mom_neutral_diffusion mom_neutral_diffusion::neutral_diffusion_cs character(len=40) character(len=40) mom_neutral_diffusion::mdl mdl = "MOM_neutral_diffusion" module name neutral_diffusion_init logical function, public logical function, public mom_neutral_diffusion::neutral_diffusion_init (Time, G, US, param_file, diag, EOS, diabatic_CSp, CS) neutral_diffusion_init Time Time G G US US param_file param_file diag diag EOS EOS diabatic_CSp diabatic_CSp CS CS Read parameters and allocate control structure for neutral_diffusion module. time Time structure g Grid structure us A dimensional unit scaling type diag Diagnostics control structure param_file Parameter file structure eos Equation of state diabatic_csp KPP control structure needed to get BLD cs Neutral diffusion control structure mom_diabatic_driver::extract_diabatic_member mdl mom_error_handler::mom_error mom_remapping::remappingdefaultscheme mom_remapping::remappingschemesdoc subroutine, public subroutine, public mom_neutral_diffusion::neutral_diffusion_calc_coeffs (G, GV, US, h, T, S, CS, p_surf) neutral_diffusion_calc_coeffs G G GV GV US US h h T T S S CS CS p_surf p_surf Calculate remapping factors for u/v columns used to map adjoining columns to a shared coordinate space. g Ocean grid structure gv ocean vertical grid structure us A dimensional unit scaling type h Layer thickness [H ~> m or kg m-2] t Potential temperature [degC] s Salinity [ppt] cs Neutral diffusion control structure p_surf Surface pressure to include in pressures used for equation of state calculations [R L2 T-2 ~> Pa] mom_lateral_boundary_diffusion::boundary_k_range mom_energetic_pbl::energetic_pbl_get_mld polynomial_functions::evaluation_polynomial find_neutral_surface_positions_continuous find_neutral_surface_positions_discontinuous interface_scalar mom_cvmix_kpp::kpp_get_bld mark_unstable_cells mom_lateral_boundary_diffusion::surface mom_tracer_hor_diff::tracer_hordiff subroutine, public subroutine, public mom_neutral_diffusion::neutral_diffusion (G, GV, h, Coef_x, Coef_y, dt, Reg, US, CS) neutral_diffusion G G GV GV h h Coef_x Coef_x Coef_y Coef_y dt dt Reg Reg US US CS CS Update tracer concentration due to neutral diffusion; layer thickness unchanged by this update. g Ocean grid structure gv ocean vertical grid structure h Layer thickness [H ~> m or kg m-2] coef_x dt * Kh * dy / dx at u-points [L2 ~> m2] coef_y dt * Kh * dx / dy at v-points [L2 ~> m2] dt Tracer time step * I_numitts [T ~> s] (I_numitts in tracer_hordiff) reg Tracer registry us A dimensional unit scaling type cs Neutral diffusion control structure neutral_surface_flux mom_tracer_hor_diff::tracer_hordiff subroutine subroutine mom_neutral_diffusion::interface_scalar (nk, h, S, Si, i_method, h_neglect) interface_scalar nk nk h h S S Si Si i_method i_method h_neglect h_neglect Returns interface scalar, Si, for a column of layer values, S. nk Number of levels h Layer thickness [H ~> m or kg m-2] s Layer scalar (conc, e.g. ppt) si Interface scalar (conc, e.g. ppt) i_method =1 use average of PLM edges =2 use continuous PPM edge interpolation h_neglect A negligibly small thickness [H ~> m or kg m-2] plm_diff ppm_edge ndiff_unit_tests_continuous neutral_diffusion_calc_coeffs neutral_surface_flux real function real function mom_neutral_diffusion::ppm_edge (hkm1, hk, hkp1, hkp2, Ak, Akp1, Pk, Pkp1, h_neglect) ppm_edge hkm1 hkm1 hk hk hkp1 hkp1 hkp2 hkp2 Ak Ak Akp1 Akp1 Pk Pk Pkp1 Pkp1 h_neglect h_neglect Returns the PPM quasi-fourth order edge value at k+1/2 following equation 1.6 in Colella & Woodward, 1984: JCP 54, 174-201. hkm1 Width of cell k-1 hk Width of cell k hkp1 Width of cell k+1 hkp2 Width of cell k+2 ak Average scalar value of cell k akp1 Average scalar value of cell k+1 pk PLM slope for cell k pkp1 PLM slope for cell k+1 h_neglect A negligibly small thickness [H ~> m or kg m-2] interface_scalar real function real function mom_neutral_diffusion::ppm_ave (xL, xR, aL, aR, aMean) ppm_ave xL xL xR xR aL aL aR aR aMean aMean Returns the average of a PPM reconstruction between two fractional positions. xl Fraction position of left bound (0,1) xr Fraction position of right bound (0,1) al Left edge scalar value, at x=0 ar Right edge scalar value, at x=1 amean Average scalar value of cell neutral_surface_flux real function real function mom_neutral_diffusion::signum (a, x) signum a a x x A true signum function that returns either -abs(a), when x<0; or abs(a) when x>0; or 0 when x=0. a The magnitude argument x The sign (or zero) argument neutral_surface_flux plm_diff ppm_left_right_edge_values subroutine subroutine mom_neutral_diffusion::plm_diff (nk, h, S, c_method, b_method, diff) plm_diff nk nk h h S S c_method c_method b_method b_method diff diff Returns PLM slopes for a column where the slopes are the difference in value across each cell. The limiting follows equation 1.8 in Colella & Woodward, 1984: JCP 54, 174-201. nk Number of levels h Layer thickness [H ~> m or kg m-2] s Layer salinity (conc, e.g. ppt) c_method Method to use for the centered difference b_method =1, use PCM in first/last cell, =2 uses linear extrapolation diff Scalar difference across layer (conc, e.g. ppt) determined by the following values for c_method: Second order finite difference (not recommended) Second order finite volume (used in original PPM) Finite-volume weighted least squares linear fit TodoThe use of c_method to choose a scheme is inefficient and should eventually be moved up the call tree. fv_diff fvlsq_slope signum interface_scalar real function real function mom_neutral_diffusion::fv_diff (hkm1, hk, hkp1, Skm1, Sk, Skp1) fv_diff hkm1 hkm1 hk hk hkp1 hkp1 Skm1 Skm1 Sk Sk Skp1 Skp1 Returns the cell-centered second-order finite volume (unlimited PLM) slope using three consecutive cell widths and average values. Slope is returned as a difference across the central cell (i.e. units of scalar S). Discretization follows equation 1.7 in Colella & Woodward, 1984: JCP 54, 174-201. hkm1 Left cell width hk Center cell width hkp1 Right cell width skm1 Left cell average value sk Center cell average value skp1 Right cell average value plm_diff test_fv_diff real function real function mom_neutral_diffusion::fvlsq_slope (hkm1, hk, hkp1, Skm1, Sk, Skp1) fvlsq_slope hkm1 hkm1 hk hk hkp1 hkp1 Skm1 Skm1 Sk Sk Skp1 Skp1 Returns the cell-centered second-order weighted least squares slope using three consecutive cell widths and average values. Slope is returned as a gradient (i.e. units of scalar S over width units). hkm1 Left cell width hk Center cell width hkp1 Right cell width skm1 Left cell average value sk Center cell average value skp1 Right cell average value plm_diff test_fvlsq_slope subroutine subroutine mom_neutral_diffusion::find_neutral_surface_positions_continuous (nk, Pl, Tl, Sl, dRdTl, dRdSl, Pr, Tr, Sr, dRdTr, dRdSr, PoL, PoR, KoL, KoR, hEff, bl_kl, bl_kr, bl_zl, bl_zr) find_neutral_surface_positions_continuous nk nk Pl Pl Tl Tl Sl Sl dRdTl dRdTl dRdSl dRdSl Pr Pr Tr Tr Sr Sr dRdTr dRdTr dRdSr dRdSr PoL PoL PoR PoR KoL KoL KoR KoR hEff hEff bl_kl bl_kl bl_kr bl_kr bl_zl bl_zl bl_zr bl_zr Returns positions within left/right columns of combined interfaces using continuous reconstructions of T/S. nk Number of levels pl Left-column interface pressure [R L2 T-2 ~> Pa] or other units tl Left-column interface potential temperature [degC] sl Left-column interface salinity [ppt] drdtl Left-column dRho/dT [R degC-1 ~> kg m-3 degC-1] drdsl Left-column dRho/dS [R ppt-1 ~> kg m-3 ppt-1] pr Right-column interface pressure [R L2 T-2 ~> Pa] or other units tr Right-column interface potential temperature [degC] sr Right-column interface salinity [ppt] drdtr Left-column dRho/dT [R degC-1 ~> kg m-3 degC-1] drdsr Left-column dRho/dS [R ppt-1 ~> kg m-3 ppt-1] pol Fractional position of neutral surface within layer KoL of left