MODULE dynadv_cen2
!!======================================================================
!! *** MODULE dynadv ***
!! Ocean dynamics: Update the momentum trend with the flux form advection
!! using a 2nd order centred scheme
!!======================================================================
!! History : 2.0 ! 2006-08 (G. Madec, S. Theetten) Original code
!! 3.2 ! 2009-07 (R. Benshila) Suppression of rigid-lid option
!! 4.5 ! 2022-06 (S. Techene, G, Madec) refactorization to reduce local memory usage
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! dyn_adv_cen2 : flux form momentum advection (ln_dynadv_cen2=T) using a 2nd order centred scheme
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and tracers
USE dom_oce ! ocean space and time domain
USE trd_oce ! trends: ocean variables
USE trddyn ! trend manager: dynamics
!
USE in_out_manager ! I/O manager
USE lib_mpp ! MPP library
USE prtctl ! Print control
IMPLICIT NONE
PRIVATE
PUBLIC dyn_adv_cen2 ! routine called by step.F90
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: dynadv_cen2.F90 14419 2021-02-09 12:22:16Z techene $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE dyn_adv_cen2( kt, Kmm, puu, pvv, Krhs, pau, pav, paw )
!!----------------------------------------------------------------------
!! *** ROUTINE dyn_adv_cen2 ***
!!
!! ** Purpose : Compute the momentum advection trend in flux form
!! and the general trend of the momentum equation.
!!
!! ** Method : Trend evaluated with a 2nd order centered scheme
!! using fields at Kmm time-level.
!! In RK3 time stepping case, the optional arguments (pau,pav,paw)
!! are present. They are used as advective velocity while
!! the advected velocity remains (puu,pvv).
!!
!! ** Action : (puu,pvv)(:,:,:,Krhs) updated with the advective trend
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt , Kmm, Krhs ! ocean time-step and level indices
REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), TARGET, INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
REAL(wp), DIMENSION(:,:,:), OPTIONAL, TARGET, INTENT(in ) :: pau, pav, paw ! advective velocity
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zzu, zzfu_kp1 ! local scalars
REAL(wp) :: zzv, zzfv_kp1 ! - -
REAL(wp), DIMENSION(A2D(1)) :: zfu_t, zfu_f, zfu
REAL(wp), DIMENSION(A2D(1)) :: zfv_t, zfv_f, zfv
REAL(wp), DIMENSION(A2D(1)) :: zfu_uw, zfv_vw, zfw
REAL(wp), DIMENSION(:,:,:) , POINTER :: zpt_u, zpt_v, zpt_w
REAL(wp), DIMENSION(:,:,:) , ALLOCATABLE :: zu_trd, zv_trd
!!----------------------------------------------------------------------
!
IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
IF( kt == nit000 .AND. lwp ) THEN
WRITE(numout,*)
WRITE(numout,*) 'dyn_adv_cen2 : 2nd order flux form momentum advection'
WRITE(numout,*) '~~~~~~~~~~~~'
ENDIF
ENDIF
!
IF( l_trddyn ) THEN ! trends: store the input trends
ALLOCATE( zu_trd(A2D(0),jpkm1), zv_trd(A2D(0),jpkm1) )
zu_trd(A2D(0),:) = puu(A2D(0),:,Krhs)
zv_trd(A2D(0),:) = pvv(A2D(0),:,Krhs)
ENDIF
!
IF( PRESENT( pau ) ) THEN ! RK3: advective velocity (pau,pav,paw) /= advected velocity (puu,pvv,ww)
zpt_u => pau(:,:,:)
zpt_v => pav(:,:,:)
zpt_w => paw(:,:,:)
ELSE ! MLF: advective velocity = (puu,pvv,ww)
zpt_u => puu(:,:,:,Kmm)
zpt_v => pvv(:,:,:,Kmm)
zpt_w => ww (:,:,: )
ENDIF
!
! !== Horizontal advection ==!
!
DO jk = 1, jpkm1 ! horizontal transport
DO_2D( 1, 1, 1, 1 )
zfu(ji,jj) = 0.25_wp * e2u(ji,jj) * e3u(ji,jj,jk,Kmm) * zpt_u(ji,jj,jk)
zfv(ji,jj) = 0.25_wp * e1v(ji,jj) * e3v(ji,jj,jk,Kmm) * zpt_v(ji,jj,jk)
END_2D
DO_2D( 1, 0, 1, 0 ) ! horizontal momentum fluxes (at T- and F-point)
zfu_t(ji+1,jj ) = ( zfu(ji,jj) + zfu(ji+1,jj) ) * ( puu(ji,jj,jk,Kmm) + puu(ji+1,jj ,jk,Kmm) )
zfv_f(ji ,jj ) = ( zfv(ji,jj) + zfv(ji+1,jj) ) * ( puu(ji,jj,jk,Kmm) + puu(ji ,jj+1,jk,Kmm) )
zfu_f(ji ,jj ) = ( zfu(ji,jj) + zfu(ji,jj+1) ) * ( pvv(ji,jj,jk,Kmm) + pvv(ji+1,jj ,jk,Kmm) )
zfv_t(ji ,jj+1) = ( zfv(ji,jj) + zfv(ji,jj+1) ) * ( pvv(ji,jj,jk,Kmm) + pvv(ji ,jj+1,jk,Kmm) )
END_2D
DO_2D( 0, 0, 0, 0 ) ! divergence of horizontal momentum fluxes
puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) - ( zfu_t(ji+1,jj) - zfu_t(ji,jj ) &
& + zfv_f(ji ,jj) - zfv_f(ji,jj-1) ) * r1_e1e2u(ji,jj) &
& / e3u(ji,jj,jk,Kmm)
pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) - ( zfu_f(ji,jj ) - zfu_f(ji-1,jj) &
& + zfv_t(ji,jj+1) - zfv_t(ji ,jj) ) * r1_e1e2v(ji,jj) &
& / e3v(ji,jj,jk,Kmm)
END_2D
END DO
!
