!||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| module hmix_del4 !BOP ! !MODULE: hmix_del4 ! !DESCRIPTION: ! This module contains routines for computing biharmonic horizontal ! diffusion of momentum and tracers. ! ! !REVISION HISTORY: ! SVN:$Id: hmix_del4.F90 26603 2011-01-28 23:09:02Z njn01 $ ! !USES: use POP_KindsMod use POP_ErrorMod use POP_FieldMod use POP_GridHorzMod use POP_HaloMod use POP_ReductionsMod use blocks use communicate use distribution use domain_size use domain use constants use grid use broadcast use io use diagnostics use exit_mod use tavg use time_management implicit none private save ! !PUBLIC MEMBER FUNCTIONS: public :: init_del4u, & init_del4t, & hdiffu_del4, & hdifft_del4 !EOP !BOC !----------------------------------------------------------------------- ! ! private module variables ! ! operator coefficients: ! ! DT{N,S,E,W} = {N,S,E,W} coefficients of 5-point stencil for the ! Del**2 operator before b.c.s have been applied ! DU{C,N,S,E,W} = central and {N,S,E,W} coefficients of 5-point ! stencil for the Del**2 operator acting at U points ! (without metric terms that mix U,V) ! DM{C,N,S,E,W} = central and {N,S,E,W} coefficients of 5-point ! stencil for the metric terms that mix U,V ! DUM = central coefficient for metric terms that do not mix U,V ! !----------------------------------------------------------------------- real (r8), dimension (:,:,:), allocatable :: & DTN,DTS,DTE,DTW, & DUC,DUN,DUS,DUE,DUW, & DMC,DMN,DMS,DME,DMW, & DUM, & AHF, &! variable mixing factor for tracer mixing AMF ! variable mixing factor for momentum mixing real (r8) :: & ah, &! horizontal tracer mixing coefficient am ! horizontal momentum mixing coefficient logical (log_kind) :: & lvariable_hmixu, &! spatially varying mixing coeffs lvariable_hmixt ! spatially varying mixing coeffs !EOC !*********************************************************************** contains !*********************************************************************** !BOP ! !IROUTINE: init_del4u ! !INTERFACE: subroutine init_del4u(errorCode) ! !DESCRIPTION: ! This routine calculates the coefficients of the 5-point stencils for ! the biharmonic operator acting on momentum fields and also ! calculates coefficients for all diffusive metric terms. See the ! description under hdiffu for the form of the operator. ! ! !REVISION HISTORY: ! same as module ! ! !OUTPUT PARAMETER: integer (POP_i4), intent(out) :: & errorCode ! returned error code !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer (int_kind) :: & i,j, &! dummy loop indices iblock, &! block index nml_error ! error flag for namelist real (r8), dimension (:,:), allocatable :: & KXU,KYU, &! metric factors DXKX,DYKY,DXKY,DYKX, &! d{x,y}k{x,y} WORK1,WORK2 ! temporary work space logical (log_kind) :: & lauto_hmix, &! flag to internally compute mixing coeff lvariable_hmix ! flag to enable spatially varying mixing namelist /hmix_del4u_nml/ lauto_hmix, lvariable_hmix, am real (r8) :: & amfmin, amfmax ! min max mixing for varible mixing !----------------------------------------------------------------------- ! ! read input namelist to set options ! !----------------------------------------------------------------------- errorCode = POP_Success lauto_hmix = .false. lvariable_hmix = .false. am = c0 if (my_task == master_task) then open (nml_in, file=nml_filename, status='old',iostat=nml_error) if (nml_error /= 0) then nml_error = -1 else nml_error = 1 endif do while (nml_error > 0) read(nml_in, nml=hmix_del4u_nml,iostat=nml_error) end do if (nml_error == 0) close(nml_in) endif call broadcast_scalar(nml_error, master_task) if (nml_error /= 0) then call exit_POP(sigAbort,'ERROR reading hmix_del4u_nml') endif if (my_task == master_task) then write(stdout,blank_fmt) write(stdout,'(a34)') 'Biharmonic momentum mixing options' write(stdout,blank_fmt) !