MODULE ldfdyn !!====================================================================== !! *** MODULE ldfdyn *** !! Ocean physics: lateral viscosity coefficient !!===================================================================== !! History : OPA ! 1997-07 (G. Madec) multi dimensional coefficients !! NEMO 1.0 ! 2002-09 (G. Madec) F90: Free form and module !! 3.7 ! 2014-01 (F. Lemarie, G. Madec) restructuration/simplification of ahm specification, !! ! add velocity dependent coefficient and optional read in file !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! ldf_dyn_init : initialization, namelist read, and parameters control !! ldf_dyn : update lateral eddy viscosity coefficients at each time step !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE ldfslp ! lateral diffusion: slopes of mixing orientation USE ldfc1d_c2d ! lateral diffusion: 1D and 2D cases ! USE in_out_manager ! I/O manager USE iom ! I/O module for ehanced bottom friction file USE timing ! Timing USE lib_mpp ! distribued memory computing library USE lbclnk ! ocean lateral boundary conditions (or mpp link) IMPLICIT NONE PRIVATE PUBLIC ldf_dyn_init ! called by nemogcm.F90 PUBLIC ldf_dyn ! called by step.F90 ! !!* Namelist namdyn_ldf : lateral mixing on momentum * LOGICAL , PUBLIC :: ln_dynldf_OFF !: No operator (i.e. no explicit diffusion) LOGICAL , PUBLIC :: ln_dynldf_lap !: laplacian operator LOGICAL , PUBLIC :: ln_dynldf_blp !: bilaplacian operator LOGICAL , PUBLIC :: ln_dynldf_lev !: iso-level direction LOGICAL , PUBLIC :: ln_dynldf_hor !: horizontal (geopotential) direction ! LOGICAL , PUBLIC :: ln_dynldf_iso !: iso-neutral direction (see ldfslp) INTEGER , PUBLIC :: nn_ahm_ijk_t !: choice of time & space variations of the lateral eddy viscosity coef. ! ! time invariant coefficients: aht = 1/2 Ud*Ld (lap case) ! ! bht = 1/12 Ud*Ld^3 (blp case) REAL(wp), PUBLIC :: rn_Uv !: lateral viscous velocity [m/s] REAL(wp), PUBLIC :: rn_Lv !: lateral viscous length [m] ! ! Smagorinsky viscosity (nn_ahm_ijk_t = 32) REAL(wp), PUBLIC :: rn_csmc !: Smagorinsky constant of proportionality REAL(wp), PUBLIC :: rn_minfac !: Multiplicative factor of theorectical minimum Smagorinsky viscosity REAL(wp), PUBLIC :: rn_maxfac !: Multiplicative factor of theorectical maximum Smagorinsky viscosity ! ! iso-neutral laplacian (ln_dynldf_lap=ln_dynldf_iso=T) REAL(wp), PUBLIC :: rn_ahm_b !: lateral laplacian background eddy viscosity [m2/s] ! !!* Parameter to control the type of lateral viscous operator INTEGER, PARAMETER, PUBLIC :: np_ERROR =-10 !: error in setting the operator INTEGER, PARAMETER, PUBLIC :: np_no_ldf = 00 !: without operator (i.e. no lateral viscous trend) ! !! laplacian ! bilaplacian ! INTEGER, PARAMETER, PUBLIC :: np_lap = 10 , np_blp = 20 !: iso-level operator INTEGER, PARAMETER, PUBLIC :: np_lap_i = 11 !: iso-neutral or geopotential operator ! INTEGER , PUBLIC :: nldf_dyn !: type of lateral diffusion used defined from ln_dynldf_... (namlist logicals) LOGICAL , PUBLIC :: l_ldfdyn_time !: flag for time variation of the lateral eddy viscosity coef. REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ahmt, ahmf !: eddy viscosity coef. at T- and F-points [m2/s or m4/s] REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dtensq !: horizontal tension squared (Smagorinsky only) REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dshesq !: horizontal shearing strain squared (Smagorinsky only) REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: esqt, esqf !: Square of the local gridscale (e1e2/(e1+e2))**2 REAL(wp) :: r1_2 = 0.5_wp ! =1/2 REAL(wp) :: r1_4 = 0.25_wp ! =1/4 REAL(wp) :: r1_8 = 0.125_wp ! =1/8 REAL(wp) :: r1_12 = 1._wp / 12._wp ! =1/12 REAL(wp) :: r1_288 = 1._wp / 288._wp ! =1/( 12^2 * 2 ) !! * Substitutions # include "do_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE ldf_dyn_init !!---------------------------------------------------------------------- !! *** ROUTINE ldf_dyn_init *** !! !! ** Purpose : set the horizontal ocean dynamics physics !! !! ** Method : the eddy viscosity coef. specification depends on: !! - the operator: !! ln_dynldf_lap = T laplacian operator !! ln_dynldf_blp = T bilaplacian operator !! - the parameter nn_ahm_ijk_t: !! nn_ahm_ijk_t = 0 => = constant !! = 10 => = F(z) : = constant with a reduction of 1/4 with depth !! =-20 => = F(i,j) = shape read in 'eddy_viscosity.nc' file !! = 20 = F(i,j) = F(e1,e2) or F(e1^3,e2^3) (lap or bilap case) !! =-30 => = F(i,j,k) = shape read in 'eddy_viscosity.nc' file !! = 30 = F(i,j,k) = 2D (case 20) + decrease with depth (case 10) !! = 31 = F(i,j,k,t) = F(local velocity) ( |u|e /12 laplacian operator !! or |u|e^3/12 bilaplacian operator ) !! = 32 = F(i,j,k,t) = F(local deformation rate and gridscale) (D and L) (Smagorinsky) !! ( L^2|D| laplacian operator !! or L^4|D|/8 bilaplacian operator ) !!---------------------------------------------------------------------- INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ioptio, ierr, inum, ios, inn ! local integer REAL(wp) :: zah0, zah_max, zUfac ! local scalar CHARACTER(len=5) :: cl_Units ! units (m2/s or m4/s) !! NAMELIST/namdyn_ldf/ ln_dynldf_OFF, ln_dynldf_lap, ln_dynldf_blp, & ! type of operator & ln_dynldf_lev, ln_dynldf_hor, ln_dynldf_iso, & ! acting direction of the operator & nn_ahm_ijk_t , rn_Uv , rn_Lv, rn_ahm_b, & ! lateral eddy coefficient & rn_csmc , rn_minfac , rn_maxfac ! Smagorinsky settings !!---------------------------------------------------------------------- ! READ ( numnam_ref, namdyn_ldf, IOSTAT = ios, ERR = 901) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_ldf in reference namelist' ) READ ( numnam_cfg, namdyn_ldf, IOSTAT = ios, ERR = 902 ) 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_ldf in configuration namelist' ) IF(lwm) WRITE ( numond, namdyn_ldf ) IF(lwp) THEN ! Parameter print WRITE(numout,*) WRITE(numout,*) 'ldf_dyn : lateral momentum physics' WRITE(numout,*) '~~~~~~~' WRITE(numout,*) ' Namelist namdyn_ldf : set lateral mixing parameters' ! WRITE(numout,*) ' type :' WRITE(numout,*) ' no explicit diffusion ln_dynldf_OFF = ', ln_dynldf_OFF WRITE(numout,*) ' laplacian operator ln_dynldf_lap = ', ln_dynldf_lap WRITE(numout,*) ' bilaplacian operator ln_dynldf_blp = ', ln_dynldf_blp ! WRITE(numout,*) ' direction of action :' WRITE(numout,*) ' iso-level ln_dynldf_lev = ', ln_dynldf_lev WRITE(numout,*) ' horizontal (geopotential) ln_dynldf_hor = ', ln_dynldf_hor WRITE(numout,*) ' iso-neutral ln_dynldf_iso = ', ln_dynldf_iso ! WRITE(numout,*) ' coefficients :' WRITE(numout,*) ' type of time-space variation nn_ahm_ijk_t = ', nn_ahm_ijk_t WRITE(numout,*) ' lateral viscous