MODULE dynzdf_exp !!============================================================================== !! *** MODULE dynzdf_exp *** !! Ocean dynamics: vertical component(s) of the momentum mixing trend !!============================================================================== !!---------------------------------------------------------------------- !! dyn_zdf_exp : update the momentum trend with the vertical diffu- !! sion using an explicit time-stepping scheme. !!---------------------------------------------------------------------- !! * Modules used USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE zdf_oce ! ocean vertical physics USE in_out_manager ! I/O manager USE taumod ! surface ocean stress USE trddyn_oce ! dynamics trends diagnostics variables IMPLICIT NONE PRIVATE !! * Routine accessibility PUBLIC dyn_zdf_exp ! called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LODYC-IPSL (2003) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_zdf_exp( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_zdf_exp *** !! !! ** Purpose : Compute the trend due to the vert. momentum diffusion !! !! ** Method : Explicit forward time stepping with a time splitting !! technique. The vertical diffusion of momentum is given by: !! diffu = dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ub) ) !! Surface boundary conditions: wind stress input !! Bottom boundary conditions : bottom stress (cf zdfbfr.F90) !! Add this trend to the general trend ua : !! ua = ua + dz( avmu dz(u) ) !! !! ** Action : - Update (ua,va) with the vertical diffusive trend !! - Save the trends in (utrd,vtrd) ('key_diatrends') !! !! History : !! ! 90-10 (B. Blanke) Original code !! ! 97-05 (G. Madec) vertical component of isopycnal !! 8.5 ! 02-08 (G. Madec) F90: Free form and module !!--------------------------------------------------------------------- !! * Arguments INTEGER, INTENT( in ) :: kt ! ocean time-step index !! * Local declarations INTEGER :: ji, jj, jk, jl ! dummy loop indices REAL(wp) :: & zrau0r, zlavmr, z2dt, zua, zva ! temporary scalars REAL(wp), DIMENSION(jpi,jpk) :: & zwx, zwy, zwz, zww ! temporary workspace arrays #if defined key_trddyn INTEGER :: & ikbu, ikbum1 , ikbv, ikbvm1 ! temporary integers #endif !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_zdf_exp : vertical momentum diffusion explicit operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' ENDIF ! Local constant initialization ! ----------------------------- zrau0r = 1. / rau0 ! inverse of the reference density zlavmr = 1. / float( n_zdfexp ) ! inverse of the number of sub time step z2dt = 2. * rdt ! Leap-frog environnement IF( neuler == 0 .AND. kt == nit000 ) z2dt = rdt ! Euler time stepping when starting from rest ! ! =============== DO jj = 2, jpjm1 ! Vertical slab ! ! =============== ! Surface boundary condition DO ji = 2, jpim1 zwy(ji,1) = taux(ji,jj) * zrau0r zww(ji,1) = tauy(ji,jj) * zrau0r END DO ! Initialization of x, z and contingently trends array DO jk = 1, jpk DO ji = 2, jpim1 zwx(ji,jk) = ub(ji,jj,jk) zwz(ji,jk) = vb(ji,jj,jk) #if defined key_trddyn utrd(ji,jj,jk,7) = ua(ji,jj,jk) vtrd(ji,jj,jk,7) = va(ji,jj,jk) #endif END DO END DO ! Time splitting loop DO jl = 1, n_zdfexp ! First vertical derivative DO jk = 2, jpk DO ji = 2, jpim1 zwy(ji,jk) = avmu(ji,jj,jk) * ( zwx(ji,jk-1) - zwx(ji,jk) ) / fse3uw(ji,jj,jk) zww(ji,jk) = avmv(ji,jj,jk) * ( zwz(ji,jk-1) - zwz(ji,jk) ) / fse3vw(ji,jj,jk) END DO END DO ! Second vertical derivative and trend estimation at kt+l*rdt/n_zdfexp DO jk = 1, jpkm1 DO ji = 2, jpim1 zua = zlavmr*( zwy(ji,jk) - zwy(ji,jk+1) ) / fse3u(ji,jj,jk) zva = zlavmr*( zww(ji,jk) - zww(ji,jk+1) ) / fse3v(ji,jj,jk) ua(ji,jj,jk) = ua(ji,jj,jk) + zua va(ji,jj,jk) = va(ji,jj,jk) + zva zwx(ji,jk) = zwx(ji,jk) + z2dt*zua*umask(ji,jj,jk) zwz(ji,jk) = zwz(ji,jk) + z2dt*zva*vmask(ji,jj,jk) END DO END DO END DO #if defined key_trddyn ! diagnose the vertical diffusive momentum trends ! save the total vertical momentum diffusive trend DO jk = 1, jpkm1 DO ji = 2, jpim1 utrd(ji,jj,jk,7) = ua(ji,jj,jk) - utrd(ji,jj,jk,7) vtrd(ji,jj,jk,7) = va(ji,jj,jk) - vtrd(ji,jj,jk,7) END DO END DO ! subtract and save surface and momentum fluxes DO ji = 2, jpim1 ! save the surface momentum fluxes tautrd(ji,jj,1) = zwy(ji,1) / fse3u(ji,jj,1) tautrd(ji,jj,2) = zww(ji,1) / fse3v(ji,jj,1) ! save bottom friction momentum fluxes ikbu = MIN( mbathy(ji+1,jj), mbathy(ji,jj) ) ikbum1 = MAX( ikbu-1, 1 ) ikbv = MIN( mbathy(ji,jj+1), mbathy(ji,jj) ) ikbvm1 = MAX( ikbv-1, 1 ) tautrd(ji,jj,3) = avmu(ji,jj,ikbu) * zwx(ji,ikbum1) & / ( fse3u(ji,jj,ikbum1) * fse3uw(ji,jj,ikbu) ) tautrd(ji,jj,4) = avmv(ji,jj,ikbv) * zwz(ji,ikbvm1) & / ( fse3v(ji,jj,ikbvm1) * fse3vw(ji,jj,ikbv) ) ! subtract surface forcing and bottom friction trend from vertical ! diffusive momentum trend utrd(ji,jj,1 ,7) = utrd(ji,jj,1 ,7) - tautrd(ji,jj,1) utrd(ji,jj,ikbum1,7) = utrd(ji,jj,ikbum1,7) - tautrd(ji,jj,3) vtrd(ji,jj,1 ,7) = vtrd(ji,jj,1 ,7) - tautrd(ji,jj,2) vtrd(ji,jj,ikbvm1,7) = vtrd(ji,jj,ikbvm1,7) - tautrd(ji,jj,4) END DO #endif ! ! =============== END DO ! End of slab ! ! =============== END SUBROUTINE dyn_zdf_exp !!============================================================================== END MODULE dynzdf_exp