(i,j)*mass(i,j+1)) / ((mass(i,j)+mass(i,j+1)) + mass\_neglect)) ) * &} 396 \textcolor{comment}{! (MEKE%MEKE(i,j+1) - MEKE%MEKE(i,j))} 397 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 398 399 \textcolor{comment}{!$OMP parallel do default(shared)} 400 \textcolor{keywordflow}{do} j=js-1,je+1 ; \textcolor{keywordflow}{do} i=is-1,ie+1 \textcolor{comment}{! del2MEKE has units [T-2 ~> s-2].} 401 del2meke(i,j) = g%IareaT(i,j) * & 402 ((meke\_uflux(i,j) - meke\_uflux(i-1,j)) + (meke\_vflux(i,j) - meke\_vflux(i,j-1))) 403 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 404 405 \textcolor{comment}{! Bi-harmonic diffusion of MEKE} 406 \textcolor{comment}{!$OMP parallel do default(shared) private(K4\_here,Inv\_K4\_max)} 407 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is-1,ie 408 k4\_here = cs%MEKE\_K4 \textcolor{comment}{! [L4 T-1 ~> m4 s-1]} 409 \textcolor{comment}{! Limit Kh to avoid CFL violations.} 410 inv\_k4\_max = 64.0 * sdt * ((g%dy\_Cu(i,j)*g%IdxCu(i,j)) * & 411 max(g%IareaT(i,j), g%IareaT(i+1,j)))**2 412 \textcolor{keywordflow}{if} (k4\_here*inv\_k4\_max > 0.3) k4\_here = 0.3 / inv\_k4\_max 413 414 \textcolor{comment}{! Here the units of MEKE\_uflux are [R Z L4 T-3 ~> kg m2 s-3].} 415 meke\_uflux(i,j) = ((k4\_here * (g%dy\_Cu(i,j)*g%IdxCu(i,j))) * & 416 ((2.0*mass(i,j)*mass(i+1,j)) / ((mass(i,j)+mass(i+1,j)) + mass\_neglect)) ) * & 417 (del2meke(i+1,j) - del2meke(i,j)) 418 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 419 \textcolor{comment}{!$OMP parallel do default(shared) private(K4\_here,Inv\_K4\_max)} 420 \textcolor{keywordflow}{do} j=js-1,je ; \textcolor{keywordflow}{do} i=is,ie 421 k4\_here = cs%MEKE\_K4 \textcolor{comment}{! [L4 T-1 ~> m4 s-1]} 422 inv\_k4\_max = 64.0 * sdt * ((g%dx\_Cv(i,j)*g%IdyCv(i,j)) * max(g%IareaT(i,j), g%IareaT(i,j+1)))**2 423 \textcolor{keywordflow}{if} (k4\_here*inv\_k4\_max > 0.3) k4\_here = 0.3 / inv\_k4\_max 424 425 \textcolor{comment}{! Here the units of MEKE\_vflux are [R Z L4 T-3 ~> kg m2 s-3].} 426 meke\_vflux(i,j) = ((k4\_here * (g%dx\_Cv(i,j)*g%IdyCv(i,j))) * & 427 ((2.0*mass(i,j)*mass(i,j+1)) / ((mass(i,j)+mass(i,j+1)) + mass\_neglect)) ) * & 428 (del2meke(i,j+1) - del2meke(i,j)) 429 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 430 \textcolor{comment}{! Store change in MEKE arising from the bi-harmonic in del4MEKE [L2 T-2 ~> m2 s-2].} 431 \textcolor{comment}{!$OMP parallel do default(shared)} 432 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 433 del4meke(i,j) = (sdt*(g%IareaT(i,j)*i\_mass(i,j))) * & 434 ((meke\_uflux(i-1,j) - meke\_uflux(i,j)) + & 435 (meke\_vflux(i,j-1) - meke\_vflux(i,j))) 436 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 437 \textcolor{keywordflow}{ endif} \textcolor{comment}{!} 438 439 \textcolor{keywordflow}{if} (cs%kh\_flux\_enabled) \textcolor{keywordflow}{then} 440 \textcolor{comment}{! Lateral diffusion of MEKE} 441 kh\_here = max(0., cs%MEKE\_Kh) 442 \textcolor{comment}{!$OMP parallel do default(shared) firstprivate(Kh\_here) private(Inv\_Kh\_max)} 443 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is-1,ie 444 \textcolor{comment}{! Limit Kh to avoid CFL violations.