column por Fractional position of neutral surface within layer KoR of right column kol Index of first left interface above neutral surface kor Index of first right interface above neutral surface heff Effective thickness between two neutral surfaces [R L2 T-2 ~> Pa] or other units following Pl and Pr. bl_kl Layer index of the boundary layer (left) bl_kr Layer index of the boundary layer (right) bl_zl Nondimensional position of the boundary layer (left) bl_zr Nondimensional position of the boundary layer (right) absolute_position interpolate_for_nondim_position ndiff_unit_tests_continuous neutral_diffusion_calc_coeffs real function real function mom_neutral_diffusion::interpolate_for_nondim_position (dRhoNeg, Pneg, dRhoPos, Ppos) interpolate_for_nondim_position dRhoNeg dRhoNeg Pneg Pneg dRhoPos dRhoPos Ppos Ppos Returns the non-dimensional position between Pneg and Ppos where the interpolated density difference equals zero. The result is always bounded to be between 0 and 1. drhoneg Negative density difference [R ~> kg m-3] pneg Position of negative density difference [R L2 T-2 ~> Pa] or [nondim] drhopos Positive density difference [R ~> kg m-3] ppos Position of positive density difference [R L2 T-2 ~> Pa] or [nondim] mom_error_handler::mom_error find_neutral_surface_positions_continuous search_other_column test_ifndp subroutine subroutine mom_neutral_diffusion::find_neutral_surface_positions_discontinuous (CS, nk, Pres_l, hcol_l, Tl, Sl, ppoly_T_l, ppoly_S_l, stable_l, Pres_r, hcol_r, Tr, Sr, ppoly_T_r, ppoly_S_r, stable_r, PoL, PoR, KoL, KoR, hEff, zeta_bot_L, zeta_bot_R, k_bot_L, k_bot_R, hard_fail_heff) find_neutral_surface_positions_discontinuous CS CS nk nk Pres_l Pres_l hcol_l hcol_l Tl Tl Sl Sl ppoly_T_l ppoly_T_l ppoly_S_l ppoly_S_l stable_l stable_l Pres_r Pres_r hcol_r hcol_r Tr Tr Sr Sr ppoly_T_r ppoly_T_r ppoly_S_r ppoly_S_r stable_r stable_r PoL PoL PoR PoR KoL KoL KoR KoR hEff hEff zeta_bot_L zeta_bot_L zeta_bot_R zeta_bot_R k_bot_L k_bot_L k_bot_R k_bot_R hard_fail_heff hard_fail_heff Higher order version of find_neutral_surface_positions. Returns positions within left/right columns of combined interfaces using intracell reconstructions of T/S. Note that the polynomial reconstrcutions of T and S are optional to aid with unit testing, but will always be passed otherwise. cs Neutral diffusion control structure nk Number of levels pres_l Left-column interface pressure [R L2 T-2 ~> Pa] hcol_l Left-column layer thicknesses [H ~> m or kg m-2] or other units tl Left-column top interface potential temperature [degC] sl Left-column top interface salinity [ppt] ppoly_t_l Left-column coefficients of T reconstruction [degC] ppoly_s_l Left-column coefficients of S reconstruction [ppt] stable_l True where the left-column is stable pres_r Right-column interface pressure [R L2 T-2 ~> Pa] hcol_r Left-column layer thicknesses [H ~> m or kg m-2] or other units tr Right-column top interface potential temperature [degC] sr Right-column top interface salinity [ppt] ppoly_t_r Right-column coefficients of T reconstruction [degC] ppoly_s_r Right-column coefficients of S reconstruction [ppt] stable_r True where the right-column is stable pol Fractional position of neutral surface within layer KoL of left column [nondim] por Fractional position of neutral surface within layer KoR of right column [nondim] kol Index of first left interface above neutral surface kor Index of first right interface above neutral surface heff Effective thickness between two neutral surfaces [H ~> m or kg m-2] or other units taken from hcol_l zeta_bot_l Non-dimensional distance to where the boundary layer intersetcs the cell (left) [nondim] zeta_bot_r Non-dimensional distance to where the boundary layer intersetcs the cell (right) [nondim] k_bot_l k-index for the boundary layer (left) [nondim] k_bot_r k-index for the boundary layer (right) [nondim] hard_fail_heff If true (default) bring