MODULE tl_uv3dmix4_mod ! !git $Id$ !svn $Id: tl_uv3dmix4_geo.h 1151 2023-02-09 03:08:53Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md ! !======================================================================= ! ! ! This subroutine computes tangent linear biharmonic mixing of ! ! momentum, rotated along geopotentials, from the horizontal ! ! divergence of the stress tensor. A transverse isotropy is ! ! assumed so the stress tensor is split into vertical and ! ! horizontal subtensors. ! ! ! ! Reference: ! ! ! ! Wajsowicz, R.C, 1993: A consistent formulation of the ! ! anisotropic stress tensor for use in models of the ! ! large-scale ocean circulation, JCP, 105, 333-338. ! ! ! ! Sadourny, R. and K. Maynard, 1997: Formulations of ! ! lateral diffusion in geophysical fluid dynamics ! ! models, In Numerical Methods of Atmospheric and ! ! Oceanic Modelling. Lin, Laprise, and Ritchie, ! ! Eds., NRC Research Press, 547-556. ! ! ! ! Griffies, S.M. and R.W. Hallberg, 2000: Biharmonic ! ! friction with a Smagorinsky-like viscosity for ! ! use in large-scale eddy-permitting ocean models, ! ! Monthly Weather Rev., 128, 8, 2935-2946. ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC tl_uv3dmix4 ! CONTAINS ! !*********************************************************************** SUBROUTINE tl_uv3dmix4 (ng, tile) !*********************************************************************** ! USE mod_param USE mod_coupling #ifdef DIAGNOSTICS_UV !! USE mod_diags #endif USE mod_grid USE mod_mixing USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! character (len=*), parameter :: MyFile = & & __FILE__ ! #include "tile.h" ! #ifdef PROFILE CALL wclock_on (ng, iTLM, 33, __LINE__, MyFile) #endif CALL tl_uv3dmix4_geo_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), nnew(ng), & #ifdef MASKING & GRID(ng) % pmask, & & GRID(ng) % rmask, & & GRID(ng) % umask, & & GRID(ng) % vmask, & #endif & GRID(ng) % om_p, & & GRID(ng) % om_r, & & GRID(ng) % om_u, & & GRID(ng) % om_v, & & GRID(ng) % on_p, & & GRID(ng) % on_r, & & GRID(ng) % on_u, & & GRID(ng) % on_v, & & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % tl_Hz, & & GRID(ng) % z_r, & & GRID(ng) % tl_z_r, & #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT & MIXING(ng) % Uvis3d_r, & & MIXING(ng) % Vvis3d_r, & & MIXING(ng) % tl_Uvis3d_r, & & MIXING(ng) % tl_Vvis3d_r, & # else & MIXING(ng) % visc3d_r, & & MIXING(ng) % tl_visc3d_r, & # endif #else & MIXING(ng) % visc4_p, & & MIXING(ng) % visc4_r, & #endif #ifdef DIAGNOSTICS_UV !! & DIAGS(ng) % DiaRUfrc, & !! & DIAGS(ng) % DiaRVfrc, & !! & DIAGS(ng) % DiaU3wrk, & !! & DIAGS(ng) % DiaV3wrk, & #endif & OCEAN(ng) % u, & & OCEAN(ng) % v, & & OCEAN(ng) % tl_u, & & OCEAN(ng) % tl_v, & & COUPLING(ng) % tl_rufrc, & & COUPLING(ng) % tl_rvfrc) #ifdef PROFILE CALL wclock_off (ng, iTLM, 33, __LINE__, MyFile) #endif ! RETURN END SUBROUTINE tl_uv3dmix4 ! !*********************************************************************** SUBROUTINE tl_uv3dmix4_geo_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nnew, & #ifdef MASKING & pmask, rmask, umask, vmask, & #endif & om_p, om_r, om_u, om_v, & & on_p, on_r, on_u, on_v, & & pm, pn, & & Hz, tl_Hz, & & z_r, tl_z_r, & #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT & Uvis3d_r, Vvis3d_r, & & tl_Uvis3d_r, tl_Vvis3d_r, & # else & visc3d_r, tl_visc3d_r, & # endif #else & visc4_p, visc4_r, & #endif #ifdef DIAGNOSTICS_UV !! & DiaRUfrc, DiaRVfrc, & !! & DiaU3wrk, DiaV3wrk, & #endif & u, v, & & tl_u, tl_v, & & tl_rufrc, tl_rvfrc) !*********************************************************************** ! USE mod_param USE mod_ncparam USE mod_scalars ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: nrhs, nnew #ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: pmask(LBi:,LBj:) real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif real(r8), intent(in) :: om_p(LBi:,LBj:) real(r8), intent(in) :: om_r(LBi:,LBj:) real(r8), intent(in) :: om_u(LBi:,LBj:) real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_p(LBi:,LBj:) real(r8), intent(in) :: on_r(LBi:,LBj:) real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: on_v(LBi:,LBj:) real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: tl_Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: tl_z_r(LBi:,LBj:,:) # ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT real(r8), intent(in) :: Uvis3d_r(LBi:,LBj:,:) real(r8), intent(in) :: Vvis3d_r(LBi:,LBj:,:) # else real(r8), intent(in) :: visc3d_r(LBi:,LBj:,:) # endif # else real(r8), intent(in) :: visc4_p(LBi:,LBj:) real(r8), intent(in) :: visc4_r(LBi:,LBj:) # endif real(r8), intent(in) :: u(LBi:,LBj:,:,:) real(r8), intent(in) :: v(LBi:,LBj:,:,:) # ifdef DIAGNOSTICS_UV !! real(r8), intent(inout) :: DiaRUfrc(LBi:,LBj:,:,:) !! real(r8), intent(inout) :: DiaRVfrc(LBi:,LBj:,:,:) !! real(r8), intent(inout) :: DiaU3wrk(LBi:,LBj:,:,:) !! real(r8), intent(inout) :: DiaV3wrk(LBi:,LBj:,:,:) # endif # ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT real(r8), intent(inout) :: tl_Uvis3d_r(LBi:,LBj:,:) real(r8), intent(inout) :: tl_Vvis3d_r(LBi:,LBj:,:) # else real(r8), intent(inout) :: tl_visc3d_r(LBi:,LBj:,:) # endif # endif real(r8), intent(inout) :: tl_rufrc(LBi:,LBj:) real(r8), intent(inout) :: tl_rvfrc(LBi:,LBj:) real(r8), intent(inout) :: tl_u(LBi:,LBj:,:,:) real(r8), intent(inout) :: tl_v(LBi:,LBj:,:,:) #else # ifdef MASKING real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: om_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: tl_Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: tl_z_r(LBi:UBi,LBj:UBj,N(ng)) # ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT real(r8), intent(in) :: Uvis3d_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Vvis3d_r(LBi:UBi,LBj:UBj,N(ng)) # else real(r8), intent(in) :: visc3d_r(LBi:UBi,LBj:UBj,N(ng)) # endif # else real(r8), intent(in) :: visc4_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: visc4_r(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(in) :: v(LBi:UBi,LBj:UBj,N(ng),2) # ifdef DIAGNOSTICS_UV !! real(r8), intent(inout) :: DiaRUfrc(LBi:UBi,LBj:UBj,3,NDM2d-1) !! real(r8), intent(inout) :: DiaRVfrc(LBi:UBi,LBj:UBj,3,NDM2d-1) !! real(r8), intent(inout) :: DiaU3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d) !! real(r8), intent(inout) :: DiaV3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d) # endif # ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT real(r8), intent(inout) :: tl_Uvis3d_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: tl_Vvis3d_r(LBi:UBi,LBj:UBj,N(ng)) # else real(r8), intent(inout) :: tl_visc3d_r(LBi:UBi,LBj:UBj,N(ng)) # endif # endif real(r8), intent(inout) :: tl_rufrc(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: tl_rvfrc(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: tl_u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(inout) :: tl_v(LBi:UBi,LBj:UBj,N(ng),2) #endif ! ! Local variable declarations. ! integer :: i, j, k, k1, k2 real(r8) :: cff, fac1, fac2, pm_p, pn_p real(r8) :: cff1, cff2, cff3, cff4 real(r8) :: cff5, cff6, cff7, cff8 real(r8) :: dmUdz, dnUdz, dmVdz, dnVdz #ifdef VISC_3DCOEF real(r8) :: Uvis_p, Vvis_p, visc_p real(r8) :: tl_fac1, tl_fac2, tl_Uvis_p, tl_Vvis_p, tl_visc_p #endif real(r8) :: tl_cff real(r8) :: tl_cff1, tl_cff2, tl_cff3, tl_cff4 real(r8) :: tl_cff5, tl_cff6, tl_cff7, tl_cff8 real(r8) :: tl_dmUdz, tl_dnUdz, tl_dmVdz, tl_dnVdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: LapU real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: LapV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: tl_LapU real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: tl_LapV real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_VFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_VFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: UFse real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: UFsx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: VFse real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: VFsx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dmUde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dmVde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dnUdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dnVdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dUdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dVdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_r real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_r real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_UFse real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_UFsx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_VFse real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_VFsx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dmUde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dmVde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dnUdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dnVdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dUdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dVdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZde_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZde_r real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZdx_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZdx_r #include "set_bounds.h" ! !