} 445 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh)) & 446 kh\_here = max(0., cs%MEKE\_Kh) + & 447 cs%KhMEKE\_Fac*0.5*(meke%Kh(i,j)+meke%Kh(i+1,j)) 448 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh\_diff)) & 449 kh\_here = max(0.,cs%MEKE\_Kh) + & 450 cs%KhMEKE\_Fac*0.5*(meke%Kh\_diff(i,j)+meke%Kh\_diff(i+1,j)) 451 inv\_kh\_max = 2.0*sdt * ((g%dy\_Cu(i,j)*g%IdxCu(i,j)) * & 452 max(g%IareaT(i,j),g%IareaT(i+1,j))) 453 \textcolor{keywordflow}{if} (kh\_here*inv\_kh\_max > 0.25) kh\_here = 0.25 / inv\_kh\_max 454 kh\_u(i,j) = kh\_here 455 456 \textcolor{comment}{! Here the units of MEKE\_uflux and MEKE\_vflux are [R Z L4 T-3 ~> kg m2 s-3].} 457 meke\_uflux(i,j) = ((kh\_here * (g%dy\_Cu(i,j)*g%IdxCu(i,j))) * & 458 ((2.0*mass(i,j)*mass(i+1,j)) / ((mass(i,j)+mass(i+1,j)) + mass\_neglect)) ) * & 459 (meke%MEKE(i,j) - meke%MEKE(i+1,j)) 460 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 461 \textcolor{comment}{!$OMP parallel do default(shared) firstprivate(Kh\_here) private(Inv\_Kh\_max)} 462 \textcolor{keywordflow}{do} j=js-1,je ; \textcolor{keywordflow}{do} i=is,ie 463 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh)) & 464 kh\_here = max(0.,cs%MEKE\_Kh) + cs%KhMEKE\_Fac * 0.5*(meke%Kh(i,j)+meke%Kh(i,j+1)) 465 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh\_diff)) & 466 kh\_here = max(0.,cs%MEKE\_Kh) + cs%KhMEKE\_Fac * 0.5*(meke%Kh\_diff(i,j)+meke%Kh\_diff(i,j+1)) 467 inv\_kh\_max = 2.0*sdt * ((g%dx\_Cv(i,j)*g%IdyCv(i,j)) * max(g%IareaT(i,j),g%IareaT(i,j+1))) 468 \textcolor{keywordflow}{if} (kh\_here*inv\_kh\_max > 0.25) kh\_here = 0.25 / inv\_kh\_max 469 kh\_v(i,j) = kh\_here 470 471 \textcolor{comment}{! Here the units of MEKE\_uflux and MEKE\_vflux are [R Z L4 T-3 ~> kg m2 s-3].} 472 meke\_vflux(i,j) = ((kh\_here * (g%dx\_Cv(i,j)*g%IdyCv(i,j))) * & 473 ((2.0*mass(i,j)*mass(i,j+1)) / ((mass(i,j)+mass(i,j+1)) + mass\_neglect)) ) * & 474 (meke%MEKE(i,j) - meke%MEKE(i,j+1)) 475 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 476 \textcolor{keywordflow}{if} (cs%MEKE\_advection\_factor>0.) \textcolor{keywordflow}{then} 477 advfac = cs%MEKE\_advection\_factor / sdt \textcolor{comment}{! [T-1 ~> s-1]} 478 \textcolor{comment}{!$OMP parallel do default(shared)} 479 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is-1,ie 480 \textcolor{comment}{! Here the units of the quantities added to MEKE\_uflux are [R Z L4 T-3 ~> kg m2 s-3].} 481 \textcolor{keywordflow}{if} (barohu(i,j)>0.) \textcolor{keywordflow}{then} 482 meke\_uflux(i,j) = meke\_uflux(i,j) + barohu(i,j)*meke%MEKE(i,j)*advfac 483 \textcolor{keywordflow}{elseif} (barohu(i,j)<0.) \textcolor{keywordflow}{then} 484 meke\_uflux(i,j) = meke\_uflux(i,j) + barohu(i,j)*meke%MEKE(i+1,j)*advfac 485 \textcolor{keywordflow}{ endif} 486 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 487 \textcolor{comment}{!$OMP parallel do default(shared)} 488 \textcolor{keywordflow}{do} j=js-1,je ; \textcolor{keywordflow}{do} i=is,ie 489 \textcolor{comment}{! Here the units of the quantities added to MEKE\_vflux are [R Z L4 T-3 ~> kg m2 s-3].