down the model if the neutral surfaces ever cross [logical] calc_delta_rho_and_derivs increment_interface mom_error_handler::mom_error search_other_column ndiff_unit_tests_discontinuous neutral_diffusion_calc_coeffs subroutine subroutine mom_neutral_diffusion::mark_unstable_cells (CS, nk, T, S, P, stable_cell) mark_unstable_cells CS CS nk nk T T S S P P stable_cell stable_cell Sweep down through the column and mark as stable if the bottom interface of a cell is denser than the top. cs Neutral diffusion control structure nk Number of levels in a column t Temperature at interfaces [degC] s Salinity at interfaces [ppt] p Pressure at interfaces [R L2 T-2 ~> Pa] stable_cell True if this cell is unstably stratified calc_delta_rho_and_derivs ndiff_unit_tests_discontinuous neutral_diffusion_calc_coeffs real function real function mom_neutral_diffusion::search_other_column (CS, ksurf, pos_last, T_from, S_from, P_from, T_top, S_top, P_top, T_bot, S_bot, P_bot, T_poly, S_poly) search_other_column CS CS ksurf ksurf pos_last pos_last T_from T_from S_from S_from P_from P_from T_top T_top S_top S_top P_top P_top T_bot T_bot S_bot S_bot P_bot P_bot T_poly T_poly S_poly S_poly Searches the "other" (searched) column for the position of the neutral surface. cs Neutral diffusion control structure ksurf Current index of neutral surface pos_last Last position within the current layer, used as the lower bound in the root finding algorithm [nondim] t_from Temperature at the searched from interface [degC] s_from Salinity at the searched from interface [ppt] p_from Pressure at the searched from interface [R L2 T-2 ~> Pa] t_top Temperature at the searched to top interface [degC] s_top Salinity at the searched to top interface [ppt] p_top Pressure at the searched to top interface [R L2 T-2 ~> Pa] interface [R L2 T-2 ~> Pa] t_bot Temperature at the searched to bottom interface [degC] s_bot Salinity at the searched to bottom interface [ppt] p_bot Pressure at the searched to bottom interface [R L2 T-2 ~> Pa] t_poly Temperature polynomial reconstruction coefficients [degC] s_poly Salinity polynomial reconstruction coefficients [ppt] calc_delta_rho_and_derivs find_neutral_pos_full find_neutral_pos_linear interpolate_for_nondim_position find_neutral_surface_positions_discontinuous subroutine subroutine mom_neutral_diffusion::increment_interface (nk, kl, ki, reached_bottom, searching_this_column, searching_other_column) increment_interface nk nk kl kl ki ki reached_bottom reached_bottom searching_this_column searching_this_column searching_other_column searching_other_column Increments the interface which was just connected and also set flags if the bottom is reached. nk Number of vertical levels kl Current layer (potentially updated) ki Current interface reached_bottom Updated when kl == nk and ki == 2 searching_this_column Updated when kl == nk and ki == 2 searching_other_column Updated when kl == nk and ki == 2 mom_error_handler::mom_error find_neutral_surface_positions_discontinuous real function real function mom_neutral_diffusion::find_neutral_pos_linear (CS, z0, T_ref, S_ref, dRdT_ref, dRdS_ref, dRdT_top, dRdS_top, dRdT_bot, dRdS_bot, ppoly_T, ppoly_S) find_neutral_pos_linear CS CS z0 z0 T_ref T_ref S_ref S_ref dRdT_ref dRdT_ref dRdS_ref dRdS_ref dRdT_top dRdT_top dRdS_top dRdS_top dRdT_bot dRdT_bot dRdS_bot dRdS_bot ppoly_T ppoly_T ppoly_S ppoly_S Search a layer to find where delta_rho = 0 based on a linear interpolation of alpha and beta of the top and bottom being searched and polynomial reconstructions of T and S. Compressibility is not needed because either, we are assuming incompressibility in the equation of state for this module or alpha and beta are calculated having been displaced to the average pressures of the two pressures We need Newton's method because the T and S reconstructions make delta_rho a polynomial function of z if using PPM or higher. If