----------------------------------------------------------------------- ! Compute horizontal biharmonic viscosity along geopotential ! surfaces. The biharmonic operator is computed by applying ! the harmonic operator twice. !----------------------------------------------------------------------- ! ! Compute horizontal and vertical gradients. Notice the recursive ! blocking sequence. It is assumed here that the mixing coefficients ! are the squared root of the biharmonic viscosity coefficient. For ! momentum balance purposes, the thickness "Hz" appears only when ! computing the second harmonic operator. The vertical placement of ! the gradients is: ! ! dZdx_r, dZde_r, dnUdx, dmVde(:,:,k1) k rho-points ! dZdx_r, dZde_r, dnUdx, dmVde(:,:,k2) k+1 rho-points ! dZdx_p, dZde_p, dnVdx, dmUde(:,:,k1) k psi-points ! dZdx_p, dZde_p, dnVdx, dmUde(:,:,k2) k+1 psi-points ! UFse, UFsx, dUdz(:,:,k1) k-1/2 WU-points ! UFse, UFsx, dUdz(:,:,k2) k+1/2 WU-points ! VFse, VFsx, dVdz(:,:,k1) k-1/2 WV-points ! VFse, VFsx, dVdz(:,:,k2) k+1/2 WV-points ! k2=1 K_LOOP1 : DO k=0,N(ng) k1=k2 k2=3-k1 IF (k.lt.N(ng)) THEN ! ! Compute slopes (nondimensional) at RHO- and PSI-points. ! DO j=Jstrm2,Jendp2 DO i=IstrUm2,Iendp2 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) #ifdef MASKING cff=cff*umask(i,j) #endif UFx(i,j)=cff*(z_r(i ,j,k+1)- & & z_r(i-1,j,k+1)) tl_UFx(i,j)=cff*(tl_z_r(i ,j,k+1)- & & tl_z_r(i-1,j,k+1)) END DO END DO DO j=JstrVm2,Jendp2 DO i=Istrm2,Iendp2 cff=0.5_r8*(pn(i,j-1)+pn(i,j)) #ifdef MASKING cff=cff*vmask(i,j) #endif VFe(i,j)=cff*(z_r(i,j ,k+1)- & & z_r(i,j-1,k+1)) tl_VFe(i,j)=cff*(tl_z_r(i,j ,k+1)- & & tl_z_r(i,j-1,k+1)) END DO END DO ! DO j=Jstrm1,Jendp2 DO i=Istrm1,Iendp2 dZdx_p(i,j,k2)=0.5_r8*(UFx(i,j-1)+ & & UFx(i,j )) tl_dZdx_p(i,j,k2)=0.5_r8*(tl_UFx(i,j-1)+ & & tl_UFx(i,j )) dZde_p(i,j,k2)=0.5_r8*(VFe(i-1,j)+ & & VFe(i ,j)) tl_dZde_p(i,j,k2)=0.5_r8*(tl_VFe(i-1,j)+ & & tl_VFe(i ,j)) END DO END DO DO j=JstrVm2,Jendp1 DO i=IstrUm2,Iendp1 dZdx_r(i,j,k2)=0.5_r8*(UFx(i ,j)+ & & UFx(i+1,j)) tl_dZdx_r(i,j,k2)=0.5_r8*(tl_UFx(i ,j)+ & & tl_UFx(i+1,j)) dZde_r(i,j,k2)=0.5_r8*(VFe(i,j )+ & & VFe(i,j+1)) tl_dZde_r(i,j,k2)=0.5_r8*(tl_VFe(i,j )+ & & tl_VFe(i,j+1)) END DO END DO ! ! Compute momentum horizontal (1/m/s) and vertical (1/s) gradients. ! DO j=JstrVm2,Jendp1 DO i=IstrUm2,Iendp1 cff=0.5_r8*pm(i,j) #ifdef MASKING cff=cff*rmask(i,j) #endif dnUdx(i,j,k2)=cff*((pn(i ,j)+pn(i+1,j))* & & u(i+1,j,k+1,nrhs)- & & (pn(i-1,j)+pn(i ,j))* & & u(i ,j,k+1,nrhs)) tl_dnUdx(i,j,k2)=cff*((pn(i ,j)+pn(i+1,j))* & & tl_u(i+1,j,k+1,nrhs)- & & (pn(i-1,j)+pn(i ,j))* & & tl_u(i ,j,k+1,nrhs)) END DO END DO DO j=Jstrm1,Jendp2 DO i=Istrm1,Iendp2 cff=0.125_r8*(pn(i-1,j )+pn(i,j )+ & & pn(i-1,j-1)+pn(i,j-1)) #ifdef MASKING cff=cff*pmask(i,j) #endif dmUde(i,j,k2)=cff*((pm(i-1,j )+pm(i,j ))* & & u(i,j ,k+1,nrhs)- & & (pm(i-1,j-1)+pm(i,j-1))* & & u(i,j-1,k+1,nrhs)) tl_dmUde(i,j,k2)=cff*((pm(i-1,j )+pm(i,j ))* & & tl_u(i,j ,k+1,nrhs)- & & (pm(i-1,j-1)+pm(i,j-1))* & & tl_u(i,j-1,k+1,nrhs)) END DO END DO DO j=Jstrm1,Jendp2 DO i=Istrm1,Iendp2 cff=0.125_r8*(pm(i-1,j )+pm(i,j )+ & & pm(i-1,j-1)+pm(i,j-1)) #ifdef MASKING cff=cff*pmask(i,j) #endif dnVdx(i,j,k2)=cff*((pn(i ,j-1)+pn(i ,j))* & & v(i ,j,k+1,nrhs)- & & (pn(i-1,j-1)+pn(i-1,j))* & & v(i-1,j,k+1,nrhs)) tl_dnVdx(i,j,k2)=cff*((pn(i ,j-1)+pn(i ,j))* & & tl_v(i ,j,k+1,nrhs)- & & (pn(i-1,j-1)+pn(i-1,j))* & & tl_v(i-1,j,k+1,nrhs)) END DO END DO DO j=JstrVm2,Jendp1 DO i=IstrUm2,Iendp1 cff=0.5_r8*pn(i,j) #ifdef MASKING cff=cff*rmask(i,j) #endif dmVde(i,j,k2)=cff*((pm(i,j )+pm(i,j+1))* & & v(i,j+1,k+1,nrhs)- & & (pm(i,j-1)+pm(i,j ))* & & v(i,j ,k+1,nrhs)) tl_dmVde(i,j,k2)=cff*((pm(i,j )+pm(i,j+1))* & & tl_v(i,j+1,k+1,nrhs)- & & (pm(i,j-1)+pm(i,j ))* & & tl_v(i,j ,k+1,nrhs)) END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstrm2,Jendp2 DO i=IstrUm2,Iendp2 dUdz(i,j,k2)=0.0_r8 tl_dUdz(i,j,k2)=0.0_r8 END DO END DO DO j=JstrVm2,Jendp2 DO i=Istrm2,Iendp2 dVdz(i,j,k2)=0.0_r8 tl_dVdz(i,j,k2)=0.0_r8 END DO END DO DO j=Jstrm1,Jendp1 DO i=IstrUm1,Iendp1 UFsx(i,j,k2)=0.0_r8 tl_UFsx(i,j,k2)=0.0_r8 UFse(i,j,k2)=0.0_r8 tl_UFse(i,j,k2)=0.0_r8 END DO END DO DO j=JstrVm1,Jendp1 DO i=Istrm1,Iendp1 VFsx(i,j,k2)=0.0_r8 tl_VFsx(i,j,k2)=0.0_r8 VFse(i,j,k2)=0.0_r8 tl_VFse(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=Jstrm2,Jendp2 DO i=IstrUm2,Iendp2 cff=1.0_r8/(0.5_r8*(z_r(i-1,j,k+1)- & & z_r(i-1,j,k )+ & & z_r(i ,j,k+1)- & & z_r(i ,j,k ))) tl_cff=-cff*cff*(0.5_r8*(tl_z_r(i-1,j,k+1)- & & tl_z_r(i-1,j,k )+ & & tl_z_r(i ,j,k+1)- & & tl_z_r(i ,j,k ))) dUdz(i,j,k2)=cff*(u(i,j,k+1,nrhs)- & & u(i,j,k ,nrhs)) tl_dUdz(i,j,k2)=tl_cff*(u(i,j,k+1,nrhs)- & & u(i,j,k ,nrhs))+ & & cff*(tl_u(i,j,k+1,nrhs)- & & tl_u(i,j,k ,nrhs)) END DO END DO DO j=JstrVm2,Jendp2 DO i=Istrm2,Iendp2 cff=1.0_r8/(0.5_r8*(z_r(i,j-1,k+1)- & & z_r(i,j-1,k )+ & & z_r(i,j ,k+1)- & & z_r(i,j ,k ))) tl_cff=-cff*cff*(0.5_r8*(tl_z_r(i,j-1,k+1)- & & tl_z_r(i,j-1,k )+ & & tl_z_r(i,j ,k+1)- & & tl_z_r(i,j ,k ))) dVdz(i,j,k2)=cff*(v(i,j,k+1,nrhs)- & & v(i,j,k ,nrhs)) tl_dVdz(i,j,k2)=tl_cff*(v(i,j,k+1,nrhs)- & & v(i,j,k ,nrhs))+ & & cff*(tl_v(i,j,k+1,nrhs)- & & tl_v(i,j,k ,nrhs)) END DO END DO END IF ! ! Compute components of the rotated viscous flux (m^4 s-^3/2) along ! geopotential surfaces in the XI- and ETA-directions. ! IF (k.gt.0) THEN DO j=JstrVm2,Jendp1 DO i=IstrUm2,Iendp1 cff1=MIN(dZdx_r(i,j,k1),0.0_r8) cff2=MAX(dZdx_r(i,j,k1),0.0_r8) cff3=MIN(dZde_r(i,j,k1),0.0_r8) cff4=MAX(dZde_r(i,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j,k1)))* & & tl_dZdx_r(i,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j,k1)))* & & tl_dZdx_r(i,j,k1) tl_cff3=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j,k1)))* & & tl_dZde_r(i,j,k1) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j,k1)))* & & tl_dZde_r(i,j,k1) cff=on_r(i,j)*(dnUdx(i,j,k1)- & & 0.5_r8*pn(i,j)* & & (cff1*(dUdz(i ,j,k1)+ & & dUdz(i+1,j,k2))+ & & cff2*(dUdz(i ,j,k2)+ & & dUdz(i+1,j,k1))))- & & om_r(i,j)*(dmVde(i,j,k1)- & & 0.5_r8*pm(i,j)* & & (cff3*(dVdz(i,j ,k1)+ & & dVdz(i,j+1,k2))+ & & cff4*(dVdz(i,j ,k2)+ & & dVdz(i,j+1,k1)))) tl_cff=on_r(i,j)*(tl_dnUdx(i,j,k1)- & & 0.5_r8*pn(i,j)* & & (tl_cff1*(dUdz(i ,j,k1)+ & & dUdz(i+1,j,k2))+ & & cff1*(tl_dUdz(i ,j,k1)+ & & tl_dUdz(i+1,j,k2))+ & & tl_cff2*(dUdz(i ,j,k2)+ & & dUdz(i+1,j,k1))+ & & cff2*(tl_dUdz(i ,j,k2)+ & & tl_dUdz(i+1,j,k1))))- & & om_r(i,j)*(tl_dmVde(i,j,k1)- & & 0.5_r8*pm(i,j)* & & (tl_cff3*(dVdz(i,j ,k1)+ & & dVdz(i,j+1,k2))+ & & cff3*(tl_dVdz(i,j ,k1)+ & & tl_dVdz(i,j+1,k2))+ & & tl_cff4*(dVdz(i,j ,k2)+ & & dVdz(i,j+1,k1))+ & & cff4*(tl_dVdz(i,j ,k2)+ & & tl_dVdz(i,j+1,k1)))) #ifdef MASKING cff=cff*rmask(i,j) tl_cff=tl_cff*rmask(i,j) #endif #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT UFx(i,j)=on_r(i,j)*on_r(i,j)*Uvis3d_r(i,j,k)*cff tl_UFx(i,j)=on_r(i,j)*on_r(i,j)* & & (tl_Uvis3d_r(i,j,k)*cff+ & & Uvis3d_r(i,j,k)*tl_cff) VFe(i,j)=om_r(i,j)*om_r(i,j)*Vvis3d_r(i,j,k)*cff tl_VFe(i,j)=om_r(i,j)*om_r(i,j)* & & (tl_Vvis3d_r(i,j,k)*cff+ & & Vvis3d_r(i,j,k)*tl_cff) # else UFx(i,j)=on_r(i,j)*on_r(i,j)*visc3d_r(i,j,k)*cff tl_UFx(i,j)=on_r(i,j)*on_r(i,j)* & & (tl_visc3d_r(i,j,k)*cff+ & & visc3d_r(i,j,k)*tl_cff) VFe(i,j)=om_r(i,j)*om_r(i,j)*visc3d_r(i,j,k)*cff tl_VFe(i,j)=om_r(i,j)*om_r(i,j)* & & (tl_visc3d_r(i,j,k)*cff+ & & visc3d_r(i,j,k)*tl_cff) # endif #else UFx(i,j)=on_r(i,j)*on_r(i,j)*visc4_r(i,j)*cff tl_UFx(i,j)=on_r(i,j)*on_r(i,j)*visc4_r(i,j)*tl_cff VFe(i,j)=om_r(i,j)*om_r(i,j)*visc4_r(i,j)*cff tl_VFe(i,j)=om_r(i,j)*om_r(i,j)*visc4_r(i,j)*tl_cff #endif END DO END DO DO j=Jstrm1,Jendp2 DO i=Istrm1,Iendp2 pm_p=0.25_r8*(pm(i-1,j-1)+pm(i-1,j)+ & & pm(i ,j-1)+pm(i ,j)) pn_p=0.25_r8*(pn(i-1,j-1)+pn(i-1,j)+ & & pn(i ,j-1)+pn(i ,j)) cff1=MIN(dZdx_p(i,j,k1),0.0_r8) cff2=MAX(dZdx_p(i,j,k1),0.0_r8) cff3=MIN(dZde_p(i,j,k1),0.0_r8) cff4=MAX(dZde_p(i,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j,k1)))* & & tl_dZdx_p(i,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j,k1)))* & & tl_dZdx_p(i,j,k1) tl_cff3=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j,k1)))* & & tl_dZde_p(i,j,k1) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j,k1)))* & & tl_dZde_p(i,j,k1) cff=on_p(i,j)*(dnVdx(i,j,k1)- & & 0.5_r8*pn_p* & & (cff1*(dVdz(i-1,j,k1)+ & & dVdz(i ,j,k2))+ & & cff2*(dVdz(i-1,j,k2)+ & & dVdz(i ,j,k1))))+ & & om_p(i,j)*(dmUde(i,j,k1)- & & 0.5_r8*pm_p* & & (cff3*(dUdz(i,j-1,k1)+ & & dUdz(i,j ,k2))+ & & cff4*(dUdz(i,j-1,k2)+ & & dUdz(i,j ,k1)))) tl_cff=on_p(i,j)*(tl_dnVdx(i,j,k1)- & & 0.5_r8*pn_p* & & (tl_cff1*(dVdz(i-1,j,k1)+ & & dVdz(i ,j,k2))+ & & cff1*(tl_dVdz(i-1,j,k1)+ & & tl_dVdz(i ,j,k2))+ & & tl_cff2*(dVdz(i-1,j,k2)+ & & dVdz(i ,j,k1))+ & & cff2*(tl_dVdz(i-1,j,k2)+ & & tl_dVdz(i ,j,k1))))+ & & om_p(i,j)*(tl_dmUde(i,j,k1)- & & 0.5_r8*pm_p* & & (tl_cff3*(dUdz(i,j-1,k1)+ & & dUdz(i,j ,k2))+ & & cff3*(tl_dUdz(i,j-1,k1)+ & & tl_dUdz(i,j ,k2))+ & & tl_cff4*(dUdz(i,j-1,k2)+ & & dUdz(i,j ,k1))+ & & cff4*(tl_dUdz(i,j-1,k2)+ & & tl_dUdz(i,j ,k1)))) #ifdef MASKING cff=cff*pmask(i,j) tl_cff=tl_cff*pmask(i,j) #endif #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT Uvis_p=0.25_r8* & & (Uvis3d_r(i-1,j-1,k)+Uvis3d_r(i-1,j,k)+ & & Uvis3d_r(i ,j-1,k)+Uvis3d_r(i ,j,k)) tl_Uvis_p=0.25_r8* & & (tl_Uvis3d_r(i-1,j-1,k)+tl_Uvis3d_r(i-1,j,k)+ & & tl_Uvis3d_r(i ,j-1,k)+tl_Uvis3d_r(i ,j,k)) Vvis_p=0.25_r8* & & (Vvis3d_r(i-1,j-1,k)+Vvis3d_r(i-1,j,k)+ & & Vvis3d_r(i ,j-1,k)+Vvis3d_r(i ,j,k)) tl_Vvis_p=0.25_r8* & & (tl_Vvis3d_r(i-1,j-1,k)+tl_Vvis3d_r(i-1,j,k)+ & & tl_Vvis3d_r(i ,j-1,k)+tl_Vvis3d_r(i ,j,k)) UFe(i,j)=om_p(i,j)*om_p(i,j)*Uvis_p*cff tl_UFe(i,j)=om_p(i,j)*om_p(i,j)* & & (tl_Uvis_p*cff+Uvis_p*tl_cff) VFx(i,j)=on_p(i,j)*on_p(i,j)*Vvis_p*cff tl_VFx(i,j)=on_p(i,j)*on_p(i,j)* & & (tl_Vvis_p*cff+Vvis_p*tl_cff) # else visc_p=0.25_r8* & & (visc3d_r(i-1,j-1,k)+visc3d_r(i-1,j,k)+ & & visc3d_r(i ,j-1,k)+visc3d_r(i ,j,k)) tl_visc_p=0.25_r8* & & (tl_visc3d_r(i-1,j-1,k)+tl_visc3d_r(i-1,j,k)+ & & tl_visc3d_r(i ,j-1,k)+tl_visc3d_r(i ,j,k)) UFe(i,j)=om_p(i,j)*om_p(i,j)*visc_p*cff tl_UFe(i,j)=om_p(i,j)*om_p(i,j)* & & (tl_visc_p*cff+visc_p*tl_cff) VFx(i,j)=on_p(i,j)*on_p(i,j)*visc_p*cff tl_VFx(i,j)=on_p(i,j)*on_p(i,j)* & & (tl_visc_p*cff+visc_p*tl_cff) # endif #else UFe(i,j)=om_p(i,j)*om_p(i,j)*visc4_p(i,j)*cff tl_UFe(i,j)=om_p(i,j)*om_p(i,j)*visc4_p(i,j)*tl_cff VFx(i,j)=on_p(i,j)*on_p(i,j)*visc4_p(i,j)*cff tl_VFx(i,j)=on_p(i,j)*on_p(i,j)*visc4_p(i,j)*tl_cff #endif END DO END DO ! ! Compute vertical flux (m^2 s^-3/2) due to sloping terrain-following ! surfaces. ! IF (k.lt.N(ng)) THEN DO j=Jstrm1,Jendp1 DO i=IstrUm1,Iendp1 #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT cff=0.125_r8* & & (Uvis3d_r(i-1,j,k )+Uvis3d_r(i,j,k )+ & & Uvis3d_r(i-1,j,k+1)+Uvis3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_Uvis3d_r(i-1,j,k )+tl_Uvis3d_r(i,j,k )+ & & tl_Uvis3d_r(i-1,j,k+1)+tl_Uvis3d_r(i,j,k+1)) # else cff=0.125_r8* & & (visc3d_r(i-1,j,k )+visc3d_r(i,j,k )+ & & visc3d_r(i-1,j,k+1)+visc3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_visc3d_r(i-1,j,k )+tl_visc3d_r(i,j,k )+ & & tl_visc3d_r(i-1,j,k+1)+tl_visc3d_r(i,j,k+1)) # endif fac1=cff*on_u(i,j) tl_fac1=tl_cff*on_u(i,j) fac2=cff*om_u(i,j) tl_fac2=tl_cff*om_u(i,j) #else cff=0.25_r8*(visc4_r(i-1,j)+visc4_r(i,j)) fac1=cff*on_u(i,j) fac2=cff*om_u(i,j) #endif cff=0.5_r8*(pn(i-1,j)+pn(i,j)) dnUdz=cff*dUdz(i,j,k2) tl_dnUdz=cff*tl_dUdz(i,j,k2) dnVdz=cff*0.25_r8*(dVdz(i-1,j+1,k2)+ & & dVdz(i ,j+1,k2)+ & & dVdz(i-1,j ,k2)+ & & dVdz(i ,j ,k2)) tl_dnVdz=cff*0.25_r8*(tl_dVdz(i-1,j+1,k2)+ & & tl_dVdz(i ,j+1,k2)+ & & tl_dVdz(i-1,j ,k2)+ & & tl_dVdz(i ,j ,k2)) cff=0.5_r8*(pm(i-1,j)+pm(i,j)) dmUdz=cff*dUdz(i,j,k2) tl_dmUdz=cff*tl_dUdz(i,j,k2) dmVdz=cff*0.25_r8*(dVdz(i-1,j+1,k2)+ & & dVdz(i ,j+1,k2)+ & & dVdz(i-1,j ,k2)+ & & dVdz(i ,j ,k2)) tl_dmVdz=cff*0.25_r8*(tl_dVdz(i-1,j+1,k2)+ & & tl_dVdz(i ,j+1,k2)+ & & tl_dVdz(i-1,j ,k2)+ & & tl_dVdz(i ,j ,k2)) cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8) cff2=MIN(dZdx_r(i ,j,k2),0.0_r8) cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8) cff4=MAX(dZdx_r(i ,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i-1,j,k1)))* & & tl_dZdx_r(i-1,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i ,j,k2)))* & & tl_dZdx_r(i ,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_r(i-1,j,k2)))* & & tl_dZdx_r(i-1,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_r(i ,j,k1)))* & & tl_dZdx_r(i ,j,k1) UFsx(i,j,k2)=fac1* & & (cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ & & cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ & & cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ & & cff4*(cff4*dnUdz-dnUdx(i ,j,k1))) tl_UFsx(i,j,k2)=fac1* & & (tl_cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ & & tl_cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ & & tl_cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ & & tl_cff4*(cff4*dnUdz-dnUdx(i ,j,k1))+ & & cff1*(tl_cff1*dnUdz+cff1*tl_dnUdz- & & tl_dnUdx(i-1,j,k1))+ & & cff2*(tl_cff2*dnUdz+cff2*tl_dnUdz- & & tl_dnUdx(i ,j,k2))+ & & cff3*(tl_cff3*dnUdz+cff3*tl_dnUdz- & & tl_dnUdx(i-1,j,k2))+ & & cff4*(tl_cff4*dnUdz+cff4*tl_dnUdz- & & tl_dnUdx(i ,j,k1))) #ifdef VISC_3DCOEF tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ & & tl_fac1* & & (cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ & & cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ & & cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ & & cff4*(cff4*dnUdz-dnUdx(i ,j,k1))) #endif cff1=MIN(dZde_p(i,j ,k1),0.0_r8) cff2=MIN(dZde_p(i,j+1,k2),0.0_r8) cff3=MAX(dZde_p(i,j ,k2),0.0_r8) cff4=MAX(dZde_p(i,j+1,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j ,k1)))* & & tl_dZde_p(i,j ,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j+1,k2)))* & & tl_dZde_p(i,j+1,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j ,k2)))* & & tl_dZde_p(i,j ,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j+1,k1)))* & & tl_dZde_p(i,j+1,k1) UFse(i,j,k2)=fac2* & & (cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ & & cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ & & cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ & & cff4*(cff4*dmUdz-dmUde(i,j+1,k1))) tl_UFse(i,j,k2)=fac2* & & (tl_cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ & & tl_cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ & & tl_cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ & & tl_cff4*(cff4*dmUdz-dmUde(i,j+1,k1))+ & & cff1*(tl_cff1*dmUdz+cff1*tl_dmUdz- & & tl_dmUde(i,j ,k1))+ & & cff2*(tl_cff2*dmUdz+cff2*tl_dmUdz- & & tl_dmUde(i,j+1,k2))+ & & cff3*(tl_cff3*dmUdz+cff3*tl_dmUdz- & & tl_dmUde(i,j ,k2))+ & & cff4*(tl_cff4*dmUdz+cff4*tl_dmUdz- & & tl_dmUde(i,j+1,k1))) #ifdef VISC_3DCOEF tl_UFse(i,j,k2)=tl_UFse(i,j,k2)+ & & tl_fac2* & & (cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ & & cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ & & cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ & & cff4*(cff4*dmUdz-dmUde(i,j+1,k1))) #endif cff1=MIN(dZde_p(i,j ,k1),0.0_r8) cff2=MIN(dZde_p(i,j+1,k2),0.0_r8) cff3=MAX(dZde_p(i,j ,k2),0.0_r8) cff4=MAX(dZde_p(i,j+1,k1),0.0_r8) cff5=MIN(dZdx_p(i,j ,k1),0.0_r8) cff6=MIN(dZdx_p(i,j+1,k2),0.0_r8) cff7=MAX(dZdx_p(i,j ,k2),0.0_r8) cff8=MAX(dZdx_p(i,j+1,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j ,k1)))* & & tl_dZde_p(i,j ,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j+1,k2)))* & & tl_dZde_p(i,j+1,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j ,k2)))* & & tl_dZde_p(i,j ,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j+1,k1)))* & & tl_dZde_p(i,j+1,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j ,k1)))* & & tl_dZdx_p(i,j ,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j+1,k2)))* & & tl_dZdx_p(i,j+1,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j ,k2)))* & & tl_dZdx_p(i,j ,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j+1,k1)))* & & tl_dZdx_p(i,j+1,k1) UFsx(i,j,k2)=UFsx(i,j,k2)+ & & fac1* & & (cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ & & cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ & & cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ & & cff4*(cff8*dnVdz-dnVdx(i,j+1,k1))) tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ & & fac1* & & (tl_cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ & & tl_cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ & & tl_cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ & & tl_cff4*(cff8*dnVdz-dnVdx(i,j+1,k1))+ & & cff1*(tl_cff5*dnVdz+cff5*tl_dnVdz- & & tl_dnVdx(i,j ,k1))+ & & cff2*(tl_cff6*dnVdz+cff6*tl_dnVdz- & & tl_dnVdx(i,j+1,k2))+ & & cff3*(tl_cff7*dnVdz+cff7*tl_dnVdz- & & tl_dnVdx(i,j ,k2))+ & & cff4*(tl_cff8*dnVdz+cff8*tl_dnVdz- & & tl_dnVdx(i,j+1,k1))) #ifdef VISC_3DCOEF tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ & & tl_fac1* & & (cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ & & cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ & & cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ & & cff4*(cff8*dnVdz-dnVdx(i,j+1,k1))) #endif cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8) cff2=MIN(dZdx_r(i ,j,k2),0.0_r8) cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8) cff4=MAX(dZdx_r(i ,j,k1),0.0_r8) cff5=MIN(dZde_r(i-1,j,k1),0.0_r8) cff6=MIN(dZde_r(i ,j,k2),0.0_r8) cff7=MAX(dZde_r(i-1,j,k2),0.0_r8) cff8=MAX(dZde_r(i ,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i-1,j,k1)))* & & tl_dZdx_r(i-1,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i ,j,k2)))* & & tl_dZdx_r(i ,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_r(i-1,j,k2)))* & & tl_dZdx_r(i-1,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_r(i ,j,k1)))* & & tl_dZdx_r(i ,j,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZde_r(i-1,j,k1)))* & & tl_dZde_r(i-1,j,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZde_r(i ,j,k2)))* & & tl_dZde_r(i ,j,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZde_r(i-1,j,k2)))* & & tl_dZde_r(i-1,j,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZde_r(i ,j,k1)))* & & tl_dZde_r(i ,j,k1) UFse(i,j,k2)=UFse(i,j,k2)- & & fac2* & & (cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ & & cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ & & cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ & & cff4*(cff8*dmVdz-dmVde(i ,j,k1))) tl_UFse(i,j,k2)=tl_UFse(i,j,k2)- & & fac2* & & (tl_cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ & & tl_cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ & & tl_cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ & & tl_cff4*(cff8*dmVdz-dmVde(i ,j,k1))+ & & cff1*(tl_cff5*dmVdz+cff5*tl_dmVdz- & & tl_dmVde(i-1,j,k1))+ & & cff2*(tl_cff6*dmVdz+cff6*tl_dmVdz- & & tl_dmVde(i ,j,k2))+ & & cff3*(tl_cff7*dmVdz+cff7*tl_dmVdz- & & tl_dmVde(i-1,j,k2))+ & & cff4*(tl_cff8*dmVdz+cff8*tl_dmVdz- & & tl_dmVde(i ,j,k1))) #ifdef VISC_3DCOEF tl_UFse(i,j,k2)=tl_UFse(i,j,k2)- & & tl_fac2* & & (cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ & & cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ & & cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ & & cff4*(cff8*dmVdz-dmVde(i ,j,k1))) #endif END DO END DO ! DO j=JstrVm1,Jendp1 DO i=Istrm1,Iendp1 #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT cff=0.125_r8* & & (Vvis3d_r(i,j-1,k )+Vvis3d_r(i,j,k )+ & & Vvis3d_r(i,j-1,k+1)+Vvis3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_Vvis3d_r(i,j-1,k )+tl_Vvis3d_r(i,j,k )+ & & tl_Vvis3d_r(i,j-1,k+1)+tl_Vvis3d_r(i,j,k+1)) # else cff=0.125_r8* & & (visc3d_r(i,j-1,k )+visc3d_r(i,j,k )+ & & visc3d_r(i,j-1,k+1)+visc3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_visc3d_r(i,j-1,k )+tl_visc3d_r(i,j,k )+ & & tl_visc3d_r(i,j-1,k+1)+tl_visc3d_r(i,j,k+1)) # endif fac1=cff*on_v(i,j) tl_fac1=tl_cff*on_v(i,j) fac2=cff*om_v(i,j) tl_fac2=tl_cff*om_v(i,j) #else cff=0.25_r8*(visc4_r(i,j-1)+visc4_r(i,j)) fac1=cff*on_v(i,j) fac2=cff*om_v(i,j) #endif cff=0.5_r8*(pn(i,j-1)+pn(i,j)) dnUdz=cff*0.25_r8*(dUdz(i ,j ,k2)+ & & dUdz(i+1,j ,k2)+ & & dUdz(i ,j-1,k2)+ & & dUdz(i+1,j-1,k2)) tl_dnUdz=cff*0.25_r8*(tl_dUdz(i ,j ,k2)+ & & tl_dUdz(i+1,j ,k2)+ & & tl_dUdz(i ,j-1,k2)+ & & tl_dUdz(i+1,j-1,k2)) dnVdz=cff*dVdz(i,j,k2) tl_dnVdz=cff*tl_dVdz(i,j,k2) cff=0.5_r8*(pm(i,j-1)+pm(i,j)) dmUdz=cff*0.25_r8*(dUdz(i ,j ,k2)+ & & dUdz(i+1,j ,k2)+ & & dUdz(i ,j-1,k2)+ & & dUdz(i+1,j-1,k2)) tl_dmUdz=cff*0.25_r8*(tl_dUdz(i ,j ,k2)+ & & tl_dUdz(i+1,j ,k2)+ & & tl_dUdz(i ,j-1,k2)+ & & tl_dUdz(i+1,j-1,k2)) dmVdz=cff*dVdz(i,j,k2) tl_dmVdz=cff*tl_dVdz(i,j,k2) cff1=MIN(dZdx_p(i ,j,k1),0.0_r8) cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8) cff3=MAX(dZdx_p(i ,j,k2),0.0_r8) cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i ,j,k1)))* & & tl_dZdx_p(i ,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i+1,j,k2)))* & & tl_dZdx_p(i+1,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_p(i ,j,k2)))* & & tl_dZdx_p(i ,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_p(i+1,j,k1)))* & & tl_dZdx_p(i+1,j,k1) VFsx(i,j,k2)=fac1* & & (cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ & & cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ & & cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ & & cff4*(cff4*dnVdz-dnVdx(i+1,j,k1))) tl_VFsx(i,j,k2)=fac1* & & (tl_cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ & & tl_cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ & & tl_cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ & & tl_cff4*(cff4*dnVdz-dnVdx(i+1,j,k1))+ & & cff1*(tl_cff1*dnVdz+cff1*tl_dnVdz- & & tl_dnVdx(i ,j,k1))+ & & cff2*(tl_cff2*dnVdz+cff2*tl_dnVdz- & & tl_dnVdx(i+1,j,k2))+ & & cff3*(tl_cff3*dnVdz+cff3*tl_dnVdz- & & tl_dnVdx(i ,j,k2))+ & & cff4*(tl_cff4*dnVdz+cff4*tl_dnVdz- & & tl_dnVdx(i+1,j,k1))) #ifdef VISC_3DCOEF tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)+ & & tl_fac1* & & (cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ & & cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ & & cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ & & cff4*(cff4*dnVdz-dnVdx(i+1,j,k1))) #endif cff1=MIN(dZde_r(i,j-1,k1),0.0_r8) cff2=MIN(dZde_r(i,j ,k2),0.0_r8) cff3=MAX(dZde_r(i,j-1,k2),0.0_r8) cff4=MAX(dZde_r(i,j ,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j-1,k1)))* & & tl_dZde_r(i,j-1,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j ,k2)))* & & tl_dZde_r(i,j ,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j-1,k2)))* & & tl_dZde_r(i,j-1,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j ,k1)))* & & tl_dZde_r(i,j ,k1) VFse(i,j,k2)=fac2* & & (cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ & & cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ & & cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ & & cff4*(cff4*dmVdz-dmVde(i,j ,k1))) tl_VFse(i,j,k2)=fac2* & & (tl_cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ & & tl_cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ & & tl_cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ & & tl_cff4*(cff4*dmVdz-dmVde(i,j ,k1))+ & & cff1*(tl_cff1*dmVdz+cff1*tl_dmVdz- & & tl_dmVde(i,j-1,k1))+ & & cff2*(tl_cff2*dmVdz+cff2*tl_dmVdz- & & tl_dmVde(i,j ,k2))+ & & cff3*(tl_cff3*dmVdz+cff3*tl_dmVdz- & & tl_dmVde(i,j-1,k2))+ & & cff4*(tl_cff4*dmVdz+cff4*tl_dmVdz- & & tl_dmVde(i,j ,k1))) #ifdef VISC_3DCOEF tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ & & tl_fac2* & & (cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ & & cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ & & cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ & & cff4*(cff4*dmVdz-dmVde(i,j ,k1))) #endif cff1=MIN(dZde_r(i,j-1,k1),0.0_r8) cff2=MIN(dZde_r(i,j ,k2),0.0_r8) cff3=MAX(dZde_r(i,j-1,k2),0.0_r8) cff4=MAX(dZde_r(i,j ,k1),0.0_r8) cff5=MIN(dZdx_r(i,j-1,k1),0.0_r8) cff6=MIN(dZdx_r(i,j ,k2),0.0_r8) cff7=MAX(dZdx_r(i,j-1,k2),0.0_r8) cff8=MAX(dZdx_r(i,j ,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j-1,k1)))* & & tl_dZde_r(i,j-1,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j ,k2)))* & & tl_dZde_r(i,j ,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j-1,k2)))* & & tl_dZde_r(i,j-1,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j ,k1)))* & & tl_dZde_r(i,j ,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j-1,k1)))* & & tl_dZdx_r(i,j-1,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j ,k2)))* & & tl_dZdx_r(i,j ,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j-1,k2)))* & & tl_dZdx_r(i,j-1,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j ,k1)))* & & tl_dZdx_r(i,j ,k1) VFsx(i,j,k2)=VFsx(i,j,k2)- & & fac1* & & (cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ & & cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ & & cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ & & cff4*(cff8*dnUdz-dnUdx(i,j ,k1))) tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)- & & fac1* & & (tl_cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ & & tl_cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ & & tl_cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ & & tl_cff4*(cff8*dnUdz-dnUdx(i,j ,k1))+ & & cff1*(tl_cff5*dnUdz+cff5*tl_dnUdz- & & tl_dnUdx(i,j-1,k1))+ & & cff2*(tl_cff6*dnUdz+cff6*tl_dnUdz- & & tl_dnUdx(i,j ,k2))+ & & cff3*(tl_cff7*dnUdz+cff7*tl_dnUdz- & & tl_dnUdx(i,j-1,k2))+ & & cff4*(tl_cff8*dnUdz+cff8*tl_dnUdz- & & tl_dnUdx(i,j ,k1))) #ifdef VISC_3DCOEF tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)- & & tl_fac1* & & (cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ & & cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ & & cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ & & cff4*(cff8*dnUdz-dnUdx(i,j ,k1))) #endif cff1=MIN(dZdx_p(i ,j,k1),0.0_r8) cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8) cff3=MAX(dZdx_p(i ,j,k2),0.0_r8) cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8) cff5=MIN(dZde_p(i ,j,k1),0.0_r8) cff6=MIN(dZde_p(i+1,j,k2),0.0_r8) cff7=MAX(dZde_p(i ,j,k2),0.0_r8) cff8=MAX(dZde_p(i+1,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i ,j,k1)))* & & tl_dZdx_p(i ,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i+1,j,k2)))* & & tl_dZdx_p(i+1,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_p(i ,j,k2)))* & & tl_dZdx_p(i ,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_p(i+1,j,k1)))* & & tl_dZdx_p(i+1,j,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZde_p(i ,j,k1)))* & & tl_dZde_p(i ,j,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZde_p(i+1,j,k2)))* & & tl_dZde_p(i+1,j,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZde_p(i ,j,k2)))* & & tl_dZde_p(i ,j,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZde_p(i+1,j,k1)))* & & tl_dZde_p(i+1,j,k1) VFse(i,j,k2)=VFse(i,j,k2)+ & & fac2* & & (cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ & & cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ & & cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ & & cff4*(cff8*dmUdz-dmUde(i+1,j,k1))) tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ & & fac2* & & (tl_cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ & & tl_cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ & & tl_cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ & & tl_cff4*(cff8*dmUdz-dmUde(i+1,j,k1))+ & & cff1*(tl_cff5*dmUdz+cff5*tl_dmUdz- & & tl_dmUde(i ,j,k1))+ & & cff2*(tl_cff6*dmUdz+cff6*tl_dmUdz- & & tl_dmUde(i+1,j,k2))+ & & cff3*(tl_cff7*dmUdz+cff7*tl_dmUdz- & & tl_dmUde(i ,j,k2))+ & & cff4*(tl_cff8*dmUdz+cff8*tl_dmUdz- & & tl_dmUde(i+1,j,k1))) #ifdef VISC_3DCOEF tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ & & tl_fac2* & & (cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ & & cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ & & cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ & & cff4*(cff8*dmUdz-dmUde(i+1,j,k1))) #endif END DO END DO END IF ! ! Compute first harmonic operator (m s^-3/2). ! DO j=Jstrm1,Jendp1 DO i=IstrUm1,Iendp1 cff=0.125_r8*(pm(i-1,j)+pm(i,j))* & & (pn(i-1,j)+pn(i,j)) cff1=1.0_r8/(0.5_r8*(Hz(i-1,j,k)+Hz(i,j,k))) tl_cff1=-cff1*cff1* & & (0.5_r8*(tl_Hz(i-1,j,k)+tl_Hz(i,j,k))) LapU(i,j,k)=cff*((pn(i-1,j)+pn(i,j))* & (UFx(i,j)-UFx(i-1,j))+ & & (pm(i-1,j)+pm(i,j))* & & (UFe(i,j+1)-UFe(i,j)))+ & & cff1*((UFsx(i,j,k2)+UFse(i,j,k2))- & & (UFsx(i,j,k1)+UFse(i,j,k1))) tl_LapU(i,j,k)=cff*((pn(i-1,j)+pn(i,j))* & (tl_UFx(i,j)-tl_UFx(i-1,j))+ & & (pm(i-1,j)+pm(i,j))* & & (tl_UFe(i,j+1)-tl_UFe(i,j)))+ & & tl_cff1*((UFsx(i,j,k2)+UFse(i,j,k2))- & & (UFsx(i,j,k1)+UFse(i,j,k1)))+ & & cff1*((tl_UFsx(i,j,k2)+tl_UFse(i,j,k2))- & & (tl_UFsx(i,j,k1)+tl_UFse(i,j,k1))) #ifdef MASKING LapU(i,j,k)=LapU(i,j,k)*umask(i,j) tl_LapU(i,j,k)=tl_LapU(i,j,k)*umask(i,j) #endif END DO END DO DO j=JstrVm1,Jendp1 DO i=Istrm1,Iendp1 cff=0.125_r8*(pm(i,j)+pm(i,j-1))* & & (pn(i,j)+pn(i,j-1)) cff1=1.0_r8/(0.5_r8*(Hz(i,j-1,k)+Hz(i,j,k))) tl_cff1=-cff1*cff1* & & (0.5_r8*(tl_Hz(i,j-1,k)+tl_Hz(i,j,k))) LapV(i,j,k)=cff*((pn(i,j-1)+pn(i,j))* & & (VFx(i+1,j)-VFx(i,j))- & & (pm(i,j-1)+pm(i,j))* & & (VFe(i,j)-VFe(i,j-1)))+ & & cff1*((VFsx(i,j,k2)+VFse(i,j,k2))- & & (VFsx(i,j,k1)+VFse(i,j,k1))) tl_LapV(i,j,k)=cff*((pn(i,j-1)+pn(i,j))* & & (tl_VFx(i+1,j)-tl_VFx(i,j))- & & (pm(i,j-1)+pm(i,j))* & & (tl_VFe(i,j)-tl_VFe(i,j-1)))+ & & tl_cff1*((VFsx(i,j,k2)+VFse(i,j,k2))- & & (VFsx(i,j,k1)+VFse(i,j,k1)))+ & & cff1*((tl_VFsx(i,j,k2)+tl_VFse(i,j,k2))- & & (tl_VFsx(i,j,k1)+tl_VFse(i,j,k1))) #ifdef MASKING LapV(i,j,k)=LapV(i,j,k)*vmask(i,j) tl_LapV(i,j,k)=tl_LapV(i,j,k)*vmask(i,j) #endif END DO END DO END IF END DO K_LOOP1 ! ! Apply boundary conditions (closed or gradient; except periodic) ! to the first harmonic operator. ! IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN IF (tl_LBC(iwest,isUvel,ng)%closed) THEN DO k=1,N(ng) DO j=Jstrm1,Jendp1 LapU(IstrU-1,j,k)=0.0_r8 tl_LapU(IstrU-1,j,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO j=Jstrm1,Jendp1 LapU(IstrU-1,j,k)=LapU(IstrU,j,k) tl_LapU(IstrU-1,j,k)=tl_LapU(IstrU,j,k) END DO END DO END IF IF (tl_LBC(iwest,isVvel,ng)%closed) THEN DO k=1,N(ng) DO j=JstrVm1,Jendp1 LapV(Istr-1,j,k)=gamma2(ng)*LapV(Istr,j,k) tl_LapV(Istr-1,j,k)=gamma2(ng)*tl_LapV(Istr,j,k) END DO END DO ELSE DO k=1,N(ng) DO j=JstrVm1,Jendp1 LapV(Istr-1,j,k)=0.0_r8 tl_LapV(Istr-1,j,k)=0.0_r8 END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN IF (tl_LBC(ieast,isUvel,ng)%closed) THEN DO k=1,N(ng) DO j=Jstrm1,Jendp1 LapU(Iend+1,j,k)=0.0_r8 tl_LapU(Iend+1,j,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO j=Jstrm1,Jendp1 LapU(Iend+1,j,k)=LapU(Iend,j,k) tl_LapU(Iend+1,j,k)=tl_LapU(Iend,j,k) END DO END DO END IF IF (tl_LBC(ieast,isVvel,ng)%closed) THEN DO k=1,N(ng) DO j=JstrVm1,Jendp1 LapV(Iend+1,j,k)=gamma2(ng)*LapV(Iend,j,k) tl_LapV(Iend+1,j,k)=gamma2(ng)*tl_LapV(Iend,j,k) END DO END DO ELSE DO k=1,N(ng) DO j=JstrVm1,Jendp1 LapV(Iend+1,j,k)=0.0_r8 tl_LapV(Iend+1,j,k)=0.0_r8 END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN IF (tl_LBC(isouth,isUvel,ng)%closed) THEN DO k=1,N(ng) DO i=IstrUm1,Iendp1 LapU(i,Jstr-1,k)=gamma2(ng)*LapU(i,Jstr,k) tl_LapU(i,Jstr-1,k)=gamma2(ng)*tl_LapU(i,Jstr,k) END DO END DO ELSE DO k=1,N(ng) DO i=IstrUm1,Iendp1 LapU(i,Jstr-1,k)=0.0_r8 tl_LapU(i,Jstr-1,k)=0.0_r8 END DO END DO END IF IF (tl_LBC(isouth,isVvel,ng)%closed) THEN DO k=1,N(ng) DO i=Istrm1,Iendp1 LapV(i,JstrV-1,k)=0.0_r8 tl_LapV(i,JstrV-1,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO i=Istrm1,Iendp1 LapV(i,JstrV-1,k)=LapV(i,JstrV,k) tl_LapV(i,JstrV-1,k)=tl_LapV(i,JstrV,k) END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN IF (tl_LBC(inorth,isUvel,ng)%closed) THEN DO k=1,N(ng) DO i=IstrUm1,Iendp1 LapU(i,Jend+1,k)=gamma2(ng)*LapU(i,Jend,k) tl_LapU(i,Jend+1,k)=gamma2(ng)*tl_LapU(i,Jend,k) END DO END DO ELSE DO k=1,N(ng) DO i=IstrUm1,Iendp1 LapU(i,Jend+1,k)=0.0_r8 tl_LapU(i,Jend+1,k)=0.0_r8 END DO END DO END IF IF (tl_LBC(inorth,isVvel,ng)%closed) THEN DO k=1,N(ng) DO i=Istrm1,Iendp1 LapV(i,Jend+1,k)=0.0_r8 tl_LapV(i,Jend+1,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO i=Istrm1,Iendp1 LapV(i,Jend+1,k)=LapV(i,Jend,k) tl_LapV(i,Jend+1,k)=tl_LapV(i,Jend,k) END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng).or. & & CompositeGrid(iwest ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN DO k=1,N(ng) LapU(Istr ,Jstr-1,k)=0.5_r8* & & (LapU(Istr+1,Jstr-1,k)+ & & LapU(Istr ,Jstr ,k)) tl_LapU(Istr ,Jstr-1,k)=0.5_r8* & & (tl_LapU(Istr+1,Jstr-1,k)+ & & tl_LapU(Istr ,Jstr ,k)) LapV(Istr-1,Jstr ,k)=0.5_r8* & & (LapV(Istr-1,Jstr+1,k)+ & & LapV(Istr ,Jstr ,k)) tl_LapV(Istr-1,Jstr ,k)=0.5_r8* & & (tl_LapV(Istr-1,Jstr+1,k)+ & & tl_LapV(Istr ,Jstr ,k)) END DO END IF END IF IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng).or. & & CompositeGrid(ieast ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%SouthEast_Corner(tile)) THEN DO k=1,N(ng) LapU(Iend+1,Jstr-1,k)=0.5_r8* & & (LapU(Iend ,Jstr-1,k)+ & & LapU(Iend+1,Jstr ,k)) tl_LapU(Iend+1,Jstr-1,k)=0.5_r8* & & (tl_LapU(Iend ,Jstr-1,k)+ & & tl_LapU(Iend+1,Jstr ,k)) LapV(Iend+1,Jstr ,k)=0.5_r8* & & (LapV(Iend ,Jstr ,k)+ & & LapV(Iend+1,Jstr+1,k)) tl_LapV(Iend+1,Jstr ,k)=0.5_r8* & & (tl_LapV(Iend ,Jstr ,k)+ & & tl_LapV(Iend+1,Jstr+1,k)) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng).or. & & CompositeGrid(iwest ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%NorthWest_Corner(tile)) THEN DO k=1,N(ng) LapU(Istr ,Jend+1,k)=0.5_r8* & & (LapU(Istr+1,Jend+1,k)+ & & LapU(Istr ,Jend ,k)) tl_LapU(Istr ,Jend+1,k)=0.5_r8* & & (tl_LapU(Istr+1,Jend+1,k)+ & & tl_LapU(Istr ,Jend ,k)) LapV(Istr-1,Jend+1,k)=0.5_r8* & & (LapV(Istr ,Jend+1,k)+ & & LapV(Istr-1,Jend ,k)) tl_LapV(Istr-1,Jend+1,k)=0.5_r8* & & (tl_LapV(Istr ,Jend+1,k)+ & & tl_LapV(Istr-1,Jend ,k)) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng).or. & & CompositeGrid(ieast ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%NorthEast_Corner(tile)) THEN DO k=1,N(ng) LapU(Iend+1,Jend+1,k)=0.5_r8* & & (LapU(Iend ,Jend+1,k)+ & & LapU(Iend+1,Jend ,k)) tl_LapU(Iend+1,Jend+1,k)=0.5_r8* & & (tl_LapU(Iend ,Jend+1,k)+ & & tl_LapU(Iend+1,Jend ,k)) LapV(Iend+1,Jend+1,k)=0.5_r8* & & (LapV(Iend ,Jend+1,k)+ & & LapV(Iend+1,Jend ,k)) tl_LapV(Iend+1,Jend+1,k)=0.5_r8* & & (tl_LapV(Iend ,Jend+1,k)+ & & tl_LapV(Iend+1,Jend ,k)) END DO END IF END IF ! ! Compute horizontal and vertical gradients associated with the ! second rotated harmonic operator. ! k2=1 K_LOOP2 : DO k=0,N(ng) k1=k2 k2=3-k1 IF (k.lt.N(ng)) THEN ! ! Compute slopes (nondimensional) at RHO- and PSI-points. ! DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) #ifdef MASKING cff=cff*umask(i,j) #endif UFx(i,j)=cff*(z_r(i ,j,k+1)- & & z_r(i-1,j,k+1)) tl_UFx(i,j)=cff*(tl_z_r(i ,j,k+1)- & & tl_z_r(i-1,j,k+1)) END DO END DO DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 cff=0.5_r8*(pn(i,j-1)+pn(i,j)) #ifdef MASKING cff=cff*vmask(i,j) #endif VFe(i,j)=cff*(z_r(i,j ,k+1)- & & z_r(i,j-1,k+1)) tl_VFe(i,j)=cff*(tl_z_r(i,j ,k+1)- & & tl_z_r(i,j-1,k+1)) END DO END DO ! DO j=Jstr,Jend+1 DO i=Istr,Iend+1 dZdx_p(i,j,k2)=0.5_r8*(UFx(i,j-1)+ & & UFx(i,j )) tl_dZdx_p(i,j,k2)=0.5_r8*(tl_UFx(i,j-1)+ & & tl_UFx(i,j )) dZde_p(i,j,k2)=0.5_r8*(VFe(i-1,j)+ & & VFe(i ,j)) tl_dZde_p(i,j,k2)=0.5_r8*(tl_VFe(i-1,j)+ & & tl_VFe(i ,j)) END DO END DO DO j=JstrV-1,Jend DO i=IstrU-1,Iend dZdx_r(i,j,k2)=0.5_r8*(UFx(i ,j)+ & & UFx(i+1,j)) tl_dZdx_r(i,j,k2)=0.5_r8*(tl_UFx(i ,j)+ & & tl_UFx(i+1,j)) dZde_r(i,j,k2)=0.5_r8*(VFe(i,j )+ & & VFe(i,j+1)) tl_dZde_r(i,j,k2)=0.5_r8*(tl_VFe(i,j )+ & & tl_VFe(i,j+1)) END DO END DO ! ! Compute momentum horizontal (m^-1 s^-3/2) and vertical (s^-3/2) ! gradients. ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff=0.5_r8*pm(i,j) #ifdef MASKING cff=cff*rmask(i,j) #endif dnUdx(i,j,k2)=cff*((pn(i ,j)+pn(i+1,j))* & & LapU(i+1,j,k+1)- & & (pn(i-1,j)+pn(i ,j))* & & LapU(i ,j,k+1)) tl_dnUdx(i,j,k2)=cff*((pn(i ,j)+pn(i+1,j))* & & tl_LapU(i+1,j,k+1)- & & (pn(i-1,j)+pn(i ,j))* & & tl_LapU(i ,j,k+1)) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend+1 cff=0.125_r8*(pn(i-1,j )+pn(i,j )+ & & pn(i-1,j-1)+pn(i,j-1)) #ifdef MASKING cff=cff*pmask(i,j) #endif dmUde(i,j,k2)=cff*((pm(i-1,j )+pm(i,j ))* & & LapU(i,j ,k+1)- & & (pm(i-1,j-1)+pm(i,j-1))* & & LapU(i,j-1,k+1)) tl_dmUde(i,j,k2)=cff*((pm(i-1,j )+pm(i,j ))* & & tl_LapU(i,j ,k+1)- & & (pm(i-1,j-1)+pm(i,j-1))* & & tl_LapU(i,j-1,k+1)) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend+1 cff=0.125_r8*(pm(i-1,j )+pm(i,j )+ & & pm(i-1,j-1)+pm(i,j-1)) #ifdef MASKING cff=cff*pmask(i,j) #endif dnVdx(i,j,k2)=cff*((pn(i ,j-1)+pn(i ,j))* & & LapV(i ,j,k+1)- & & (pn(i-1,j-1)+pn(i-1,j))* & & LapV(i-1,j,k+1)) tl_dnVdx(i,j,k2)=cff*((pn(i ,j-1)+pn(i ,j))* & & tl_LapV(i ,j,k+1)- & & (pn(i-1,j-1)+pn(i-1,j))* & & tl_LapV(i-1,j,k+1)) END DO END DO DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff=0.5_r8*pn(i,j) #ifdef MASKING cff=cff*rmask(i,j) #endif dmVde(i,j,k2)=cff*((pm(i,j )+pm(i,j+1))* & & LapV(i,j+1,k+1)- & & (pm(i,j-1)+pm(i,j ))* & & LapV(i,j ,k+1)) tl_dmVde(i,j,k2)=cff*((pm(i,j )+pm(i,j+1))* & & tl_LapV(i,j+1,k+1)- & & (pm(i,j-1)+pm(i,j ))* & & tl_LapV(i,j ,k+1)) END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 dUdz(i,j,k2)=0.0_r8 tl_dUdz(i,j,k2)=0.0_r8 END DO END DO DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 dVdz(i,j,k2)=0.0_r8 tl_dVdz(i,j,k2)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend UFsx(i,j,k2)=0.0_r8 tl_UFsx(i,j,k2)=0.0_r8 UFse(i,j,k2)=0.0_r8 tl_UFse(i,j,k2)=0.0_r8 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend VFsx(i,j,k2)=0.0_r8 tl_VFsx(i,j,k2)=0.0_r8 VFse(i,j,k2)=0.0_r8 tl_VFse(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 cff=1.0_r8/(0.5_r8*(z_r(i-1,j,k+1)- & & z_r(i-1,j,k )+ & & z_r(i ,j,k+1)- & & z_r(i ,j,k ))) tl_cff=-cff*cff*(0.5_r8*(tl_z_r(i-1,j,k+1)- & & tl_z_r(i-1,j,k )+ & & tl_z_r(i ,j,k+1)- & & tl_z_r(i ,j,k ))) dUdz(i,j,k2)=cff*(LapU(i,j,k+1)- & & LapU(i,j,k )) tl_dUdz(i,j,k2)=tl_cff*(LapU(i,j,k+1)- & & LapU(i,j,k ))+ & & cff*(tl_LapU(i,j,k+1)- & & tl_LapU(i,j,k )) END DO END DO DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 cff=1.0_r8/(0.5_r8*(z_r(i,j-1,k+1)- & & z_r(i,j-1,k )+ & & z_r(i,j ,k+1)- & & z_r(i,j ,k ))) tl_cff=-cff*cff*(0.5_r8*(tl_z_r(i,j-1,k+1)- & & tl_z_r(i,j-1,k )+ & & tl_z_r(i,j ,k+1)- & & tl_z_r(i,j ,k ))) dVdz(i,j,k2)=cff*(LapV(i,j,k+1)- & & LapV(i,j,k )) tl_dVdz(i,j,k2)=tl_cff*(LapV(i,j,k+1)- & & LapV(i,j,k ))+ & & cff*(tl_LapV(i,j,k+1)- & & tl_LapV(i,j,k )) END DO END DO END IF ! ! Compute components of the rotated viscous flux (m5/s2) along ! geopotential surfaces in the XI- and ETA-directions. ! IF (k.gt.0) THEN DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff1=MIN(dZdx_r(i,j,k1),0.0_r8) cff2=MAX(dZdx_r(i,j,k1),0.0_r8) cff3=MIN(dZde_r(i,j,k1),0.0_r8) cff4=MAX(dZde_r(i,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j,k1)))* & & tl_dZdx_r(i,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j,k1)))* & & tl_dZdx_r(i,j,k1) tl_cff3=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j,k1)))* & & tl_dZde_r(i,j,k1) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j,k1)))* & & tl_dZde_r(i,j,k1) #ifdef VISC_3DCOEF cff=Hz(i,j,k)* & & (on_r(i,j)*(dnUdx(i,j,k1)- & & 0.5_r8*pn(i,j)* & & (cff1*(dUdz(i ,j,k1)+ & & dUdz(i+1,j,k2))+ & & cff2*(dUdz(i ,j,k2)+ & & dUdz(i+1,j,k1))))- & & om_r(i,j)*(dmVde(i,j,k1)- & & 0.5_r8*pm(i,j)* & & (cff3*(dVdz(i,j ,k1)+ & & dVdz(i,j+1,k2))+ & & cff4*(dVdz(i,j ,k2)+ & & dVdz(i,j+1,k1))))) #else !^ cff=Hz(i,j,k)* & !^ & (on_r(i,j)*(dnUdx(i,j,k1)- & !^ & 0.5_r8*pn(i,j)* & !^ & (cff1*(dUdz(i ,j,k1)+ & !^ & dUdz(i+1,j,k2))+ & !^ & cff2*(dUdz(i ,j,k2)+ & !^ & dUdz(i+1,j,k1))))- & !^ & om_r(i,j)*(dmVde(i,j,k1)- & !^ & 0.5_r8*pm(i,j)* & !^ & (cff3*(dVdz(i,j ,k1)+ & !^ & dVdz(i,j+1,k2))+ & !^ & cff4*(dVdz(i,j ,k2)+ & !^ & dVdz(i,j+1,k1))))) !^ #endif tl_cff=tl_Hz(i,j,k)* & & (on_r(i,j)*(dnUdx(i,j,k1)- & & 0.5_r8*pn(i,j)* & & (cff1*(dUdz(i ,j,k1)+ & & dUdz(i+1,j,k2))+ & & cff2*(dUdz(i ,j,k2)+ & & dUdz(i+1,j,k1))))- & & om_r(i,j)*(dmVde(i,j,k1)- & & 0.5_r8*pm(i,j)* & & (cff3*(dVdz(i,j ,k1)+ & & dVdz(i,j+1,k2))+ & & cff4*(dVdz(i,j ,k2)+ & & dVdz(i,j+1,k1)))))+ & & Hz(i,j,k)* & & (on_r(i,j)*(tl_dnUdx(i,j,k1)- & & 0.5_r8*pn(i,j)* & & (tl_cff1*(dUdz(i ,j,k1)+ & & dUdz(i+1,j,k2))+ & & cff1*(tl_dUdz(i ,j,k1)+ & & tl_dUdz(i+1,j,k2))+ & & tl_cff2*(dUdz(i ,j,k2)+ & & dUdz(i+1,j,k1))+ & & cff2*(tl_dUdz(i ,j,k2)+ & & tl_dUdz(i+1,j,k1))))- & & om_r(i,j)*(tl_dmVde(i,j,k1)- & & 0.5_r8*pm(i,j)* & & (tl_cff3*(dVdz(i,j ,k1)+ & & dVdz(i,j+1,k2))+ & & cff3*(tl_dVdz(i,j ,k1)+ & & tl_dVdz(i,j+1,k2))+ & & tl_cff4*(dVdz(i,j ,k2)+ & & dVdz(i,j+1,k1))+ & & cff4*(tl_dVdz(i,j ,k2)+ & & tl_dVdz(i,j+1,k1))))) #ifdef MASKING # ifdef VISC_3DCOEF cff=cff*rmask(i,j) # else !^ cff=cff*rmask(i,j) !^ # endif tl_cff=tl_cff*rmask(i,j) #endif #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT !^ UFx(i,j)=on_r(i,j)*on_r(i,j)*Uvis3d_r(i,j,k)*cff !^ tl_UFx(i,j)=on_r(i,j)*on_r(i,j)* & & (tl_Uvis3d_r(i,j,k)*cff+ & & Uvis3d_r(i,j,k)*tl_cff) !^ VFe(i,j)=om_r(i,j)*om_r(i,j)*Vvis3d_r(i,j,k)*cff !^ tl_VFe(i,j)=om_r(i,j)*om_r(i,j)* & & (tl_Vvis3d_r(i,j,k)*cff+ & & Vvis3d_r(i,j,k)*tl_cff) # else !^ UFx(i,j)=on_r(i,j)*on_r(i,j)*visc3d_r(i,j,k)*cff !^ tl_UFx(i,j)=on_r(i,j)*on_r(i,j)* & & (tl_visc3d_r(i,j,k)*cff+ & & visc3d_r(i,j,k)*tl_cff) !^ VFe(i,j)=om_r(i,j)*om_r(i,j)*visc3d_r(i,j,k)*cff !^ tl_VFe(i,j)=om_r(i,j)*om_r(i,j)* & & (tl_visc3d_r(i,j,k)*cff+ & & visc3d_r(i,j,k)*tl_cff) # endif #else !^ UFx(i,j)=on_r(i,j)*on_r(i,j)*visc4_r(i,j)*cff !^ tl_UFx(i,j)=on_r(i,j)*on_r(i,j)*visc4_r(i,j)*tl_cff !^ VFe(i,j)=om_r(i,j)*om_r(i,j)*visc4_r(i,j)*cff !^ tl_VFe(i,j)=om_r(i,j)*om_r(i,j)*visc4_r(i,j)*tl_cff #endif END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend+1 pm_p=0.25_r8*(pm(i-1,j-1)+pm(i-1,j)+ & & pm(i ,j-1)+pm(i ,j)) pn_p=0.25_r8*(pn(i-1,j-1)+pn(i-1,j)+ & & pn(i ,j-1)+pn(i ,j)) cff1=MIN(dZdx_p(i,j,k1),0.0_r8) cff2=MAX(dZdx_p(i,j,k1),0.0_r8) cff3=MIN(dZde_p(i,j,k1),0.0_r8) cff4=MAX(dZde_p(i,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j,k1)))* & & tl_dZdx_p(i,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j,k1)))* & & tl_dZdx_p(i,j,k1) tl_cff3=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j,k1)))* & & tl_dZde_p(i,j,k1) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j,k1)))* & & tl_dZde_p(i,j,k1) #ifdef VISC_3DCOEF cff=0.25_r8* & & (Hz(i-1,j ,k)+Hz(i,j ,k)+ & & Hz(i-1,j-1,k)+Hz(i,j-1,k))* & & (on_p(i,j)*(dnVdx(i,j,k1)- & & 0.5_r8*pn_p* & & (cff1*(dVdz(i-1,j,k1)+ & & dVdz(i ,j,k2))+ & & cff2*(dVdz(i-1,j,k2)+ & & dVdz(i ,j,k1))))+ & & om_p(i,j)*(dmUde(i,j,k1)- & & 0.5_r8*pm_p* & & (cff3*(dUdz(i,j-1,k1)+ & & dUdz(i,j ,k2))+ & & cff4*(dUdz(i,j-1,k2)+ & & dUdz(i,j ,k1))))) #else !^ cff=0.25_r8* & !^ & (Hz(i-1,j ,k)+Hz(i,j ,k)+ & !^ & Hz(i-1,j-1,k)+Hz(i,j-1,k))* & !^ & (on_p(i,j)*(dnVdx(i,j,k1)- & !^ & 0.5_r8*pn_p* & !^ & (cff1*(dVdz(i-1,j,k1)+ & !^ & dVdz(i ,j,k2))+ & !^ & cff2*(dVdz(i-1,j,k2)+ & !^ & dVdz(i ,j,k1))))+ & !^ & om_p(i,j)*(dmUde(i,j,k1)- & !^ & 0.5_r8*pm_p* & !^ & (cff3*(dUdz(i,j-1,k1)+ & !^ & dUdz(i,j ,k2))+ & !^ & cff4*(dUdz(i,j-1,k2)+ & !^ & dUdz(i,j ,k1))))) !^ #endif tl_cff=0.25_r8* & & ((tl_Hz(i-1,j ,k)+tl_Hz(i,j ,k)+ & & tl_Hz(i-1,j-1,k)+tl_Hz(i,j-1,k))* & & (on_p(i,j)*(dnVdx(i,j,k1)- & & 0.5_r8*pn_p* & & (cff1*(dVdz(i-1,j,k1)+ & & dVdz(i ,j,k2))+ & & cff2*(dVdz(i-1,j,k2)+ & & dVdz(i ,j,k1))))+ & & om_p(i,j)*(dmUde(i,j,k1)- & & 0.5_r8*pm_p* & & (cff3*(dUdz(i,j-1,k1)+ & & dUdz(i,j ,k2))+ & & cff4*(dUdz(i,j-1,k2)+ & & dUdz(i,j ,k1)))))+ & & (Hz(i-1,j ,k)+Hz(i,j ,k)+ & & Hz(i-1,j-1,k)+Hz(i,j-1,k))* & & (on_p(i,j)*(tl_dnVdx(i,j,k1)- & & 0.5_r8*pn_p* & & (tl_cff1*(dVdz(i-1,j,k1)+ & & dVdz(i ,j,k2))+ & & cff1*(tl_dVdz(i-1,j,k1)+ & & tl_dVdz(i ,j,k2))+ & & tl_cff2*(dVdz(i-1,j,k2)+ & & dVdz(i ,j,k1))+ & & cff2*(tl_dVdz(i-1,j,k2)+ & & tl_dVdz(i ,j,k1))))+ & & om_p(i,j)*(tl_dmUde(i,j,k1)- & & 0.5_r8*pm_p* & & (tl_cff3*(dUdz(i,j-1,k1)+ & & dUdz(i,j ,k2))+ & & cff3*(tl_dUdz(i,j-1,k1)+ & & tl_dUdz(i,j ,k2))+ & & tl_cff4*(dUdz(i,j-1,k2)+ & & dUdz(i,j ,k1))+ & & cff4*(tl_dUdz(i,j-1,k2)+ & & tl_dUdz(i,j ,k1)))))) #ifdef MASKING # ifdef VISC_3DCOEF cff=cff*pmask(i,j) # else !^ cff=cff*pmask(i,j) !^ # endif tl_cff=tl_cff*pmask(i,j) #endif #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT Uvis_p=0.25_r8* & & (Uvis3d_r(i-1,j-1,k)+Uvis3d_r(i-1,j,k)+ & & Uvis3d_r(i ,j-1,k)+Uvis3d_r(i ,j,k)) tl_Uvis_p=0.25_r8* & & (tl_Uvis3d_r(i-1,j-1,k)+tl_Uvis3d_r(i-1,j,k)+ & & tl_Uvis3d_r(i ,j-1,k)+tl_Uvis3d_r(i ,j,k)) Vvis_p=0.25_r8* & & (Vvis3d_r(i-1,j-1,k)+Vvis3d_r(i-1,j,k)+ & & Vvis3d_r(i ,j-1,k)+Vvis3d_r(i ,j,k)) tl_Vvis_p=0.25_r8* & & (tl_Vvis3d_r(i-1,j-1,k)+tl_Vvis3d_r(i-1,j,k)+ & & tl_Vvis3d_r(i ,j-1,k)+tl_Vvis3d_r(i ,j,k)) !^ UFe(i,j)=om_p(i,j)*om_p(i,j)*Uvis_p*cff !^ tl_UFe(i,j)=om_p(i,j)*om_p(i,j)* & & (tl_Uvis_p*cff+Uvis_p*tl_cff) !^ VFx(i,j)=on_p(i,j)*on_p(i,j)*Vvis_p*cff !^ tl_VFx(i,j)=on_p(i,j)*on_p(i,j)* & & (tl_Vvis_p*cff+Vvis_p*tl_cff) # else visc_p=0.25_r8* & & (visc3d_r(i-1,j-1,k)+visc3d_r(i-1,j,k)+ & & visc3d_r(i ,j-1,k)+visc3d_r(i ,j,k)) tl_visc_p=0.25_r8* & & (tl_visc3d_r(i-1,j-1,k)+tl_visc3d_r(i-1,j,k)+ & & tl_visc3d_r(i ,j-1,k)+tl_visc3d_r(i ,j,k)) !^ UFe(i,j)=om_p(i,j)*om_p(i,j)*visc_p*cff !^ tl_UFe(i,j)=om_p(i,j)*om_p(i,j)* & & (tl_visc_p*cff+visc_p*tl_cff) !^ VFx(i,j)=on_p(i,j)*on_p(i,j)*visc_p*cff !^ tl_VFx(i,j)=on_p(i,j)*on_p(i,j)* & & (tl_visc_p*cff+visc_p*tl_cff) # endif #else !^ UFe(i,j)=om_p(i,j)*om_p(i,j)*visc4_p(i,j)*cff !^ tl_UFe(i,j)=om_p(i,j)*om_p(i,j)*visc4_p(i,j)*tl_cff !^ VFx(i,j)=on_p(i,j)*on_p(i,j)*visc4_p(i,j)*cff !^ tl_VFx(i,j)=on_p(i,j)*on_p(i,j)*visc4_p(i,j)*tl_cff #endif END DO END DO ! ! Compute vertical flux (m2/s2) due to sloping terrain-following ! surfaces. ! IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=IstrU,Iend #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT cff=0.125_r8* & & (Uvis3d_r(i-1,j,k )+Uvis3d_r(i,j,k )+ & & Uvis3d_r(i-1,j,k+1)+Uvis3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_Uvis3d_r(i-1,j,k )+tl_Uvis3d_r(i,j,k )+ & & tl_Uvis3d_r(i-1,j,k+1)+tl_Uvis3d_r(i,j,k+1)) # else cff=0.125_r8* & & (visc3d_r(i-1,j,k )+visc3d_r(i,j,k )+ & & visc3d_r(i-1,j,k+1)+visc3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_visc3d_r(i-1,j,k )+tl_visc3d_r(i,j,k )+ & & tl_visc3d_r(i-1,j,k+1)+tl_visc3d_r(i,j,k+1)) # endif fac1=cff*on_u(i,j) tl_fac1=tl_cff*on_u(i,j) fac2=cff*om_u(i,j) tl_fac2=tl_cff*om_u(i,j) #else cff=0.25_r8*(visc4_r(i-1,j)+visc4_r(i,j)) fac1=cff*on_u(i,j) fac2=cff*om_u(i,j) #endif cff=0.5_r8*(pn(i-1,j)+pn(i,j)) dnUdz=cff*dUdz(i,j,k2) tl_dnUdz=cff*tl_dUdz(i,j,k2) dnVdz=cff*0.25_r8*(dVdz(i-1,j+1,k2)+ & & dVdz(i ,j+1,k2)+ & & dVdz(i-1,j ,k2)+ & & dVdz(i ,j ,k2)) tl_dnVdz=cff*0.25_r8*(tl_dVdz(i-1,j+1,k2)+ & & tl_dVdz(i ,j+1,k2)+ & & tl_dVdz(i-1,j ,k2)+ & & tl_dVdz(i ,j ,k2)) cff=0.5_r8*(pm(i-1,j)+pm(i,j)) dmUdz=cff*dUdz(i,j,k2) tl_dmUdz=cff*tl_dUdz(i,j,k2) dmVdz=cff*0.25_r8*(dVdz(i-1,j+1,k2)+ & & dVdz(i ,j+1,k2)+ & & dVdz(i-1,j ,k2)+ & & dVdz(i ,j ,k2)) tl_dmVdz=cff*0.25_r8*(tl_dVdz(i-1,j+1,k2)+ & & tl_dVdz(i ,j+1,k2)+ & & tl_dVdz(i-1,j ,k2)+ & & tl_dVdz(i ,j ,k2)) cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8) cff2=MIN(dZdx_r(i ,j,k2),0.0_r8) cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8) cff4=MAX(dZdx_r(i ,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i-1,j,k1)))* & & tl_dZdx_r(i-1,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i ,j,k2)))* & & tl_dZdx_r(i ,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_r(i-1,j,k2)))* & & tl_dZdx_r(i-1,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_r(i ,j,k1)))* & tl_dZdx_r(i ,j,k1) !