} 490 \textcolor{keywordflow}{if} (barohv(i,j)>0.) \textcolor{keywordflow}{then} 491 meke\_vflux(i,j) = meke\_vflux(i,j) + barohv(i,j)*meke%MEKE(i,j)*advfac 492 \textcolor{keywordflow}{elseif} (barohv(i,j)<0.) \textcolor{keywordflow}{then} 493 meke\_vflux(i,j) = meke\_vflux(i,j) + barohv(i,j)*meke%MEKE(i,j+1)*advfac 494 \textcolor{keywordflow}{ endif} 495 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 496 \textcolor{keywordflow}{ endif} 497 498 \textcolor{comment}{!$OMP parallel do default(shared)} 499 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 500 meke%MEKE(i,j) = meke%MEKE(i,j) + (sdt*(g%IareaT(i,j)*i\_mass(i,j))) * & 501 ((meke\_uflux(i-1,j) - meke\_uflux(i,j)) + & 502 (meke\_vflux(i,j-1) - meke\_vflux(i,j))) 503 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 504 \textcolor{keywordflow}{ endif} \textcolor{comment}{! MEKE\_KH>0} 505 506 \textcolor{comment}{! Add on bi-harmonic tendency} 507 \textcolor{keywordflow}{if} (cs%MEKE\_K4 >= 0.0) \textcolor{keywordflow}{then} 508 \textcolor{comment}{!$OMP parallel do default(shared)} 509 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 510 meke%MEKE(i,j) = meke%MEKE(i,j) + del4meke(i,j) 511 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 512 \textcolor{keywordflow}{ endif} 513 514 \textcolor{comment}{! Second stage of Strang splitting} 515 \textcolor{keywordflow}{if} (cs%MEKE\_KH >= 0.0 .or. cs%MEKE\_K4 >= 0.0) \textcolor{keywordflow}{then} 516 \textcolor{keywordflow}{if} (sdt>sdt\_damp) \textcolor{keywordflow}{then} 517 \textcolor{comment}{! Recalculate the drag rate, since MEKE has changed.} 518 \textcolor{keywordflow}{if} (use\_drag\_rate) \textcolor{keywordflow}{then} 519 \textcolor{comment}{!$OMP parallel do default(shared)} 520 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 521 drag\_rate(i,j) = (us%L\_to\_Z*rho0 * i\_mass(i,j)) * sqrt( drag\_rate\_visc(i,j)**2 + & 522 cdrag2 * ( max(0.0, 2.0*bottomfac2(i,j)*meke%MEKE(i,j)) + cs%MEKE\_Uscale**2 ) ) 523 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 524 \textcolor{comment}{!$OMP parallel do default(shared)} 525 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 526 ldamping = cs%MEKE\_damping + drag\_rate(i,j) * bottomfac2(i,j) 527 \textcolor{keywordflow}{if} (meke%MEKE(i,j) < 0.) ldamping = 0. 528 \textcolor{comment}{! notice that the above line ensures a damping only if MEKE is positive,} 529 \textcolor{comment}{! while leaving MEKE unchanged if it is negative} 530 meke%MEKE(i,j) = meke%MEKE(i,j) / (1.0 + sdt\_damp*ldamping) 531 meke\_decay(i,j) = ldamping*g%mask2dT(i,j) 532 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 533 \textcolor{keywordflow}{ endif} 534 \textcolor{keywordflow}{ endif} 535 \textcolor{keywordflow}{ endif} \textcolor{comment}{! MEKE\_KH>=0} 536 537 \textcolor{comment}{! do j=js,je ; do i=is,ie} 538 \textcolor{comment}{! MEKE%MEKE(i,j) = MAX(MEKE%MEKE(i,j),0.0)} 539 \textcolor{comment}{! enddo ; enddo} 540 541 \textcolor{keyword}{call }cpu\_clock\_begin(cs%id\_clock\_pass) 542 \textcolor{keyword}{call }do\_group\_pass(cs%pass\_MEKE, g%Domain) 