*** !*** automatically set horizontal mixing coefficients !*** if requested !*** if (lauto_hmix) then am = -0.6e20_r8*(1280.0_r8/float(nx_global)) write(stdout,'(a44)') & 'Horizontal viscosity computed automatically:' else write(stdout,'(a33)') 'Using input horizontal viscosity:' endif write(stdout,'(a7,2x,1pe12.5)') ' am =',am lvariable_hmixu = lvariable_hmix if (.not. lvariable_hmixu) then write(stdout,'(a44)') & 'Variable horizontal momentum mixing disabled' endif endif call broadcast_scalar(lvariable_hmixu, master_task) call broadcast_scalar(am, master_task) !----------------------------------------------------------------------- ! ! set spatially variable mixing arrays if requested ! ! this applies only to momentum or tracer mixing ! with del2 or del4 options ! ! functions describing spatial dependence of horizontal mixing ! coefficients: am -> am*AHM ! ! for standard laplacian mixing they scale like (cell area)**0.5 ! (note: these forms assume a global mesh with a grid line along ! the equator, and the mixing coefficients are the set relative ! to the average grid spacing at the equator - for cells of ! this size AMF = AHF = 1.0). ! !----------------------------------------------------------------------- if (lvariable_hmixu) then amfmin = c1 amfmax = c1 allocate(AMF(nx_block,ny_block,nblocks_clinic)) do iblock=1,nblocks_clinic AMF(:,:,iblock) = (UAREA(:,:,iblock)/uarea_equator)**1.5 end do amfmin = POP_GlobalMinval(AMF, POP_distrbClinic, errorCode, CALCU) amfmax = POP_GlobalMaxval(AMF, POP_distrbClinic, errorCode, CALCU) if (my_task == master_task) then write(stdout,'(a37)') 'Variable horizontal viscosity enabled' write(stdout,'(a12,1x,1pe12.5,3x,a9,1x,1pe12.5)') & ' Min AMF =',amfmin,'Max AMF =',amfmax endif call POP_HaloUpdate(AMF, POP_haloClinic, POP_gridHorzLocNECorner,& POP_fieldKindScalar, errorCode, & fillValue = 0.0_POP_r8) if (errorCode /= POP_Success) then call POP_ErrorSet(errorCode, & 'init_del4u: error updating halo for AMF') return endif else !*** allocate AMF temporarily to simplify setup allocate(AMF(nx_block,ny_block,nblocks_clinic)) AMF = c1 endif !----------------------------------------------------------------------- ! ! calculate operator weights ! !----------------------------------------------------------------------- allocate(DUC(nx_block,ny_block,nblocks_clinic), & DUN(nx_block,ny_block,nblocks_clinic), & DUS(nx_block,ny_block,nblocks_clinic), & DUE(nx_block,ny_block,nblocks_clinic), & DUW(nx_block,ny_block,nblocks_clinic), & DMC(nx_block,ny_block,nblocks_clinic), & DMN(nx_block,ny_block,nblocks_clinic), & DMS(nx_block,ny_block,nblocks_clinic), & DME(nx_block,ny_block,nblocks_clinic), & DMW(nx_block,ny_block,nblocks_clinic), & DUM(nx_block,ny_block,nblocks_clinic)) allocate(KXU (nx_block,ny_block), & KYU (nx_block,ny_block), & DXKX (nx_block,ny_block), & DYKY (nx_block,ny_block), & DXKY (nx_block,ny_block), & DYKX (nx_block,ny_block), & WORK1 (nx_block,ny_block), & WORK2 (nx_block,ny_block)) do iblock=1,nblocks_clinic !----------------------------------------------------------------------- ! ! calculate central and {N,S,E,W} coefficients for ! Del**2 (without metric terms) acting on momentum. ! !