mom_vert_friction mom_vert_friction::vertvisc_cs subroutine, public subroutine, public mom_vert_friction::vertvisc (u, v, h, forces, visc, dt, OBC, ADp, CDp, G, GV, US, CS, taux_bot, tauy_bot, Waves) vertvisc u u v v h h forces forces visc visc dt dt OBC OBC ADp ADp CDp CDp G G GV GV US US CS CS taux_bot taux_bot tauy_bot tauy_bot Waves Waves Perform a fully implicit vertical diffusion of momentum. Stress top and bottom boundary conditions are used. This is solving the tridiagonal system \[ \left(h_k + a_{k + 1/2} + a_{k - 1/2} + r_k\right) u_k^{n+1} = h_k u_k^n + a_{k + 1/2} u_{k+1}^{n+1} + a_{k - 1/2} u_{k-1}^{n+1} \] where $a_{k + 1/2} = \Delta t \nu_{k + 1/2} / h_{k + 1/2}$ is the interfacial coupling thickness per time step, encompassing background viscosity as well as contributions from enhanced mixed and bottom layer viscosities. $r_k$ is a Rayleight drag term due to channel drag. There is an additional stress term on the right-hand side if DIRECT_STRESS is true, applied to the surface layer. g Ocean grid structure gv Ocean vertical grid structure us A dimensional unit scaling type u Zonal velocity [L T-1 ~> m s-1] v Meridional velocity [L T-1 ~> m s-1] h Layer thickness [H ~> m or kg m-2] forces A structure with the driving mechanical forces visc Viscosities and bottom drag dt Time increment [T ~> s] obc Open boundary condition structure adp Accelerations in the momentum equations for diagnostics cdp Continuity equation terms cs Vertical viscosity control structure taux_bot Zonal bottom stress from ocean to tauy_bot Meridional bottom stress from ocean to waves Container for wave/Stokes information mom_error_handler::mom_error vertvisc_limit_vel mom_dynamics_unsplit::step_mom_dyn_unsplit mom_dynamics_unsplit_rk2::step_mom_dyn_unsplit_rk2 subroutine, public subroutine, public mom_vert_friction::vertvisc_remnant (visc, visc_rem_u, visc_rem_v, dt, G, GV, US, CS) vertvisc_remnant visc visc visc_rem_u visc_rem_u visc_rem_v visc_rem_v dt dt G G GV GV US US CS CS Calculate the fraction of momentum originally in a layer that remains after a time-step of viscosity, and the fraction of a time-step's worth of barotropic acceleration that a layer experiences after viscosity is applied. g Ocean grid structure gv Ocean vertical grid structure visc Viscosities and bottom drag visc_rem_u Fraction of a time-step's worth of a visc_rem_v Fraction of a time-step's worth of a dt Time increment [T ~> s] us A dimensional unit scaling type cs Vertical viscosity control structure mom_error_handler::mom_error subroutine, public subroutine, public mom_vert_friction::vertvisc_coef (u, v, h, forces, visc, dt, G, GV, US, CS, OBC) vertvisc_coef u u v v h h forces forces visc visc dt dt G G GV GV US US CS CS OBC OBC Calculate the coupling coefficients (CSa_u and CSa_v) and effective layer thicknesses (CSh_u and CSh_v) for later use in the applying the implicit vertical viscosity via vertvisc(). g Ocean grid structure gv Ocean vertical grid structure us A dimensional unit scaling type u Zonal velocity [L T-1 ~> m s-1] v Meridional velocity [L T-1 ~> m s-1] h Layer thickness [H ~> m or kg m-2] forces A structure with the driving mechanical forces visc Viscosities and bottom drag dt Time increment [T ~> s] cs Vertical viscosity control structure obc Open boundary condition structure find_coupling_coef mom_error_handler::mom_error mom_open_boundary::obc_direction_n mom_open_boundary::obc_direction_s mom_open_boundary::obc_direction_w mom_dynamics_unsplit::step_mom_dyn_unsplit mom_dynamics_unsplit_rk2::step_mom_dyn_unsplit_rk2 subroutine subroutine mom_vert_friction::find_coupling_coef (a_cpl, hvel, do_i, h_harm, bbl_thick, kv_bbl, z_i, h_ml, dt, j, G, GV, US, CS, visc, forces, work_on_u, OBC, shelf) find_coupling_coef a_cpl a_cpl hvel hvel do_i do_i h_harm h_harm bbl_thick bbl_thick kv_bbl kv_bbl z_i z_i h_ml h_ml dt dt j j G G GV GV US US CS CS visc visc forces forces work_on_u work_on_u OBC OBC shelf shelf Calculate the 'coupling coefficient' (a_cpl) at the interfaces. If BOTTOMDRAGLAW is defined, the minimum of Hbbl and half the adjacent layer thicknesses are used to calculate a_cpl near the bottom. g Ocean grid structure gv Ocean vertical grid structure us A dimensional unit scaling type a_cpl Coupling coefficient across interfaces [Z T-1 ~> m s-1]. hvel Thickness at velocity points [H ~> m or kg m-2] do_i If true, determine coupling coefficient for a column h_harm Harmonic mean of thicknesses around a velocity bbl_thick Bottom boundary layer thickness [H ~> m or kg m-2] kv_bbl Bottom boundary layer viscosity [Z2 T-1 ~> m2 s-1]. z_i Estimate of interface heights above the bottom, h_ml Mixed layer depth [H ~> m or kg m-2] j j-index to find coupling coefficient for dt Time increment [T ~> s] cs Vertical viscosity control structure visc Structure containing viscosities and