^ UFsx(i,j,k2)=fac1* & !^ & (cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ & !^ & cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ & !^ & cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ & !^ & cff4*(cff4*dnUdz-dnUdx(i ,j,k1))) !^ tl_UFsx(i,j,k2)=fac1* & & (tl_cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ & & tl_cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ & & tl_cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ & & tl_cff4*(cff4*dnUdz-dnUdx(i ,j,k1))+ & & cff1*(tl_cff1*dnUdz+cff1*tl_dnUdz- & & tl_dnUdx(i-1,j,k1))+ & & cff2*(tl_cff2*dnUdz+cff2*tl_dnUdz- & & tl_dnUdx(i ,j,k2))+ & & cff3*(tl_cff3*dnUdz+cff3*tl_dnUdz- & & tl_dnUdx(i-1,j,k2))+ & & cff4*(tl_cff4*dnUdz+cff4*tl_dnUdz- & & tl_dnUdx(i ,j,k1))) #ifdef VISC_3DCOEF tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ & & tl_fac1* & & (cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ & & cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ & & cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ & & cff4*(cff4*dnUdz-dnUdx(i ,j,k1))) #endif cff1=MIN(dZde_p(i,j ,k1),0.0_r8) cff2=MIN(dZde_p(i,j+1,k2),0.0_r8) cff3=MAX(dZde_p(i,j ,k2),0.0_r8) cff4=MAX(dZde_p(i,j+1,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j ,k1)))* & & tl_dZde_p(i,j ,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j+1,k2)))* & & tl_dZde_p(i,j+1,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j ,k2)))* & & tl_dZde_p(i,j ,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j+1,k1)))* & tl_dZde_p(i,j+1,k1) !^ UFse(i,j,k2)=fac2* & !^ & (cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ & !^ & cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ & !^ & cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ & !^ & cff4*(cff4*dmUdz-dmUde(i,j+1,k1))) !^ tl_UFse(i,j,k2)=fac2* & & (tl_cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ & & tl_cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ & & tl_cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ & & tl_cff4*(cff4*dmUdz-dmUde(i,j+1,k1))+ & & cff1*(tl_cff1*dmUdz+cff1*tl_dmUdz- & & tl_dmUde(i,j ,k1))+ & & cff2*(tl_cff2*dmUdz+cff2*tl_dmUdz- & & tl_dmUde(i,j+1,k2))+ & & cff3*(tl_cff3*dmUdz+cff3*tl_dmUdz- & & tl_dmUde(i,j ,k2))+ & & cff4*(tl_cff4*dmUdz+cff4*tl_dmUdz- & & tl_dmUde(i,j+1,k1))) #ifdef VISC_3DCOEF tl_UFse(i,j,k2)=tl_UFse(i,j,k2)+ & & tl_fac2* & & (cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ & & cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ & & cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ & & cff4*(cff4*dmUdz-dmUde(i,j+1,k1))) #endif cff1=MIN(dZde_p(i,j ,k1),0.0_r8) cff2=MIN(dZde_p(i,j+1,k2),0.0_r8) cff3=MAX(dZde_p(i,j ,k2),0.0_r8) cff4=MAX(dZde_p(i,j+1,k1),0.0_r8) cff5=MIN(dZdx_p(i,j ,k1),0.0_r8) cff6=MIN(dZdx_p(i,j+1,k2),0.0_r8) cff7=MAX(dZdx_p(i,j ,k2),0.0_r8) cff8=MAX(dZdx_p(i,j+1,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j ,k1)))* & & tl_dZde_p(i,j ,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j+1,k2)))* & & tl_dZde_p(i,j+1,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j ,k2)))* & & tl_dZde_p(i,j ,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j+1,k1)))* & & tl_dZde_p(i,j+1,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j ,k1)))* & & tl_dZdx_p(i,j ,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j+1,k2)))* & & tl_dZdx_p(i,j+1,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j ,k2)))* & & tl_dZdx_p(i,j ,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j+1,k1)))* & & tl_dZdx_p(i,j+1,k1) !^ UFsx(i,j,k2)=UFsx(i,j,k2)+ & !^ & fac1* & !^ & (cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ & !^ & cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ & !^ & cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ & !^ & cff4*(cff8*dnVdz-dnVdx(i,j+1,k1))) !^ tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ & & fac1* & & (tl_cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ & & tl_cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ & & tl_cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ & & tl_cff4*(cff8*dnVdz-dnVdx(i,j+1,k1))+ & & cff1*(tl_cff5*dnVdz+cff5*tl_dnVdz- & & tl_dnVdx(i,j ,k1))+ & & cff2*(tl_cff6*dnVdz+cff6*tl_dnVdz- & & tl_dnVdx(i,j+1,k2))+ & & cff3*(tl_cff7*dnVdz+cff7*tl_dnVdz- & & tl_dnVdx(i,j ,k2))+ & & cff4*(tl_cff8*dnVdz+cff8*tl_dnVdz- & & tl_dnVdx(i,j+1,k1))) #ifdef VISC_3DCOEF tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ & & tl_fac1* & & (cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ & & cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ & & cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ & & cff4*(cff8*dnVdz-dnVdx(i,j+1,k1))) #endif cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8) cff2=MIN(dZdx_r(i ,j,k2),0.0_r8) cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8) cff4=MAX(dZdx_r(i ,j,k1),0.0_r8) cff5=MIN(dZde_r(i-1,j,k1),0.0_r8) cff6=MIN(dZde_r(i ,j,k2),0.0_r8) cff7=MAX(dZde_r(i-1,j,k2),0.0_r8) cff8=MAX(dZde_r(i ,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i-1,j,k1)))* & & tl_dZdx_r(i-1,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i ,j,k2)))* & & tl_dZdx_r(i ,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_r(i-1,j,k2)))* & & tl_dZdx_r(i-1,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_r(i ,j,k1)))* & & tl_dZdx_r(i ,j,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZde_r(i-1,j,k1)))* & & tl_dZde_r(i-1,j,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZde_r(i ,j,k2)))* & & tl_dZde_r(i ,j,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZde_r(i-1,j,k2)))* & & tl_dZde_r(i-1,j,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZde_r(i ,j,k1)))* & & tl_dZde_r(i ,j,k1) !^ UFse(i,j,k2)=UFse(i,j,k2)- & !^ & fac2* & !^ & (cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ & !^ & cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ & !^ & cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ & !^ & cff4*(cff8*dmVdz-dmVde(i ,j,k1))) !^ tl_UFse(i,j,k2)=tl_UFse(i,j,k2)- & & fac2* & & (tl_cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ & & tl_cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ & & tl_cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ & & tl_cff4*(cff8*dmVdz-dmVde(i ,j,k1))+ & & cff1*(tl_cff5*dmVdz+cff5*tl_dmVdz- & & tl_dmVde(i-1,j,k1))+ & & cff2*(tl_cff6*dmVdz+cff6*tl_dmVdz- & & tl_dmVde(i ,j,k2))+ & & cff3*(tl_cff7*dmVdz+cff7*tl_dmVdz- & & tl_dmVde(i-1,j,k2))+ & & cff4*(tl_cff8*dmVdz+cff8*tl_dmVdz- & & tl_dmVde(i ,j,k1))) #ifdef VISC_3DCOEF tl_UFse(i,j,k2)=tl_UFse(i,j,k2)- & & tl_fac2* & & (cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ & & cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ & & cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ & & cff4*(cff8*dmVdz-dmVde(i ,j,k1))) #endif END DO END DO ! DO j=JstrV,Jend DO i=Istr,Iend #ifdef VISC_3DCOEF # ifdef UV_U3ADV_SPLIT cff=0.125_r8* & & (Vvis3d_r(i,j-1,k )+Vvis3d_r(i,j,k )+ & & Vvis3d_r(i,j-1,k+1)+Vvis3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_Vvis3d_r(i,j-1,k )+tl_Vvis3d_r(i,j,k )+ & & tl_Vvis3d_r(i,j-1,k+1)+tl_Vvis3d_r(i,j,k+1)) # else cff=0.125_r8* & & (visc3d_r(i,j-1,k )+visc3d_r(i,j,k )+ & & visc3d_r(i,j-1,k+1)+visc3d_r(i,j,k+1)) tl_cff=0.125_r8* & & (tl_visc3d_r(i,j-1,k )+tl_visc3d_r(i,j,k )+ & & tl_visc3d_r(i,j-1,k+1)+tl_visc3d_r(i,j,k+1)) # endif fac1=cff*on_v(i,j) tl_fac1=tl_cff*on_v(i,j) fac2=cff*om_v(i,j) tl_fac2=tl_cff*om_v(i,j) #else cff=0.25_r8*(visc4_r(i,j-1)+visc4_r(i,j)) fac1=cff*on_v(i,j) fac2=cff*om_v(i,j) #endif cff=0.5_r8*(pn(i,j-1)+pn(i,j)) dnUdz=cff*0.25_r8*(dUdz(i ,j ,k2)+ & & dUdz(i+1,j ,k2)+ & & dUdz(i ,j-1,k2)+ & & dUdz(i+1,j-1,k2)) tl_dnUdz=cff*0.25_r8*(tl_dUdz(i ,j ,k2)+ & & tl_dUdz(i+1,j ,k2)+ & & tl_dUdz(i ,j-1,k2)+ & & tl_dUdz(i+1,j-1,k2)) dnVdz=cff*dVdz(i,j,k2) tl_dnVdz=cff*tl_dVdz(i,j,k2) cff=0.5_r8*(pm(i,j-1)+pm(i,j)) dmUdz=cff*0.25_r8*(dUdz(i ,j ,k2)+ & & dUdz(i+1,j ,k2)+ & & dUdz(i ,j-1,k2)+ & & dUdz(i+1,j-1,k2)) tl_dmUdz=cff*0.25_r8*(tl_dUdz(i ,j ,k2)+ & & tl_dUdz(i+1,j ,k2)+ & & tl_dUdz(i ,j-1,k2)+ & & tl_dUdz(i+1,j-1,k2)) dmVdz=cff*dVdz(i,j,k2) tl_dmVdz=cff*tl_dVdz(i,j,k2) cff1=MIN(dZdx_p(i ,j,k1),0.0_r8) cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8) cff3=MAX(dZdx_p(i ,j,k2),0.0_r8) cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i ,j,k1)))* & & tl_dZdx_p(i ,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i+1,j,k2)))* & & tl_dZdx_p(i+1,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_p(i ,j,k2)))* & & tl_dZdx_p(i ,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_p(i+1,j,k1)))* & & tl_dZdx_p(i+1,j,k1) !^ VFsx(i,j,k2)=fac1* & !^ & (cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ & !^ & cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ & !^ & cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ & !^ & cff4*(cff4*dnVdz-dnVdx(i+1,j,k1))) !