Newton's method would search fall out of the interval [0,1], a bisection step would be taken instead. Also this linearization of alpha, beta means that second derivatives of the EOS are not needed. Note that delta in variable names below refers to horizontal differences and 'd' refers to vertical differences. cs Control structure with parameters for this module z0 Lower bound of position, also serves as the initial guess [nondim] t_ref Temperature at the searched from interface [degC] s_ref Salinity at the searched from interface [ppt] drdt_ref dRho/dT at the searched from interface [R degC-1 ~> kg m-3 degC-1] drds_ref dRho/dS at the searched from interface [R ppt-1 ~> kg m-3 ppt-1] drdt_top dRho/dT at top of layer being searched [R degC-1 ~> kg m-3 degC-1] drds_top dRho/dS at top of layer being searched [R ppt-1 ~> kg m-3 ppt-1] drdt_bot dRho/dT at bottom of layer being searched [R degC-1 ~> kg m-3 degC-1] drds_bot dRho/dS at bottom of layer being searched [R ppt-1 ~> kg m-3 ppt-1] ppoly_t Coefficients of the polynomial reconstruction of T within the layer to be searched [degC]. ppoly_s Coefficients of the polynomial reconstruction of S within the layer to be searched [ppt]. Position where drho = 0 [nondim] polynomial_functions::evaluation_polynomial polynomial_functions::first_derivative_polynomial mom_error_handler::mom_error ndiff_unit_tests_discontinuous search_other_column real function real function mom_neutral_diffusion::find_neutral_pos_full (CS, z0, T_ref, S_ref, P_ref, P_top, P_bot, ppoly_T, ppoly_S) find_neutral_pos_full CS CS z0 z0 T_ref T_ref S_ref S_ref P_ref P_ref P_top P_top P_bot P_bot ppoly_T ppoly_T ppoly_S ppoly_S Use the full equation of state to calculate the difference in locally referenced potential density. The derivatives in this case are not trivial to calculate, so instead we use a regula falsi method. cs Control structure with parameters for this module z0 Lower bound of position, also serves as the initial guess [nondim] t_ref Temperature at the searched from interface [degC] s_ref Salinity at the searched from interface [ppt] p_ref Pressure at the searched from interface [R L2 T-2 ~> Pa] p_top Pressure at top of layer being searched [R L2 T-2 ~> Pa] p_bot Pressure at bottom of layer being searched [R L2 T-2 ~> Pa] ppoly_t Coefficients of the polynomial reconstruction of T within the layer to be searched [degC] ppoly_s Coefficients of the polynomial reconstruction of T within the layer to be searched [ppt] Position where drho = 0 [nondim] calc_delta_rho_and_derivs polynomial_functions::evaluation_polynomial search_other_column subroutine subroutine mom_neutral_diffusion::calc_delta_rho_and_derivs (CS, T1, S1, p1_in, T2, S2, p2_in, drho, drdt1_out, drds1_out, drdt2_out, drds2_out) calc_delta_rho_and_derivs CS CS T1 T1 S1 S1 p1_in p1_in T2 T2 S2 S2 p2_in p2_in drho drho drdt1_out drdt1_out drds1_out drds1_out drdt2_out drdt2_out drds2_out drds2_out Calculate the difference in density between two points in a variety of ways. cs Neutral diffusion control structure t1 Temperature at point 1 [degC] s1 Salinity at point 1 [ppt] p1_in Pressure at point 1 [R L2 T-2 ~> Pa] t2 Temperature at point 2 [degC] s2 Salinity at point 2 [ppt] p2_in Pressure at point 2 [R L2 T-2 ~> Pa] drho Difference in density between the two points [R ~> kg m-3] drdt1_out drho_dt at point 1 [R degC-1 ~> kg m-3 degC-1] drds1_out drho_ds at point 1 [R ppt-1 ~> kg m-3 ppt-1] drdt2_out drho_dt at point 2 [R degC-1 ~> kg m-3 degC-1] drds2_out drho_ds at point 2 [R ppt-1 ~> kg m-3 ppt-1] delta_rho_from_derivs mom_error_handler::mom_error find_neutral_pos_full find_neutral_surface_positions_discontinuous mark_unstable_cells search_other_column real function real function mom_neutral_diffusion::delta_rho_from_derivs (T1, S1, P1, dRdT1, dRdS1, T2, S2, P2, dRdT2, dRdS2) delta_rho_from_derivs T1 T1 S1 S1 P1 P1 dRdT1 dRdT1 dRdS1 dRdS1 T2 T2 S2 S2 P2 P2 dRdT2 