MODULE dynzdf_imp_jki !!============================================================================== !! *** MODULE dynzdf_imp_jki *** !! Ocean dynamics: vertical component(s) of the momentum mixing trend !!============================================================================== !! History : 8.5 ! 02-08 (G. Madec) auto-tasking option !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_zdf_imp_jki : update the momentum trend with the vertical !! diffusion using an implicit time-stepping and !! j-k-i loops. !!---------------------------------------------------------------------- !! * 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 IMPLICIT NONE PRIVATE !! * Routine accessibility PUBLIC dyn_zdf_imp_jki ! called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LOCEAN-IPSL (2005) !! $Header$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_zdf_imp_jki( kt, p2dt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_zdf_imp_jki *** !! !! ** Purpose : Compute the trend due to the vert. momentum diffusion !! and the surface forcing, and add it to the general trend of !! the momentum equations. !! !! ** Method : The vertical momentum mixing trend is given by : !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) !! backward time stepping !! Surface boundary conditions: wind stress input !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) !! Add this trend to the general trend ua : !! ua = ua + dz( avmu dz(u) ) !! !! ** Action : - Update (ua,va) arrays with the after vertical diffusive !! mixing trend. !!--------------------------------------------------------------------- !! * Arguments INTEGER , INTENT( in ) :: kt ! ocean time-step index REAL(wp), INTENT( in ) :: p2dt ! ocean time-step index !! * Local declarations INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ikst, ikenm2, ikstp1 ! temporary integers REAL(wp) :: zrau0r, z2dtf, zcoef, zzws ! temporary scalars REAL(wp), DIMENSION(jpi,jpk) :: zwx, zwy, zwz, & ! workspace & zwd, zws, zwi, zwt !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_jki : vertical momentum diffusion implicit operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ auto-task case (j-k-i loop)' ENDIF ! 0. Local constant initialization ! -------------------------------- zrau0r = 1. / rau0 ! inverse of the reference density ! ! =============== DO jj = 2, jpjm1 ! Vertical slab ! ! =============== ! 1. Vertical diffusion on u ! --------------------------- ! Matrix and second member construction ! bottom boundary condition: only zws must be masked as avmu can take ! non zero value at the ocean bottom depending on the bottom friction ! used (see zdfmix.F) DO jk = 1, jpkm1 DO ji = 2, jpim1 zcoef = - p2dt / fse3u(ji,jj,jk) zwi(ji,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) zws(ji,jk) = zzws * umask(ji,jj,jk+1) zwd(ji,jk) = 1. - zwi(ji,jk) - zzws zwy(ji,jk) = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk) END DO END DO ! Surface boudary conditions DO ji = 2, jpim1 z2dtf = p2dt / ( fse3u(ji,jj,1)*rau0 ) zwi(ji,1) = 0. zwd(ji,1) = 1. - zws(ji,1) zwy(ji,1) = zwy(ji,1) + z2dtf * taux(ji,jj) END DO ! Matrix inversion starting from the first level ikst = 1 !!---------------------------------------------------------------------- !! ZDF.MATRIXSOLVER !! ******************** !!---------------------------------------------------------------------- !! Matrix inversion ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) ! ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) ! ( ... )( ... ) ( ... ) ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) ! ! m is decomposed in the product of an upper and lower triangular ! matrix ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi ! The second member is in 2d array zwy ! The solution is in 2d array zwx ! The 2d arry zwt and zwz are work space arrays ! ! N.B. the starting vertical index (ikst) is equal to 1 except for ! the resolution of tke matrix where surface tke value is prescribed ! so that ikstrt=2. !!---------------------------------------------------------------------- ikstp1 = ikst + 1 ikenm2 = jpk - 2 DO ji = 2, jpim1 zwt(ji,ikst) = zwd(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwz(ji,ikst) = zwy(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) END DO DO jk = ikenm2, ikst, -1 DO ji = 2, jpim1 zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) END DO END DO ! Normalization to obtain the general momentum trend ua DO jk = 1, jpkm1 DO ji = 2, jpim1 ua(ji,jj,jk) = ( zwx(ji,jk) - ub(ji,jj,jk) ) / p2dt END DO END DO ! 2. Vertical diffusion on v ! --------------------------- ! Matrix and second member construction ! bottom boundary condition: only zws must be masked as avmv can take ! non zero value at the ocean bottom depending on the bottom friction ! used (see zdfmix.F) DO jk = 1, jpkm1 DO ji = 2, jpim1 zcoef = -p2dt/fse3v(ji,jj,jk) zwi(ji,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) zws(ji,jk) = zzws * vmask(ji,jj,jk+1) zwd(ji,jk) = 1. - zwi(ji,jk) - zzws zwy(ji,jk) = vb(ji,jj,jk) + p2dt * va(ji,jj,jk) END DO END DO ! Surface boudary conditions DO ji = 2, jpim1 z2dtf = p2dt / ( fse3v(ji,jj,1)*rau0 ) zwi(ji,1) = 0.e0 zwd(ji,1) = 1. - zws(ji,1) zwy(ji,1) = zwy(ji,1) + z2dtf * tauy(ji,jj) END DO ! Matrix inversion starting from the first level ikst = 1 !!---------------------------------------------------------------------- !! ZDF.MATRIXSOLVER !! ******************** !!---------------------------------------------------------------------- !! Matrix inversion ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) ! ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) ! ( ... )( ... ) ( ... ) ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) ! ! m is decomposed in the product of an upper and lower triangular ! matrix ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi ! The second member is in 2d array zwy ! The solution is in 2d array zwx ! The 2d arry zwt and zwz are work space arrays ! ! N.B. the starting vertical index (ikst) is equal to 1 except for ! the resolution of tke matrix where surface tke value is prescribed ! so that ikstrt=2. !!---------------------------------------------------------------------- ikstp1 = ikst + 1 ikenm2 = jpk - 2 DO ji = 2, jpim1 zwt(ji,ikst) = zwd(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwz(ji,ikst) = zwy(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) END DO DO jk = ikenm2, ikst, -1 DO ji = 2, jpim1 zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) END DO END DO ! Normalization to obtain the general momentum trend va DO jk = 1, jpkm1 DO ji = 2, jpim1 va(ji,jj,jk) = ( zwx(ji,jk) - vb(ji,jj,jk) ) / p2dt END DO END DO ! ! =============== END DO ! End of slab ! ! =============== END SUBROUTINE dyn_zdf_imp_jki !!============================================================================== END MODULE dynzdf_imp_jki