543 \textcolor{keyword}{call }cpu\_clock\_end(cs%id\_clock\_pass) 544 545 \textcolor{comment}{! Calculate diffusivity for main model to use} 546 \textcolor{keywordflow}{if} (cs%MEKE\_KhCoeff>0.) \textcolor{keywordflow}{then} 547 \textcolor{keywordflow}{if} (.not.cs%MEKE\_GEOMETRIC) \textcolor{keywordflow}{then} 548 \textcolor{keywordflow}{if} (cs%use\_old\_lscale) \textcolor{keywordflow}{then} 549 \textcolor{keywordflow}{if} (cs%Rd\_as\_max\_scale) \textcolor{keywordflow}{then} 550 \textcolor{comment}{!$OMP parallel do default(shared)} 551 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 552 meke%Kh(i,j) = (cs%MEKE\_KhCoeff * & 553 sqrt(2.*max(0.,barotrfac2(i,j)*meke%MEKE(i,j))*g%areaT(i,j)) ) * & 554 min(meke%Rd\_dx\_h(i,j), 1.0) 555 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 556 \textcolor{keywordflow}{else} 557 \textcolor{comment}{!$OMP parallel do default(shared)} 558 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 559 meke%Kh(i,j) = cs%MEKE\_KhCoeff * & 560 sqrt(2.*max(0., barotrfac2(i,j)*meke%MEKE(i,j))*g%areaT(i,j)) 561 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 562 \textcolor{keywordflow}{ endif} 563 \textcolor{keywordflow}{else} 564 \textcolor{comment}{!$OMP parallel do default(shared)} 565 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 566 meke%Kh(i,j) = cs%MEKE\_KhCoeff * & 567 sqrt(2.*max(0., barotrfac2(i,j)*meke%MEKE(i,j))) * lmixscale(i,j) 568 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 569 \textcolor{keywordflow}{ endif} 570 \textcolor{keywordflow}{ endif} 571 \textcolor{keywordflow}{ endif} 572 573 \textcolor{comment}{! Calculate viscosity for the main model to use} 574 \textcolor{keywordflow}{if} (cs%viscosity\_coeff\_Ku /=0.) \textcolor{keywordflow}{then} 575 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 576 meke%Ku(i,j) = cs%viscosity\_coeff\_Ku * sqrt(2.*max(0.,meke%MEKE(i,j))) * lmixscale(i,j) 577 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 578 \textcolor{keywordflow}{ endif} 579 580 \textcolor{keywordflow}{if} (cs%viscosity\_coeff\_Au /=0.) \textcolor{keywordflow}{then} 581 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 582 meke%Au(i,j) = cs%viscosity\_coeff\_Au * sqrt(2.*max(0.,meke%MEKE(i,j))) * lmixscale(i,j)**3 583 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 584 \textcolor{keywordflow}{ endif} 585 586 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(meke%Kh) .or. \textcolor{keyword}{associated}(meke%Ku) .or. \textcolor{keyword}{associated}(meke%Au)) \textcolor{keywordflow}{then} 587 \textcolor{keyword}{call }cpu\_clock\_begin(cs%id\_clock\_pass) 588 \textcolor{keyword}{call }do\_group\_pass(cs%pass\_Kh, g%Domain) 589 \textcolor{keyword}{call }cpu\_clock\_end(cs%id\_clock\_pass) 590 \textcolor{keywordflow}{ endif} 591 592 \textcolor{comment}{! Offer fields for averaging.} 593 \textcolor{keywordflow}{if} (any([cs%id\_Ue, cs%id\_Ub, cs%id\_Ut] > 0)) & 594 tmp(:,:) = 0. 