dRdT2 dRdS2 dRdS2 Calculate delta rho from derivatives and gradients of properties $ \Delta \rho = \frac{1}{2}\left[ (\alpha_1 + \alpha_2)*(T_1-T_2) + (\beta_1 + \beta_2)*(S_1-S_2) + (\gamma^{-1}_1 + \gamma^{-1}_2)*(P_1-P_2) \right] $. t1 Temperature at point 1 [degC] s1 Salinity at point 1 [ppt] p1 Pressure at point 1 [R L2 T-2 ~> Pa] drdt1 The partial derivative of density with temperature at point 1 [R degC-1 ~> kg m-3 degC-1] drds1 The partial derivative of density with salinity at point 1 [R ppt-1 ~> kg m-3 ppt-1] t2 Temperature at point 2 [degC] s2 Salinity at point 2 [ppt] p2 Pressure at point 2 [R L2 T-2 ~> Pa] drdt2 The partial derivative of density with temperature at point 2 [R degC-1 ~> kg m-3 degC-1] drds2 The partial derivative of density with salinity at point 2 [R ppt-1 ~> kg m-3 ppt-1] calc_delta_rho_and_derivs real function real function mom_neutral_diffusion::absolute_position (n, ns, Pint, Karr, NParr, k_surface) absolute_position n n ns ns Pint Pint Karr Karr NParr NParr k_surface k_surface Converts non-dimensional position within a layer to absolute position (for debugging) n Number of levels ns Number of neutral surfaces pint Position of interfaces [R L2 T-2 ~> Pa] or other units karr Index of interface above position nparr Non-dimensional position within layer Karr(:) [nondim] k_surface k-interface to query The absolute position of a location [R L2 T-2 ~> Pa] or other units following Pint absolute_positions find_neutral_surface_positions_continuous real function, dimension(ns) real function, dimension(ns) mom_neutral_diffusion::absolute_positions (n, ns, Pint, Karr, NParr) absolute_positions n n ns ns Pint Pint Karr Karr NParr NParr Converts non-dimensional positions within layers to absolute positions (for debugging) n Number of levels ns Number of neutral surfaces pint Position of interface [R L2 T-2 ~> Pa] or other units karr Indexes of interfaces about positions nparr Non-dimensional positions within layers Karr(:) Absolute positions [R L2 T-2 ~> Pa] or other units following Pint absolute_position ndiff_unit_tests_continuous subroutine subroutine mom_neutral_diffusion::neutral_surface_flux (nk, nsurf, deg, hl, hr, Tl, Tr, PiL, PiR, KoL, KoR, hEff, Flx, continuous, h_neglect, remap_CS, h_neglect_edge) neutral_surface_flux nk nk nsurf nsurf deg deg hl hl hr hr Tl Tl Tr Tr PiL PiL PiR PiR KoL KoL KoR KoR hEff hEff Flx Flx continuous continuous h_neglect h_neglect remap_CS remap_CS h_neglect_edge h_neglect_edge Returns a single column of neutral diffusion fluxes of a tracer. nk Number of levels nsurf Number of neutral surfaces deg Degree of polynomial reconstructions hl Left-column layer thickness [H ~> m or kg m-2] hr Right-column layer thickness [H ~> m or kg m-2] tl Left-column layer tracer (conc, e.g. degC) tr Right-column layer tracer (conc, e.g. degC) pil Fractional position of neutral surface within layer KoL of left column pir Fractional position of neutral surface within layer KoR of right column kol Index of first left interface above neutral surface kor Index of first right interface above neutral surface heff Effective thickness between two neutral surfaces [H ~> m or kg m-2] flx Flux of tracer between pairs of neutral layers (conc H) continuous True if using continuous reconstruction h_neglect A negligibly small width for the purpose of cell reconstructions [H ~> m or kg m-2] remap_cs Remapping control structure used to create sublayers h_neglect_edge A negligibly small width used for edge value calculations if continuous is false [H ~> m or kg m-2] interface_scalar neutral_surface_t_eval ppm_ave ppm_left_right_edge_values signum ndiff_unit_tests_continuous neutral_diffusion subroutine subroutine mom_neutral_diffusion::neutral_surface_t_eval (nk, ns, k_sub, Ks, Ps, T_mean, T_int, deg, iMethod, T_poly, T_top, T_bot, T_sub, T_top_int, T_bot_int, T_layer) neutral_surface_t_eval nk nk ns ns k_sub k_sub Ks Ks