velocity (if cst) rn_Uv = ', rn_Uv, ' m/s' WRITE(numout,*) ' lateral viscous length (if cst) rn_Lv = ', rn_Lv, ' m' WRITE(numout,*) ' background viscosity (iso-lap case) rn_ahm_b = ', rn_ahm_b, ' m2/s' ! WRITE(numout,*) ' Smagorinsky settings (nn_ahm_ijk_t = 32) :' WRITE(numout,*) ' Smagorinsky coefficient rn_csmc = ', rn_csmc WRITE(numout,*) ' factor multiplier for eddy visc.' WRITE(numout,*) ' lower limit (default 1.0) rn_minfac = ', rn_minfac WRITE(numout,*) ' upper limit (default 1.0) rn_maxfac = ', rn_maxfac ENDIF ! ! !== type of lateral operator used ==! (set nldf_dyn) ! !=====================================! ! nldf_dyn = np_ERROR ioptio = 0 IF( ln_dynldf_OFF ) THEN ; nldf_dyn = np_no_ldf ; ioptio = ioptio + 1 ; ENDIF IF( ln_dynldf_lap ) THEN ; ioptio = ioptio + 1 ; ENDIF IF( ln_dynldf_blp ) THEN ; ioptio = ioptio + 1 ; ENDIF IF( ioptio /= 1 ) CALL ctl_stop( 'dyn_ldf_init: use ONE of the 3 operator options (NONE/lap/blp)' ) ! IF(.NOT.ln_dynldf_OFF ) THEN !== direction ==>> type of operator ==! ioptio = 0 IF( ln_dynldf_lev ) ioptio = ioptio + 1 IF( ln_dynldf_hor ) ioptio = ioptio + 1 IF( ln_dynldf_iso ) ioptio = ioptio + 1 IF( ioptio /= 1 ) CALL ctl_stop( 'dyn_ldf_init: use ONE of the 3 direction options (level/hor/iso)' ) ! ! ! Set nldf_dyn, the type of lateral diffusion, from ln_dynldf_... logicals ierr = 0 IF( ln_dynldf_lap ) THEN ! laplacian operator IF( ln_zco ) THEN ! z-coordinate IF ( ln_dynldf_lev ) nldf_dyn = np_lap ! iso-level = horizontal (no rotation) IF ( ln_dynldf_hor ) nldf_dyn = np_lap ! iso-level = horizontal (no rotation) IF ( ln_dynldf_iso ) nldf_dyn = np_lap_i ! iso-neutral ( rotation) ENDIF IF( ln_zps ) THEN ! z-coordinate with partial step IF ( ln_dynldf_lev ) nldf_dyn = np_lap ! iso-level (no rotation) IF ( ln_dynldf_hor ) nldf_dyn = np_lap ! iso-level (no rotation) IF ( ln_dynldf_iso ) nldf_dyn = np_lap_i ! iso-neutral ( rotation) ENDIF IF( ln_sco ) THEN ! s-coordinate IF ( ln_dynldf_lev ) nldf_dyn = np_lap ! iso-level = horizontal (no rotation) IF ( ln_dynldf_hor ) nldf_dyn = np_lap_i ! horizontal ( rotation) IF ( ln_dynldf_iso ) nldf_dyn = np_lap_i ! iso-neutral ( rotation) ENDIF ENDIF ! IF( ln_dynldf_blp ) THEN ! bilaplacian operator IF( ln_zco ) THEN ! z-coordinate IF( ln_dynldf_lev ) nldf_dyn = np_blp ! iso-level = horizontal (no rotation) IF( ln_dynldf_hor ) nldf_dyn = np_blp ! iso-level = horizontal (no rotation) IF( ln_dynldf_iso ) ierr = 2 ! iso-neutral ( rotation) ENDIF IF( ln_zps ) THEN ! z-coordinate with partial step IF( ln_dynldf_lev ) nldf_dyn = np_blp ! iso-level (no rotation) IF( ln_dynldf_hor ) nldf_dyn = np_blp ! iso-level (no rotation) IF( ln_dynldf_iso ) ierr = 2 ! iso-neutral ( rotation) ENDIF IF( ln_sco ) THEN ! s-coordinate IF( ln_dynldf_lev ) nldf_dyn = np_blp ! iso-level (no rotation) IF( ln_dynldf_hor ) ierr = 2 ! horizontal ( rotation) IF( ln_dynldf_iso ) ierr = 2 ! iso-neutral ( rotation) ENDIF ENDIF ! IF( ierr == 2 ) CALL ctl_stop( 'rotated bi-laplacian operator does not exist' ) ! IF( nldf_dyn == np_lap_i ) l_ldfslp = .TRUE. ! rotation require the computation of the slopes ! ENDIF ! IF(lwp) THEN WRITE(numout,*) SELECT CASE( nldf_dyn ) CASE( np_no_ldf ) ; WRITE(numout,*) ' ==>>> NO lateral viscosity' CASE( np_lap ) ; WRITE(numout,*) ' ==>>> iso-level laplacian operator' CASE( np_lap_i ) ; WRITE(numout,*) ' ==>>> rotated laplacian operator with iso-level background' CASE( np_blp ) ; WRITE(numout,*) ' ==>>> iso-level bi-laplacian operator' END SELECT WRITE(numout,*) ENDIF ! ! !