IF( l_trddyn ) THEN ! trends: send trend to trddyn for diagnostic
zu_trd(A2D(0),:) = puu(A2D(0),:,Krhs) - zu_trd(A2D(0),:)
zv_trd(A2D(0),:) = pvv(A2D(0),:,Krhs) - zv_trd(A2D(0),:)
CALL trd_dyn( zu_trd, zv_trd, jpdyn_keg, kt, Kmm )
zu_trd(A2D(0),:) = puu(A2D(0),:,Krhs)
zv_trd(A2D(0),:) = pvv(A2D(0),:,Krhs)
ENDIF
!
! !== Vertical advection ==!
!
! ! surface vertical fluxes
!
IF( ln_linssh ) THEN ! linear free surface: advection through the surface z=0
DO_2D( 0, 0, 0, 0 )
zfu_uw(ji,jj) = 0.5_wp * ( e1e2t(ji,jj) * zpt_w(ji,jj,1) + e1e2t(ji+1,jj) * zpt_w(ji+1,jj,1) ) * puu(ji,jj,1,Kmm)
zfv_vw(ji,jj) = 0.5_wp * ( e1e2t(ji,jj) * zpt_w(ji,jj,1) + e1e2t(ji,jj+1) * zpt_w(ji,jj+1,1) ) * pvv(ji,jj,1,Kmm)
END_2D
ELSE ! non linear free: surface advective fluxes set to zero
DO_2D( 0, 0, 0, 0 )
zfu_uw(ji,jj) = 0._wp
zfv_vw(ji,jj) = 0._wp
END_2D
ENDIF
!
DO jk = 1, jpk-2 ! divergence of advective fluxes
!
DO_2D( 0, 1, 0, 1 ) ! 1/4 * Vertical transport at level k+1
zfw(ji,jj) = 0.25_wp * e1e2t(ji,jj) * zpt_w(ji,jj,jk+1)
END_2D
DO_2D( 0, 0, 0, 0 )
! ! vertical flux at level k+1
zzfu_kp1 = ( zfw(ji,jj) + zfw(ji+1,jj ) ) * ( puu(ji,jj,jk+1,Kmm) + puu(ji,jj,jk,Kmm) )
zzfv_kp1 = ( zfw(ji,jj) + zfw(ji ,jj+1) ) * ( pvv(ji,jj,jk+1,Kmm) + pvv(ji,jj,jk,Kmm) )
! ! divergence of vertical momentum flux
puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) - ( zfu_uw(ji,jj) - zzfu_kp1 ) * r1_e1e2u(ji,jj) &
& / e3u(ji,jj,jk,Kmm)
pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) - ( zfv_vw(ji,jj) - zzfv_kp1 ) * r1_e1e2v(ji,jj) &
& / e3v(ji,jj,jk,Kmm)
! ! store vertical flux for next level calculation
zfu_uw(ji,jj) = zzfu_kp1
zfv_vw(ji,jj) = zzfv_kp1
END_2D
END DO
!
jk = jpkm1
DO_2D( 0, 0, 0, 0 )
puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) - zfu_uw(ji,jj) * r1_e1e2u(ji,jj) &
& / e3u(ji,jj,jk,Kmm)
pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) - zfv_vw(ji,jj) * r1_e1e2v(ji,jj) &
& / e3v(ji,jj,jk,Kmm)
END_2D
!
IF( l_trddyn ) THEN ! trends: send trend to trddyn for diagnostic
zu_trd(A2D(0),:) = puu(A2D(0),:,Krhs) - zu_trd(A2D(0),:)
zv_trd(A2D(0),:) = pvv(A2D(0),:,Krhs) - zv_trd(A2D(0),:)
CALL trd_dyn( zu_trd, zv_trd, jpdyn_zad, kt, Kmm )
DEALLOCATE( zu_trd, zv_trd )
ENDIF
! ! Control print
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Krhs), clinfo1=' cen2 adv - Ua: ', mask1=umask, &
& tab3d_2=pvv(:,:,:,Krhs), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
!
END SUBROUTINE dyn_adv_cen2
!!==============================================================================
END MODULE dynadv_cen2