----------------------------------------------------------------------- WORK1 = HUS(:,:,iblock)/HTE(:,:,iblock) DUS(:,:,iblock) = WORK1*UAREA_R(:,:,iblock) DUN(:,:,iblock) = eoshift(WORK1,dim=2,shift=1)*UAREA_R(:,:,iblock) !*** DUN invalid now in northernmost ghost cell WORK1 = HUW(:,:,iblock)/HTN(:,:,iblock) DUW(:,:,iblock) = WORK1*UAREA_R(:,:,iblock) DUE(:,:,iblock) = eoshift(WORK1,dim=1,shift=1)*UAREA_R(:,:,iblock) !*** DUE invalid now in easternmost ghost cell !----------------------------------------------------------------------- ! ! coefficients for metric terms in Del**2(U) ! and for metric advection terms (KXU,KYU) ! !----------------------------------------------------------------------- KXU = (eoshift(HUW(:,:,iblock),dim=1,shift=1) - & HUW(:,:,iblock))*UAREA_R(:,:,iblock) !*** KXU invalid in easternmost ghost cell KYU = (eoshift(HUS(:,:,iblock),dim=2,shift=1) - & HUS(:,:,iblock))*UAREA_R(:,:,iblock) !*** KYU invalid in northernmost ghost cell WORK1 = (HTE(:,:,iblock) - & eoshift(HTE(:,:,iblock),dim=1,shift=-1))* & TAREA_R(:,:,iblock) ! KXT !*** WORK1 invalid in westernmost ghost cell WORK2 = eoshift(WORK1,dim=1,shift=1) - WORK1 !*** WORK2 invalid in both easternmost and !*** westernmost ghost cell DXKX = p5*(WORK2 + eoshift(WORK2,dim=2,shift=1))*DXUR(:,:,iblock) !*** DXKX invalid in east/west/northernmost ghost cells WORK2 = eoshift(WORK1,dim=2,shift=1) - WORK1 !*** WORK2 invalid in west/northernmost ghost cells DYKX = p5*(WORK2 + eoshift(WORK2,dim=1,shift=1))*DYUR(:,:,iblock) !*** DYKX invalid in east/west/northernmost ghost cells WORK1 = (HTN(:,:,iblock) - & eoshift(HTN(:,:,iblock),dim=2,shift=-1))* & TAREA_R(:,:,iblock) ! KYT !*** WORK1 invalid in southernmost ghost cell WORK2 = eoshift(WORK1,dim=2,shift=1) - WORK1 !*** WORK2 invalid in north/southernmost ghost cells DYKY = p5*(WORK2 + eoshift(WORK2,dim=1,shift=1))*DYUR(:,:,iblock) !*** DYKY invalid in east/north/southernmost ghost cells WORK2 = eoshift(WORK1,dim=1,shift=1) - WORK1 !*** WORK2 invalid in east/southernmost ghost cells DXKY = p5*(WORK2 + eoshift(WORK2,dim=2,shift=1))*DXUR(:,:,iblock) !*** DYKY invalid in east/north/southernmost ghost cells DUM(:,:,iblock) = -(DXKX + DYKY + c2*(KXU**2 + KYU**2)) DMC(:,:,iblock) = DXKY - DYKX !----------------------------------------------------------------------- ! ! calculate central and {N,S,E,W} coefficients for ! metric mixing terms which mix U,V. ! !----------------------------------------------------------------------- DME(:,:,iblock) = c2*KYU/(HTN(:,:,iblock) + & eoshift(HTN(:,:,iblock),dim=1,shift=1)) DMN(:,:,iblock) = -c2*KXU/(HTE(:,:,iblock) + & eoshift(HTE(:,:,iblock),dim=2,shift=1)) end do DUC = -(DUN + DUS + DUE + DUW) ! scalar laplacian DMW = -DME DMS = -DMN !----------------------------------------------------------------------- ! ! free up memory ! !----------------------------------------------------------------------- deallocate(KXU, KYU, & DXKX, DYKY, DXKY, DYKX, & WORK1, WORK2) if (.not. lvariable_hmixu) deallocate(AMF) !----------------------------------------------------------------------- !EOC end subroutine init_del4u !*********************************************************************** !BOP ! !IROUTINE: init_del4t ! !INTERFACE: subroutine init_del4t(errorCode) ! !DESCRIPTION: ! This routine reads parameters for biharmonic tracer mixing and ! calculates the coefficients of the 5-point stencils for ! the biharmonic operator acting on tracer fields. See the hdifft ! routine for a description of the operator. ! ! !REVISION HISTORY: ! same as module ! ! !OUTPUT PARAMETERS: integer (POP_i4), intent(out) :: & errorCode ! returned error code !