^ tl_VFsx(i,j,k2)=fac1* & & (tl_cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ & & tl_cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ & & tl_cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ & & tl_cff4*(cff4*dnVdz-dnVdx(i+1,j,k1))+ & & cff1*(tl_cff1*dnVdz+cff1*tl_dnVdz- & & tl_dnVdx(i ,j,k1))+ & & cff2*(tl_cff2*dnVdz+cff2*tl_dnVdz- & & tl_dnVdx(i+1,j,k2))+ & & cff3*(tl_cff3*dnVdz+cff3*tl_dnVdz- & & tl_dnVdx(i ,j,k2))+ & & cff4*(tl_cff4*dnVdz+cff4*tl_dnVdz- & & tl_dnVdx(i+1,j,k1))) #ifdef VISC_3DCOEF tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)+ & & tl_fac1* & & (cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ & & cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ & & cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ & & cff4*(cff4*dnVdz-dnVdx(i+1,j,k1))) #endif cff1=MIN(dZde_r(i,j-1,k1),0.0_r8) cff2=MIN(dZde_r(i,j ,k2),0.0_r8) cff3=MAX(dZde_r(i,j-1,k2),0.0_r8) cff4=MAX(dZde_r(i,j ,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j-1,k1)))* & & tl_dZde_r(i,j-1,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j ,k2)))* & & tl_dZde_r(i,j ,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j-1,k2)))* & & tl_dZde_r(i,j-1,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j ,k1)))* & & tl_dZde_r(i,j ,k1) !^ VFse(i,j,k2)=fac2* & !^ & (cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ & !^ & cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ & !^ & cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ & !^ & cff4*(cff4*dmVdz-dmVde(i,j ,k1))) !^ tl_VFse(i,j,k2)=fac2* & & (tl_cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ & & tl_cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ & & tl_cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ & & tl_cff4*(cff4*dmVdz-dmVde(i,j ,k1))+ & & cff1*(tl_cff1*dmVdz+cff1*tl_dmVdz- & & tl_dmVde(i,j-1,k1))+ & & cff2*(tl_cff2*dmVdz+cff2*tl_dmVdz- & & tl_dmVde(i,j ,k2))+ & & cff3*(tl_cff3*dmVdz+cff3*tl_dmVdz- & & tl_dmVde(i,j-1,k2))+ & & cff4*(tl_cff4*dmVdz+cff4*tl_dmVdz- & & tl_dmVde(i,j ,k1))) #ifdef VISC_3DCOEF tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ & & tl_fac2* & & (cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ & & cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ & & cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ & & cff4*(cff4*dmVdz-dmVde(i,j ,k1))) #endif cff1=MIN(dZde_r(i,j-1,k1),0.0_r8) cff2=MIN(dZde_r(i,j ,k2),0.0_r8) cff3=MAX(dZde_r(i,j-1,k2),0.0_r8) cff4=MAX(dZde_r(i,j ,k1),0.0_r8) cff5=MIN(dZdx_r(i,j-1,k1),0.0_r8) cff6=MIN(dZdx_r(i,j ,k2),0.0_r8) cff7=MAX(dZdx_r(i,j-1,k2),0.0_r8) cff8=MAX(dZdx_r(i,j ,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j-1,k1)))* & & tl_dZde_r(i,j-1,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j ,k2)))* & & tl_dZde_r(i,j ,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j-1,k2)))* & & tl_dZde_r(i,j-1,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j ,k1)))* & & tl_dZde_r(i,j ,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j-1,k1)))* & & tl_dZdx_r(i,j-1,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j ,k2)))* & & tl_dZdx_r(i,j ,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j-1,k2)))* & & tl_dZdx_r(i,j-1,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j ,k1)))* & & tl_dZdx_r(i,j ,k1) !^ VFsx(i,j,k2)=VFsx(i,j,k2)- & !^ & fac1* & !^ & (cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ & !^ & cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ & !^ & cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ & !^ & cff4*(cff8*dnUdz-dnUdx(i,j ,k1))) !^ tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)- & & fac1* & & (tl_cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ & & tl_cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ & & tl_cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ & & tl_cff4*(cff8*dnUdz-dnUdx(i,j ,k1))+ & & cff1*(tl_cff5*dnUdz+cff5*tl_dnUdz- & & tl_dnUdx(i,j-1,k1))+ & & cff2*(tl_cff6*dnUdz+cff6*tl_dnUdz- & & tl_dnUdx(i,j ,k2))+ & & cff3*(tl_cff7*dnUdz+cff7*tl_dnUdz- & & tl_dnUdx(i,j-1,k2))+ & & cff4*(tl_cff8*dnUdz+cff8*tl_dnUdz- & & tl_dnUdx(i,j ,k1))) #ifdef VISC_3DCOEF tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)- & & tl_fac1* & & (cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ & & cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ & & cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ & & cff4*(cff8*dnUdz-dnUdx(i,j ,k1))) #endif cff1=MIN(dZdx_p(i ,j,k1),0.0_r8) cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8) cff3=MAX(dZdx_p(i ,j,k2),0.0_r8) cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8) cff5=MIN(dZde_p(i ,j,k1),0.0_r8) cff6=MIN(dZde_p(i+1,j,k2),0.0_r8) cff7=MAX(dZde_p(i ,j,k2),0.0_r8) cff8=MAX(dZde_p(i+1,j,k1),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i ,j,k1)))* & & tl_dZdx_p(i ,j,k1) tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i+1,j,k2)))* & & tl_dZdx_p(i+1,j,k2) tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_p(i ,j,k2)))* & & tl_dZdx_p(i ,j,k2) tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_p(i+1,j,k1)))* & & tl_dZdx_p(i+1,j,k1) tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZde_p(i ,j,k1)))* & & tl_dZde_p(i ,j,k1) tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZde_p(i+1,j,k2)))* & & tl_dZde_p(i+1,j,k2) tl_cff7=(0.5_r8+SIGN(0.5_r8, dZde_p(i ,j,k2)))* & & tl_dZde_p(i ,j,k2) tl_cff8=(0.5_r8+SIGN(0.5_r8, dZde_p(i+1,j,k1)))* & & tl_dZde_p(i+1,j,k1) !^ VFse(i,j,k2)=VFse(i,j,k2)+ & !^ & fac2* & !^ & (cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ & !^ & cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ & !^ & cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ & !^ & cff4*(cff8*dmUdz-dmUde(i+1,j,k1))) !^ tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ & & fac2* & & (tl_cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ & & tl_cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ & & tl_cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ & & tl_cff4*(cff8*dmUdz-dmUde(i+1,j,k1))+ & & cff1*(tl_cff5*dmUdz+cff5*tl_dmUdz- & & tl_dmUde(i ,j,k1))+ & & cff2*(tl_cff6*dmUdz+cff6*tl_dmUdz- & & tl_dmUde(i+1,j,k2))+ & & cff3*(tl_cff7*dmUdz+cff7*tl_dmUdz- & & tl_dmUde(i ,j,k2))+ & & cff4*(tl_cff8*dmUdz+cff8*tl_dmUdz- & & tl_dmUde(i+1,j,k1))) #ifdef VISC_3DCOEF tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ & & tl_fac2* & & (cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ & & cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ & & cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ & & cff4*(cff8*dmUdz-dmUde(i+1,j,k1))) #endif END DO END DO END IF ! ! Time-step biharmonic, geopotential viscosity term. Notice that ! momentum at this stage is HzU and HzV and has m2/s units. Add ! contribution for barotropic forcing terms. #ifdef DIAGNOSTICS_UV !! The rotated vertical term cannot be split from the horizontal !! terms because of the 2D/3D momentum coupling. #endif ! DO j=Jstr,Jend DO i=IstrU,Iend cff=dt(ng)*0.25_r8*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j)) !^ cff1=0.5_r8*(pn(i-1,j)+pn(i,j))*(UFx(i,j )-UFx(i-1,j)) !^ tl_cff1=0.5_r8*(pn(i-1,j)+pn(i,j))* & & (tl_UFx(i,j )-tl_UFx(i-1,j)) !^ cff2=0.5_r8*(pm(i-1,j)+pm(i,j))*(UFe(i,j+1)-UFe(i ,j)) !^ tl_cff2=0.5_r8*(pm(i-1,j)+pm(i,j))* & & (tl_UFe(i,j+1)-tl_UFe(i ,j)) !^ cff3=UFsx(i,j,k2)-UFsx(i,j,k1) !^ tl_cff3=tl_UFsx(i,j,k2)-tl_UFsx(i,j,k1) !^ cff4=UFse(i,j,k2)-UFse(i,j,k1) !^ tl_cff4=tl_UFse(i,j,k2)-tl_UFse(i,j,k1) !^ cff5=cff*(cff1+cff2) !^ tl_cff5=cff*(tl_cff1+tl_cff2) !^ cff6=dt(ng)*(cff3+cff4) !^ tl_cff6=dt(ng)*(tl_cff3+tl_cff4) !^ rufrc(i,j)=rufrc(i,j)-cff1-cff2-cff3-cff4 !^ tl_rufrc(i,j)=tl_rufrc(i,j)- & & tl_cff1-tl_cff2-tl_cff3-tl_cff4 !^ u(i,j,k,nnew)=u(i,j,k,nnew)-cff5-cff6 !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)-tl_cff5-tl_cff6 #ifdef DIAGNOSTICS_UV !! DiaRUfrc(i,j,3,M2hvis)=DiaRUfrc(i,j,3,M2hvis)-cff1-cff2- & !! & cff3-cff4 !! DiaRUfrc(i,j,3,M2xvis)=DiaRUfrc(i,j,3,M2xvis)-cff1-cff3 !! DiaRUfrc(i,j,3,M2yvis)=DiaRUfrc(i,j,3,M2yvis)-cff2-cff4 !! DiaU3wrk(i,j,k,M3hvis)=-cff5-cff6 !! DiaU3wrk(i,j,k,M3xvis)=-cff*cff1-dt(ng)*cff3 !! DiaU3wrk(i,j,k,M3yvis)=-cff*cff2-dt(ng)*cff4 #endif END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=dt(ng)*0.25_r8*(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) !^ cff1=0.5_r8*(pn(i,j-1)+pn(i,j))*(VFx(i+1,j)-VFx(i,j )) !^ tl_cff1=0.5_r8*(pn(i,j-1)+pn(i,j))* & & (tl_VFx(i+1,j)-tl_VFx(i,j )) !^ cff2=0.5_r8*(pm(i,j-1)+pm(i,j))*(VFe(i ,j)-VFe(i,j-1)) !^ tl_cff2=0.5_r8*(pm(i,j-1)+pm(i,j))* & & (tl_VFe(i ,j)-tl_VFe(i,j-1)) !^ cff3=VFsx(i,j,k2)-VFsx(i,j,k1) !^ tl_cff3=tl_VFsx(i,j,k2)-tl_VFsx(i,j,k1) !^ cff4=VFse(i,j,k2)-VFse(i,j,k1) !^ tl_cff4=tl_VFse(i,j,k2)-tl_VFse(i,j,k1) !^ cff5=cff*(cff1-cff2) !^ tl_cff5=cff*(tl_cff1-tl_cff2) !^ cff6=dt(ng)*(cff3+cff4) !^ tl_cff6=dt(ng)*(tl_cff3+tl_cff4) !^ rvfrc(i,j)=rvfrc(i,j)-cff1+cff2-cff3-cff4 !^ tl_rvfrc(i,j)=tl_rvfrc(i,j)- & & tl_cff1+tl_cff2-tl_cff3-tl_cff4 !^ v(i,j,k,nnew)=v(i,j,k,nnew)-cff5-cff6 !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)-tl_cff5-tl_cff6 #ifdef DIAGNOSTICS_UV !! DiaRVfrc(i,j,3,M2hvis)=DiaRVfrc(i,j,3,M2hvis)-cff1+cff2- & !! & cff3-cff4 !! DiaRVfrc(i,j,3,M2xvis)=DiaRVfrc(i,j,3,M2xvis)-cff1-cff3 !! DiaRVfrc(i,j,3,M2yvis)=DiaRVfrc(i,j,3,M2yvis)+cff2-cff4 !! DiaV3wrk(i,j,k,M3hvis)=-cff5-cff6 !! DiaV3wrk(i,j,k,M3xvis)=-cff*cff1-dt(ng)*cff3 !! DiaV3wrk(i,j,k,M3yvis)= cff*cff2-dt(ng)*cff4 #endif END DO END DO END IF END DO K_LOOP2 ! RETURN END SUBROUTINE tl_uv3dmix4_geo_tile END MODULE tl_uv3dmix4_mod