bottom drag forces A structure with the driving mechanical forces work_on_u If true, u-points are being calculated, otherwise they are v-points obc Open boundary condition structure shelf If present and true, use a surface boundary condition appropriate for an ice shelf. mom_open_boundary::obc_direction_n mom_open_boundary::obc_direction_s mom_open_boundary::obc_direction_w vertvisc_coef subroutine, public subroutine, public mom_vert_friction::vertvisc_limit_vel (u, v, h, ADp, CDp, forces, visc, dt, G, GV, US, CS) vertvisc_limit_vel u u v v h h ADp ADp CDp CDp forces forces visc visc dt dt G G GV GV US US CS CS Velocity components which exceed a threshold for physically reasonable values are truncated. Optionally, any column with excessive velocities may be sent to a diagnostic reporting subroutine. g Ocean grid structure gv Ocean vertical grid structure us A dimensional unit scaling type u Zonal velocity [L T-1 ~> m s-1] v Meridional velocity [L T-1 ~> m s-1] h Layer thickness [H ~> m or kg m-2] adp Acceleration diagnostic pointers cdp Continuity diagnostic pointers forces A structure with the driving mechanical forces visc Viscosities and bottom drag dt Time increment [T ~> s] cs Vertical viscosity control structure vertvisc subroutine, public subroutine, public mom_vert_friction::vertvisc_init (MIS, Time, G, GV, US, param_file, diag, ADp, dirs, ntrunc, CS) vertvisc_init MIS MIS Time Time G G GV GV US US param_file param_file diag diag ADp ADp dirs dirs ntrunc ntrunc CS CS Initialize the vertical friction module. mis The "MOM Internal State", a set of pointers time Current model time g Ocean grid structure gv Ocean vertical grid structure us A dimensional unit scaling type param_file File to parse for parameters diag Diagnostic control structure adp Acceleration diagnostic pointers dirs Relevant directory paths ntrunc Number of velocity truncations cs Vertical viscosity control structure mom_error_handler::mom_error subroutine, public subroutine, public mom_vert_friction::updatecfltruncationvalue (Time, CS, activate) updatecfltruncationvalue Time Time CS CS activate activate Update the CFL truncation value as a function of time. If called with the optional argument activate=.true., record the value of Time as the beginning of the ramp period. time Current model time cs Vertical viscosity control structure activate Specifiy whether to record the value of Time as the beginning of the ramp period mom_error_handler::mom_error mom_dynamics_split_rk2::step_mom_dyn_split_rk2 subroutine, public subroutine, public mom_vert_friction::vertvisc_end (CS) vertvisc_end CS CS Clean up and deallocate the vertical friction module. cs Vertical viscosity control structure that will be deallocated in this subroutine. Implements vertical viscosity (vertvisc) Robert Hallberg April 1994 - October 2006 The vertical diffusion of momentum is fully implicit. This is necessary to allow for vanishingly small layers. The coupling is based on the distance between the centers of adjacent layers, except where a layer is close to the bottom compared with a bottom boundary layer thickness when a bottom drag law is used. A stress top b.c. and a no slip bottom b.c. are used. There is no limit on the time step for vertvisc. Near the bottom, the horizontal thickness interpolation scheme changes to an upwind biased estimate to control the effect of spurious Montgomery potential gradients at the bottom where nearly massless layers layers ride over the topography. Within a few boundary layer depths of the bottom, the harmonic mean thickness (i.e. (2 h+ h-) / (h+ + h-) ) is used if the velocity is from the thinner side and the arithmetic mean thickness (i.e. (h+ + h-)/2) is used if the velocity is from the thicker side. Both of these thickness estimates are second order accurate. Above this the arithmetic mean thickness is used. In addition, vertvisc truncates any velocity component that exceeds maxvel to truncvel. This basically keeps instabilities spatially localized. The number of times the velocity is truncated is reported each time the energies are saved, and if exceeds CSMaxtrunc the model will stop itself and change the time to a large value. This has proven very useful in (1) diagnosing model failures and (2) letting the model settle down to a meaningful integration from a poorly specified initial condition. The same code is used for the two velocity components, by indirectly referencing the velocities and defining a handful of direction-specific defined variables. Macros written all in capital letters are defined in MOM_memory.h. A small fragment of the grid is shown below: j+1 x ^ x ^ x At x: q j+1 > o > o > At ^: v, frhatv, tauy j x ^ x ^ x At >: u, frhatu, taux j > o > o > At o: h j-1 x ^ x ^ x i-1 i i+1 At x & ^: i i+1 At > & o: The boundaries always run through q grid points (x).