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer (int_kind) :: & i,j, &! dummy loop indices iblock, &! block index nml_error ! error flag for namelist real (r8), dimension (:,:), allocatable :: & WORK1 ! temporary work space logical (log_kind) :: & lauto_hmix, &! true to automatically determine mixing coeff lvariable_hmix ! true for spatially varying mixing namelist /hmix_del4t_nml/ lauto_hmix, lvariable_hmix, ah real (r8) :: & ahfmin, ahfmax ! min max mixing for varible mixing !----------------------------------------------------------------------- ! ! read input namelist to set options ! !----------------------------------------------------------------------- errorCode = POP_Success lauto_hmix = .false. lvariable_hmix = .false. ah = c0 if (my_task == master_task) then open (nml_in, file=nml_filename, status='old',iostat=nml_error) if (nml_error /= 0) then nml_error = -1 else nml_error = 1 endif do while (nml_error > 0) read(nml_in, nml=hmix_del4t_nml,iostat=nml_error) end do if (nml_error == 0) close(nml_in) endif call broadcast_scalar(nml_error, master_task) if (nml_error /= 0) then call exit_POP(sigAbort,'ERROR reading hmix_del4t_nml') endif if (my_task == master_task) then write(stdout,blank_fmt) write(stdout,'(a32)') 'Biharmonic tracer mixing options' write(stdout,blank_fmt) !*** !*** automatically set horizontal mixing coefficients !*** if requested !*** if (lauto_hmix) then ah = -0.2e20_r8*(1280.0_r8/float(nx_global)) write(stdout,'(a46)') & 'Horizontal diffusivity computed automatically:' else write(stdout,'(a35)') 'Using input horizontal diffusivity:' endif write(stdout,'(a7,2x,1pe12.5)') ' ah =',ah lvariable_hmixt = lvariable_hmix if (.not. lvariable_hmixt) then write(stdout,'(a43)') & 'Variable horizontal tracer mixing disabled' endif endif call broadcast_scalar(lvariable_hmixt, master_task) call broadcast_scalar(ah, master_task) !----------------------------------------------------------------------- ! ! set spatially variable mixing arrays if requested ! ! this applies only to momentum or tracer mixing ! with del2 or del4 options ! ! functions describing spatial dependence of horizontal mixing ! coefficients: ah -> ah*AHF ! ! for standard laplacian mixing they scale like (cell area)**0.5 ! (note: these forms assume a global mesh with a grid line along ! the equator, and the mixing coefficients are the set relative ! to the average grid spacing at the equator - for cells of ! this size AMF = AHF = 1.0). ! !----------------------------------------------------------------------- if (lvariable_hmixt) then ahfmin = c1 ahfmax = c1 allocate(AHF(nx_block,ny_block,nblocks_clinic)) do iblock=1,nblocks_clinic AHF(:,:,iblock) = (TAREA(:,:,iblock)/uarea_equator)**1.5 end do ahfmin = POP_GlobalMinval(AHF, POP_distrbClinic, errorCode, CALCT) ahfmax = POP_GlobalMaxval(AHF, POP_distrbClinic, errorCode, CALCT) if (my_task == master_task) then write(stdout,'(a39)') & 'Variable horizontal diffusivity enabled' write(stdout,'(a12,1x,1pe12.5,3x,a9,1x,1pe12.5)') & ' Min AHF =',ahfmin,'Max AHF =',ahfmax endif call POP_HaloUpdate(AHF, POP_haloClinic, POP_gridHorzLocCenter, & POP_fieldKindScalar, errorCode, & fillValue = 0.0_POP_r8) if (errorCode /= POP_Success) then call POP_ErrorSet(errorCode, & 'init_del4t: error updating halo for AHF') return endif endif !----------------------------------------------------------------------- ! ! calculate {N,S,E,W} coefficients for Del**2 acting on tracer ! fields (for tracers, the central coefficient is calculated as ! minus the sum of these after boundary conditions are applied). ! !