595 \textcolor{keywordflow}{if} (cs%id\_MEKE>0) \textcolor{keyword}{call }post\_data(cs%id\_MEKE, meke%MEKE, cs%diag) 596 \textcolor{keywordflow}{if} (cs%id\_Ue>0) \textcolor{keywordflow}{then} 597 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 598 tmp(i,j) = sqrt(max(0., 2. * meke%MEKE(i,j))) 599 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 600 \textcolor{keyword}{call }post\_data(cs%id\_Ue, tmp, cs%diag) 601 \textcolor{keywordflow}{ endif} 602 \textcolor{keywordflow}{if} (cs%id\_Ub>0) \textcolor{keywordflow}{then} 603 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 604 tmp(i,j) = sqrt(max(0., 2. * meke%MEKE(i,j) * bottomfac2(i,j))) 605 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 606 \textcolor{keyword}{call }post\_data(cs%id\_Ub, tmp, cs%diag) 607 \textcolor{keywordflow}{ endif} 608 \textcolor{keywordflow}{if} (cs%id\_Ut>0) \textcolor{keywordflow}{then} 609 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 610 tmp(i,j) = sqrt(max(0., 2. * meke%MEKE(i,j) * barotrfac2(i,j))) 611 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 612 \textcolor{keyword}{call }post\_data(cs%id\_Ut, tmp, cs%diag) 613 \textcolor{keywordflow}{ endif} 614 \textcolor{keywordflow}{if} (cs%id\_Kh>0) \textcolor{keyword}{call }post\_data(cs%id\_Kh, meke%Kh, cs%diag) 615 \textcolor{keywordflow}{if} (cs%id\_Ku>0) \textcolor{keyword}{call }post\_data(cs%id\_Ku, meke%Ku, cs%diag) 616 \textcolor{keywordflow}{if} (cs%id\_Au>0) \textcolor{keyword}{call }post\_data(cs%id\_Au, meke%Au, cs%diag) 617 \textcolor{keywordflow}{if} (cs%id\_KhMEKE\_u>0) \textcolor{keyword}{call }post\_data(cs%id\_KhMEKE\_u, kh\_u, cs%diag) 618 \textcolor{keywordflow}{if} (cs%id\_KhMEKE\_v>0) \textcolor{keyword}{call }post\_data(cs%id\_KhMEKE\_v, kh\_v, cs%diag) 619 \textcolor{keywordflow}{if} (cs%id\_src>0) \textcolor{keyword}{call }post\_data(cs%id\_src, src, cs%diag) 620 \textcolor{keywordflow}{if} (cs%id\_decay>0) \textcolor{keyword}{call }post\_data(cs%id\_decay, meke\_decay, cs%diag) 621 \textcolor{keywordflow}{if} (cs%id\_GM\_src>0) \textcolor{keyword}{call }post\_data(cs%id\_GM\_src, meke%GM\_src, cs%diag) 622 \textcolor{keywordflow}{if} (cs%id\_mom\_src>0) \textcolor{keyword}{call }post\_data(cs%id\_mom\_src, meke%mom\_src, cs%diag) 623 \textcolor{keywordflow}{if} (cs%id\_GME\_snk>0) \textcolor{keyword}{call }post\_data(cs%id\_GME\_snk, meke%GME\_snk, cs%diag) 624 \textcolor{keywordflow}{if} (cs%id\_Le>0) \textcolor{keyword}{call }post\_data(cs%id\_Le, lmixscale, cs%diag) 625 \textcolor{keywordflow}{if} (cs%id\_gamma\_b>0) \textcolor{keywordflow}{then} 626 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 627 bottomfac2(i,j) = sqrt(bottomfac2(i,j)) 628 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 629 \textcolor{keyword}{call }post\_data(cs%id\_gamma\_b, bottomfac2, cs%diag) 630 \textcolor{keywordflow}{ endif} 631 \textcolor{keywordflow}{if} (cs%id\_gamma\_t>0) \textcolor{keywordflow}{then} 632 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie 633 barotrfac2(i,j) = sqrt(barotrfac2(i,j)) 634 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 635 \textcolor{keyword}{call }post\_data(cs%id\_gamma\_t, barotrfac2, cs%diag) 636 \textcolor{keywordflow}{ endif} 637 \end{DoxyCode}