Ps Ps T_mean T_mean T_int T_int deg deg iMethod iMethod T_poly T_poly T_top T_top T_bot T_bot T_sub T_sub T_top_int T_top_int T_bot_int T_bot_int T_layer T_layer Evaluate various parts of the reconstructions to calculate gradient-based flux limter. nk Number of cell everages ns Number of neutral surfaces k_sub Index of current neutral layer ks List of the layers associated with each neutral surface ps List of the positions within a layer of each surface t_mean Cell average of tracer t_int Cell interface values of tracer from reconstruction deg Degree of reconstruction polynomial (e.g. 1 is linear) imethod Method of integration to use t_poly Coefficients of polynomial reconstructions t_top Tracer value at top (across discontinuity if necessary) t_bot Tracer value at bottom (across discontinuity if necessary) t_sub Average of the tracer value over the sublayer t_top_int Tracer value at top interface of neutral layer t_bot_int Tracer value at bottom interface of neutral layer t_layer Cell-average that the the reconstruction belongs to mom_remapping::average_value_ppoly polynomial_functions::evaluation_polynomial mom_error_handler::mom_error neutral_surface_flux subroutine subroutine mom_neutral_diffusion::ppm_left_right_edge_values (nk, Tl, Ti, aL, aR) ppm_left_right_edge_values nk nk Tl Tl Ti Ti aL aL aR aR Discontinuous PPM reconstructions of the left/right edge values within a cell. nk Number of levels tl Layer tracer (conc, e.g. degC) ti Interface tracer (conc, e.g. degC) al Left edge value of tracer (conc, e.g. degC) ar Right edge value of tracer (conc, e.g. degC) signum neutral_surface_flux logical function, public logical function, public mom_neutral_diffusion::neutral_diffusion_unit_tests (verbose) neutral_diffusion_unit_tests verbose verbose Returns true if unit tests of neutral_diffusion functions fail. Otherwise returns false. verbose If true, write results to stdout ndiff_unit_tests_continuous ndiff_unit_tests_discontinuous mom_unit_tests::unit_tests logical function logical function mom_neutral_diffusion::ndiff_unit_tests_continuous (verbose) ndiff_unit_tests_continuous verbose verbose Returns true if unit tests of neutral_diffusion functions fail. Otherwise returns false. verbose If true, write results to stdout absolute_positions find_neutral_surface_positions_continuous interface_scalar neutral_surface_flux test_data1d test_fv_diff test_fvlsq_slope test_ifndp test_nsp neutral_diffusion_unit_tests logical function logical function mom_neutral_diffusion::ndiff_unit_tests_discontinuous (verbose) ndiff_unit_tests_discontinuous verbose verbose verbose It true, write results to stdout mom_eos::eos_linear find_neutral_pos_linear find_neutral_surface_positions_discontinuous mark_unstable_cells test_nsp test_rnp neutral_diffusion_unit_tests logical function logical function mom_neutral_diffusion::test_fv_diff (verbose, hkm1, hk, hkp1, Skm1, Sk, Skp1, Ptrue, title) test_fv_diff verbose verbose hkm1 hkm1 hk hk hkp1 hkp1 Skm1 Skm1 Sk Sk Skp1 Skp1 Ptrue Ptrue title title Returns true if a test of fv_diff() fails, and conditionally writes results to stream. verbose If true, write results to stdout hkm1 Left cell width [nondim] hk Center cell width [nondim] hkp1 Right cell width [nondim] skm1 Left cell average value sk Center cell average value skp1 Right cell average value ptrue True answer [nondim] title Title for messages fv_diff ndiff_unit_tests_continuous logical function logical function mom_neutral_diffusion::test_fvlsq_slope (verbose, hkm1, hk, hkp1, Skm1, Sk, Skp1, Ptrue, title) test_fvlsq_slope verbose verbose hkm1 hkm1 hk hk hkp1 hkp1 Skm1 Skm1 Sk Sk Skp1 Skp1 Ptrue Ptrue title title Returns true if a test of fvlsq_slope() fails, and conditionally writes results to stream. verbose If true, write results to stdout hkm1 Left cell width hk Center cell width hkp1 Right cell width skm1 Left cell average value sk Center cell average value