----------------------------------------------------------------------- allocate(DTN(nx_block,ny_block,nblocks_clinic), & DTS(nx_block,ny_block,nblocks_clinic), & DTE(nx_block,ny_block,nblocks_clinic), & DTW(nx_block,ny_block,nblocks_clinic)) allocate(WORK1 (nx_block,ny_block)) do iblock=1,nblocks_clinic WORK1 = HTN(:,:,iblock)/HUW(:,:,iblock) DTN(:,:,iblock) = WORK1*TAREA_R(:,:,iblock) DTS(:,:,iblock) = eoshift(WORK1,dim=2,shift=-1)* & TAREA_R(:,:,iblock) WORK1 = HTE(:,:,iblock)/HUS(:,:,iblock) DTE(:,:,iblock) = WORK1*TAREA_R(:,:,iblock) DTW(:,:,iblock) = eoshift(WORK1,dim=1,shift=-1)* & TAREA_R(:,:,iblock) end do !----------------------------------------------------------------------- ! ! free up memory ! !----------------------------------------------------------------------- deallocate(WORK1) !----------------------------------------------------------------------- !EOC end subroutine init_del4t !*********************************************************************** !BOP ! !IROUTINE: hdiffu_del4 ! !INTERFACE: subroutine hdiffu_del4(k,HDUK,HDVK,UMIXK,VMIXK,this_block) ! !DESCRIPTION: ! This routine computes the horizontial diffusion of momentum ! using a biharmonic ($\nabla^4$) operator, where the biharmonic ! operator is implemented using a repeated application of the ! Laplacian operator: ! \begin{equation} ! D_H(u) = \nabla^2(A_M\nabla^2(u)) ! \end{equation} ! where ! \begin{eqnarray} ! \nabla^2(u) & = & \Delta_x\delta_x[\Delta_y\delta_x(u)]/AREA ! + \Delta_y\delta_y[\Delta_x\delta_y(u)]/AREA \\ ! & & - u*[dxkx - dyky + 2(k_x^2 + k_y^2)] ! + 2hy\delta_x(v) - 2k_x\delta_y(v) \nonumber \\ ! \nabla^2(v) & = & \Delta_x\delta_x[\Delta_y\delta_x(v)]/AREA ! + \Delta_y\delta_y[\Delta_x\delta_y(v)]/AREA \\ ! & & - v*[dxkx - dyky + 2(k_x^2 + k_y^2)] ! - 2hy\delta_x(u) + 2k_x\delta_y(u) \nonumber ! \end{eqnarray} ! ! Boundary conditions are not explicitly imposed on ! $\nabla^2(u,v)$ since $u = v = 0$ on the boundaries. ! In this version of the model, the boundary conditions ! on $\nabla^2$ acting on $\nabla^2(u,v)$ are also that ! $\nabla^2(u,v)$ vanishes at land points. ! ! !REVISION HISTORY: ! same as module ! !INPUT PARAMETERS: integer (int_kind), intent(in) :: k ! depth level index real (r8), dimension(nx_block,ny_block), intent(in) :: & UMIXK, &! U velocity at level k and mix time level VMIXK ! V velocity at level k and mix time level type (block), intent(in) :: & this_block ! block info for this sub block ! !OUTPUT PARAMETERS: real (r8), dimension(nx_block,ny_block), intent(out) :: & HDUK, &! Hdiff(Ub) at level k HDVK ! Hdiff(Vb) at level k !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer (int_kind) :: & i,j, &! loop indices bid ! local address of current block real (r8), dimension (nx_block,ny_block) :: & D2UK,D2VK, &! intermediate Del**2 results CC, &! central 5-point weight CN,CS,CE,CW, &! additional weights for partial bottom cells HDIFFCFL ! local hdiff cfl number for diagnostics !----------------------------------------------------------------------- ! ! biharmonic mixing ! !----------------------------------------------------------------------- bid = this_block%local_id !----------------------------------------------------------------------- ! ! calculate Del**2(U,V) without metric terms that mix U,V ! add metric terms that mix U,V, and zero fields at land points ! !----------------------------------------------------------------------- !*** add metric contribution to central coefficient CC = DUC(:,:,bid) + DUM(:,:,bid) D2UK = c0 D2VK = c0 if (partial_bottom_cells) then do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 CN(i,j) = DUN(i,j,bid)*min(DZU(i,j+1,k,bid), & DZU(i,j ,k,bid))/DZU(i,j ,k,bid) CS(i,j) = DUS(i,j,bid)*min(DZU(i,j-1,k,bid), & DZU(i,j ,k,bid))/DZU(i,j ,k,bid) CE(i,j) = DUE(i,j,bid)*min(DZU(i+1,j,k,bid), & DZU(i ,j,k,bid))/DZU(i ,j,k,bid) CW(i,j) = DUW(i,j,bid)*min(DZU(i-1,j,k,bid), & DZU(i ,j,k,bid))/DZU(i ,j,k,bid) end do end do do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 D2UK(i,j) = (CC (i,j )*UMIXK(i ,j ) + & CN (i,j )*UMIXK(i ,j+1) + & CS (i,j )*UMIXK(i ,j-1) + & CE (i,j )*UMIXK(i+1,j ) + & CW (i,j )*UMIXK(i-1,j ))+ & (DMC(i,j,bid)*VMIXK(i ,j ) + & DMN(i,j,bid)*VMIXK(i ,j+1) + & DMS(i,j,bid)*VMIXK(i ,j-1) + & DME(i,j,bid)*VMIXK(i+1,j ) + & DMW(i,j,bid)*VMIXK(i-1,j )) end do end do do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 D2VK(i,j) = (CC (i,j )*VMIXK(i ,j ) + & CN (i,j )*VMIXK(i ,j+1) + & CS (i,j )*VMIXK(i ,j-1) + & CE (i,j )*VMIXK(i+1,j ) + & CW (i,j )*VMIXK(i-1,j ))- & (DMC(i,j,bid)*UMIXK(i ,j ) + & DMN(i,j,bid)*UMIXK(i ,j+1) + & DMS(i,j,bid)*UMIXK(i ,j-1) + & DME(i,j,bid)*UMIXK(i+1,j ) + & DMW(i,j,bid)*UMIXK(i-1,j )) end do end do else ! no partial bottom cells do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 D2UK(i,j) =(CC (i,j )*UMIXK(i ,j ) + & DUN(i,j,bid)*UMIXK(i ,j+1) + & DUS(i,j,bid)*UMIXK(i ,j-1) + & DUE(i,j,bid)*UMIXK(i+1,j ) + & DUW(i,j,bid)*UMIXK(i-1,j ))+ & (DMC(i,j,bid)*VMIXK(i ,j ) + & DMN(i,j,bid)*VMIXK(i ,j+1) + & DMS(i,j,bid)*VMIXK(i ,j-1) + & DME(i,j,bid)*VMIXK(i+1,j ) + & DMW(i,j,bid)*VMIXK(i-1,j )) end do end do do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 D2VK(i,j) =(CC (i,j )*VMIXK(i ,j ) + & DUN(i,j,bid)*VMIXK(i ,j+1) + & DUS(i,j,bid)*VMIXK(i ,j-1) + & DUE(i,j,bid)*VMIXK(i+1,j ) + & DUW(i,j,bid)*VMIXK(i-1,j ))- & (DMC(i,j,bid)*UMIXK(i ,j ) + & DMN(i,j,bid)*UMIXK(i ,j+1) + & DMS(i,j,bid)*UMIXK(i ,j-1) + & DME(i,j,bid)*UMIXK(i+1,j ) + & DMW(i,j,bid)*UMIXK(i-1,j )) end do end do endif ! partial bottom cells if (lvariable_hmixu) then where (k <= KMU(:,:,bid)) D2UK = AMF(:,:,bid)*D2UK D2VK = AMF(:,:,bid)*D2VK elsewhere D2UK = c0 D2VK = c0 end where else where (k > KMU(:,:,bid)) D2UK = c0 D2VK = c0 endwhere endif !----------------------------------------------------------------------- ! ! calculate Del**2(Del**2(U,V)) without metric terms that mix U,V ! add metric terms, and zero fields at land points ! !----------------------------------------------------------------------- HDUK = c0 HDVK = c0 if (partial_bottom_cells) then do j=this_block%jb,this_block%je do i=this_block%ib,this_block%ie HDUK(i,j) = am*((CC (i,j )*D2UK(i ,j ) + & CN (i,j )*D2UK(i ,j+1) + & CS (i,j )*D2UK(i ,j-1) + & CE (i,j )*D2UK(i+1,j ) + & CW (i,j )*D2UK(i-1,j ))+ & (DMC(i,j,bid)*D2VK(i ,j ) + & DMN(i,j,bid)*D2VK(i ,j+1) + & DMS(i,j,bid)*D2VK(i ,j-1) + & DME(i,j,bid)*D2VK(i+1,j ) + & DMW(i,j,bid)*D2VK(i-1,j ))) end do end do do j=this_block%jb,this_block%je do i=this_block%ib,this_block%ie HDVK(i,j) = am*((CC (i,j )*D2VK(i ,j ) + & CN (i,j )*D2VK(i ,j+1) + & CS (i,j )*D2VK(i ,j-1) + & CE (i,j )*D2VK(i+1,j ) + & CW (i,j )*D2VK(i-1,j ))- & (DMC(i,j,bid)*D2UK(i ,j ) + & DMN(i,j,bid)*D2UK(i ,j+1) + & DMS(i,j,bid)*D2UK(i ,j-1) + & DME(i,j,bid)*D2UK(i+1,j ) + & DMW(i,j,bid)*D2UK(i-1,j ))) end do end do else ! no partial bottom cells do j=this_block%jb,this_block%je do i=this_block%ib,this_block%ie HDUK(i,j) = am*((CC (i,j )*D2UK(i ,j ) + & DUN(i,j,bid)*D2UK(i ,j+1) + & DUS(i,j,bid)*D2UK(i ,j-1) + & DUE(i,j,bid)*D2UK(i+1,j ) + & DUW(i,j,bid)*D2UK(i-1,j ))+ & (DMC(i,j,bid)*D2VK(i ,j ) + & DMN(i,j,bid)*D2VK(i ,j+1) + & DMS(i,j,bid)*D2VK(i ,j-1) + & DME(i,j,bid)*D2VK(i+1,j ) + & DMW(i,j,bid)*D2VK(i-1,j ))) end do end do do j=this_block%jb,this_block%je do i=this_block%ib,this_block%ie HDVK(i,j) = am*((CC (i,j )*D2VK(i ,j ) + & DUN(i,j,bid)*D2VK(i ,j+1) + & DUS(i,j,bid)*D2VK(i ,j-1) + & DUE(i,j,bid)*D2VK(i+1,j ) + & DUW(i,j,bid)*D2VK(i-1,j ))- & (DMC(i,j,bid)*D2UK(i ,j ) + & DMN(i,j,bid)*D2UK(i ,j+1) + & DMS(i,j,bid)*D2UK(i ,j-1) + & DME(i,j,bid)*D2UK(i+1,j ) + & DMW(i,j,bid)*D2UK(i-1,j ))) end do end do endif ! partial bottom cells where (k > KMU(:,:,bid)) HDUK = c0 HDVK = c0 endwhere !----------------------------------------------------------------------- ! ! compute cfl diagnostics if it is time ! !----------------------------------------------------------------------- if (ldiag_cfl) then if (lvariable_hmixu) then HDIFFCFL = merge(-c16*am*AMF(:,:,bid)* & (DXUR(:,:,bid)**2 + DYUR(:,:,bid)**2)**2, & c0, KMU(:,:,bid) > k) else HDIFFCFL = merge(-c16*am* & (DXUR(:,:,bid)**2 + DYUR(:,:,bid)**2)**2, & c0, KMU(:,:,bid) > k) endif HDIFFCFL = abs(HDIFFCFL) call cfl_hdiff(k,bid,HDIFFCFL,2,this_block) endif !----------------------------------------------------------------------- !EOC end subroutine hdiffu_del4 !*********************************************************************** !BOP ! !IROUTINE: hdifft_del4 ! !INTERFACE: subroutine hdifft_del4(k,HDTK,TMIX,tavg_HDIFE_TRACER,tavg_HDIFN_TRACER,this_block) ! !DESCRIPTION: ! This routine computes the horizontial diffusion of tracers ! using a biharmonic ($\nabla^4$) operator, where the biharmonic ! operator is implemented using a repeated application of the ! Laplacian operator: ! \begin{equation} ! D_H(\phi) = \nabla^2(A_H\nabla^2(\phi)) ! \end{equation} ! with ! \begin{equation} ! \nabla^2(\phi) = \Delta_x\delta_x[\Delta_y\delta_x(\phi)]/AREA ! + \Delta_y\delta_y[\Delta_x\delta_y(\phi)]/AREA ! \end{equation} ! ! The boundary conditions are the same on both ! applications of the $\nabla^2$ operator: the gradient of both ! $T$ and $\nabla^2(T)$ vanishes across lateral boundaries. ! ! !REVISION HISTORY: ! same as module ! !INPUT PARAMETERS: integer (int_kind), intent(in) :: k ! depth level index real (r8), dimension(nx_block,ny_block,km,nt), intent(in) :: & TMIX ! tracers at mix time level integer (int_kind), dimension(nt), intent(in) :: & tavg_HDIFE_TRACER, &! tavg id for east face diffusive flux of tracer tavg_HDIFN_TRACER ! tavg id for north face diffusive flux of tracer type (block), intent(in) :: & this_block ! block info for this sub block ! !OUTPUT PARAMETERS: real (r8), dimension(nx_block,ny_block,nt) :: & HDTK ! HDIFF(T) for tracer n at level k !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer (int_kind) :: & i,j,n, &! dummy loop indices bid ! local block address real (r8), dimension(nx_block,ny_block) :: & D2TK, &! intermediate Del**2 result CC,CN,CS,CE,CW, &! five point stencil coefficients WORK, &! temp array for tavg quantities HDIFFCFL ! local hdiff cfl number for diagnostics !----------------------------------------------------------------------- ! ! biharmonic mixing ! !----------------------------------------------------------------------- bid = this_block%local_id !----------------------------------------------------------------------- ! ! implement boundary conditions by setting ! stencil coefficients to zero at land points. ! !