skp1 Right cell average value ptrue True answer title Title for messages fvlsq_slope ndiff_unit_tests_continuous logical function logical function mom_neutral_diffusion::test_ifndp (verbose, rhoNeg, Pneg, rhoPos, Ppos, Ptrue, title) test_ifndp verbose verbose rhoNeg rhoNeg Pneg Pneg rhoPos rhoPos Ppos Ppos Ptrue Ptrue title title Returns true if a test of interpolate_for_nondim_position() fails, and conditionally writes results to stream. verbose If true, write results to stdout rhoneg Lighter density [R ~> kg m-3] pneg Interface position of lighter density [nondim] rhopos Heavier density [R ~> kg m-3] ppos Interface position of heavier density [nondim] ptrue True answer [nondim] title Title for messages interpolate_for_nondim_position ndiff_unit_tests_continuous logical function logical function mom_neutral_diffusion::test_data1d (verbose, nk, Po, Ptrue, title) test_data1d verbose verbose nk nk Po Po Ptrue Ptrue title title Returns true if comparison of Po and Ptrue fails, and conditionally writes results to stream. verbose If true, write results to stdout nk Number of layers po Calculated answer ptrue True answer title Title for messages ndiff_unit_tests_continuous logical function logical function mom_neutral_diffusion::test_data1di (verbose, nk, Po, Ptrue, title) test_data1di verbose verbose nk nk Po Po Ptrue Ptrue title title Returns true if comparison of Po and Ptrue fails, and conditionally writes results to stream. verbose If true, write results to stdout nk Number of layers po Calculated answer ptrue True answer title Title for messages logical function logical function mom_neutral_diffusion::test_nsp (verbose, ns, KoL, KoR, pL, pR, hEff, KoL0, KoR0, pL0, pR0, hEff0, title) test_nsp verbose verbose ns ns KoL KoL KoR KoR pL pL pR pR hEff hEff KoL0 KoL0 KoR0 KoR0 pL0 pL0 pR0 pR0 hEff0 hEff0 title title Returns true if output of find_neutral_surface_positions() does not match correct values, and conditionally writes results to stream. verbose If true, write results to stdout ns Number of surfaces kol Index of first left interface above neutral surface kor Index of first right interface above neutral surface pl Fractional position of neutral surface within layer KoL of left column pr Fractional position of neutral surface within layer KoR of right column heff Effective thickness between two neutral surfaces [R L2 T-2 ~> Pa] kol0 Correct value for KoL kor0 Correct value for KoR pl0 Correct value for pL pr0 Correct value for pR heff0 Correct value for hEff title Title for messages compare_nsp_row mom_error_handler::mom_error ndiff_unit_tests_continuous ndiff_unit_tests_discontinuous logical function logical function mom_neutral_diffusion::compare_nsp_row (KoL, KoR, pL, pR, KoL0, KoR0, pL0, pR0) compare_nsp_row KoL KoL KoR KoR pL pL pR pR KoL0 KoL0 KoR0 KoR0 pL0 pL0 pR0 pR0 Compares a single row, k, of output from find_neutral_surface_positions() kol Index of first left interface above neutral surface kor Index of first right interface above neutral surface pl Fractional position of neutral surface within layer KoL of left column pr Fractional position of neutral surface within layer KoR of right column kol0 Correct value for KoL kor0 Correct value for KoR pl0 Correct value for pL pr0 Correct value for pR test_nsp logical function logical function mom_neutral_diffusion::test_rnp (expected_pos, test_pos, title) test_rnp expected_pos expected_pos test_pos test_pos title title Compares output position from refine_nondim_position with an expected value. expected_pos The expected position test_pos The position returned by the code title A label for this test ndiff_unit_tests_discontinuous subroutine, public subroutine, public mom_neutral_diffusion::neutral_diffusion_end (CS) neutral_diffusion_end CS CS Deallocates neutral_diffusion control structure. cs Neutral diffusion control structure A column-wise toolbox for implementing neutral diffusion.