----------------------------------------------------------------------- if (partial_bottom_cells) then CN = c0 CS = c0 CE = c0 CW = c0 do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 CN(i,j) = DTN(i,j,bid)*min(DZT(i,j ,k,bid), & DZT(i,j+1,k,bid))/DZT(i,j ,k,bid) CS(i,j) = DTS(i,j,bid)*min(DZT(i,j ,k,bid), & DZT(i,j-1,k,bid))/DZT(i,j ,k,bid) CE(i,j) = DTE(i,j,bid)*min(DZT(i ,j,k,bid), & DZT(i+1,j,k,bid))/DZT(i ,j,k,bid) CW(i,j) = DTW(i,j,bid)*min(DZT(i ,j,k,bid), & DZT(i-1,j,k,bid))/DZT(i ,j,k,bid) end do end do where (k > KMT(:,:,bid) .or. k > KMTN(:,:,bid)) CN = c0 where (k > KMT(:,:,bid) .or. k > KMTS(:,:,bid)) CS = c0 where (k > KMT(:,:,bid) .or. k > KMTE(:,:,bid)) CE = c0 where (k > KMT(:,:,bid) .or. k > KMTW(:,:,bid)) CW = c0 else CN = merge(DTN(:,:,bid), c0, (k <= KMTN(:,:,bid)) .and. & (k <= KMT (:,:,bid))) CS = merge(DTS(:,:,bid), c0, (k <= KMTS(:,:,bid)) .and. & (k <= KMT (:,:,bid))) CE = merge(DTE(:,:,bid), c0, (k <= KMTE(:,:,bid)) .and. & (k <= KMT (:,:,bid))) CW = merge(DTW(:,:,bid), c0, (k <= KMTW(:,:,bid)) .and. & (k <= KMT (:,:,bid))) endif CC = -(CN + CS + CE + CW) ! central coefficient WORK = c0 do n = 1,nt !----------------------------------------------------------------------- ! ! calculate Del**2(T) ! !----------------------------------------------------------------------- if (lvariable_hmixt) then do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 D2TK(i,j) = AHF(i,j,bid)* & (CC(i,j)*TMIX(i ,j ,k,n) + & CN(i,j)*TMIX(i ,j+1,k,n) + & CS(i,j)*TMIX(i ,j-1,k,n) + & CE(i,j)*TMIX(i+1,j ,k,n) + & CW(i,j)*TMIX(i-1,j ,k,n)) end do end do else do j=this_block%jb-1,this_block%je+1 do i=this_block%ib-1,this_block%ie+1 D2TK(i,j) = CC(i,j)*TMIX(i ,j ,k,n) + & CN(i,j)*TMIX(i ,j+1,k,n) + & CS(i,j)*TMIX(i ,j-1,k,n) + & CE(i,j)*TMIX(i+1,j ,k,n) + & CW(i,j)*TMIX(i-1,j ,k,n) end do end do endif !----------------------------------------------------------------------- ! ! calculate Del**2(Del**2(T)) ! multiply by diffusivity ! !----------------------------------------------------------------------- HDTK(:,:,n) = c0 do j=this_block%jb,this_block%je do i=this_block%ib,this_block%ie HDTK(i,j,n) = ah*(CC(i,j)*D2TK(i ,j ) + & CN(i,j)*D2TK(i ,j+1) + & CS(i,j)*D2TK(i ,j-1) + & CE(i,j)*D2TK(i+1,j ) + & CW(i,j)*D2TK(i-1,j )) end do end do if (mix_pass /= 1) then if (accumulate_tavg_now(tavg_HDIFE_TRACER(n))) then do j=this_block%jb,this_block%je do i=this_block%ib,this_block%ie WORK(i,j) = ah*CE(i,j)*(D2TK(i+1,j)-D2TK(i,j)) enddo enddo call accumulate_tavg_field(WORK,tavg_HDIFE_TRACER(n),bid,k) endif if (accumulate_tavg_now(tavg_HDIFN_TRACER(n))) then do j=this_block%jb,this_block%je do i=this_block%ib,this_block%ie WORK(i,j) = ah*CN(i,j)*(D2TK(i,j+1)-D2TK(i,j)) enddo enddo call accumulate_tavg_field(WORK,tavg_HDIFN_TRACER(n),bid,k) endif endif enddo !----------------------------------------------------------------------- ! ! compute cfl diagnostics if it is time ! !----------------------------------------------------------------------- if (ldiag_cfl) then if (lvariable_hmixt) then HDIFFCFL = merge(-c16*ah*AHF(:,:,bid)* & (DXTR(:,:,bid)**2 + DYTR(:,:,bid)**2)**2, & c0, KMT(:,:,bid) > k) else HDIFFCFL = merge(-c16*ah* & (DXTR(:,:,bid)**2 + DYTR(:,:,bid)**2)**2, & c0, KMT(:,:,bid) > k) endif HDIFFCFL = abs(HDIFFCFL) call cfl_hdiff(k,bid,HDIFFCFL,1,this_block) endif !----------------------------------------------------------------------- !EOC end subroutine hdifft_del4 !*********************************************************************** end module hmix_del4 !|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||