== Space/time variation of eddy coefficients ==! ! !=================================================! ! l_ldfdyn_time = .FALSE. ! no time variation except in case defined below ! IF( ln_dynldf_OFF ) THEN IF(lwp) WRITE(numout,*) ' ==>>> No viscous operator selected. ahmt and ahmf are not allocated' RETURN ! ELSE !== a lateral diffusion operator is used ==! ! ! ! allocate the ahm arrays ALLOCATE( ahmt(jpi,jpj,jpk) , ahmf(jpi,jpj,jpk) , STAT=ierr ) IF( ierr /= 0 ) CALL ctl_stop( 'STOP', 'ldf_dyn_init: failed to allocate arrays') ! ahmt(:,:,:) = 0._wp ! init to 0 needed ahmf(:,:,:) = 0._wp ! ! ! value of lap/blp eddy mixing coef. IF( ln_dynldf_lap ) THEN ; zUfac = r1_2 *rn_Uv ; inn = 1 ; cl_Units = ' m2/s' ! laplacian ELSEIF( ln_dynldf_blp ) THEN ; zUfac = r1_12*rn_Uv ; inn = 3 ; cl_Units = ' m4/s' ! bilaplacian ENDIF zah0 = zUfac * rn_Lv**inn ! mixing coefficient zah_max = zUfac * (ra*rad)**inn ! maximum reachable coefficient (value at the Equator) ! SELECT CASE( nn_ahm_ijk_t ) !* Specification of space-time variations of ahmt, ahmf ! CASE( 0 ) !== constant ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity. = constant = ', zah0, cl_Units ahmt(:,:,1:jpkm1) = zah0 ahmf(:,:,1:jpkm1) = zah0 ! CASE( 10 ) !== fixed profile ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity = F( depth )' IF(lwp) WRITE(numout,*) ' surface viscous coef. = constant = ', zah0, cl_Units ahmt(:,:,1) = zah0 ! constant surface value ahmf(:,:,1) = zah0 CALL ldf_c1d( 'DYN', ahmt(:,:,1), ahmf(:,:,1), ahmt, ahmf ) ! CASE ( -20 ) !== fixed horizontal shape read in file ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity = F(i,j) read in eddy_viscosity.nc file' CALL iom_open( 'eddy_viscosity_2D.nc', inum ) CALL iom_get ( inum, jpdom_data, 'ahmt_2d', ahmt(:,:,1) ) CALL iom_get ( inum, jpdom_data, 'ahmf_2d', ahmf(:,:,1) ) CALL iom_close( inum ) DO jk = 2, jpkm1 ahmt(:,:,jk) = ahmt(:,:,1) ahmf(:,:,jk) = ahmf(:,:,1) END DO ! CASE( 20 ) !== fixed horizontal shape ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity = F( e1, e2 ) or F( e1^3, e2^3 ) (lap. or blp. case)' IF(lwp) WRITE(numout,*) ' using a fixed viscous velocity = ', rn_Uv ,' m/s and Lv = Max(e1,e2)' IF(lwp) WRITE(numout,*) ' maximum reachable coefficient (at the Equator) = ', zah_max, cl_Units, ' for e1=1°)' CALL ldf_c2d( 'DYN', zUfac , inn , ahmt, ahmf ) ! surface value proportional to scale factor^inn ! CASE( -30 ) !== fixed 3D shape read in file ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity = F(i,j,k) read in eddy_viscosity_3D.nc file' CALL iom_open( 'eddy_viscosity_3D.nc', inum ) CALL iom_get ( inum, jpdom_data, 'ahmt_3d', ahmt ) CALL iom_get ( inum, jpdom_data, 'ahmf_3d', ahmf ) CALL iom_close( inum ) ! CASE( 30 ) !== fixed 3D shape ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity = F( latitude, longitude, depth )' IF(lwp) WRITE(numout,*) ' using a fixed viscous velocity = ', rn_Uv ,' m/s and Ld = Max(e1,e2)' IF(lwp) WRITE(numout,*) ' maximum reachable coefficient (at the Equator) = ', zah_max, cl_Units, ' for e1=1°)' CALL ldf_c2d( 'DYN', zUfac , inn , ahmt, ahmf ) ! surface value proportional to scale factor^inn CALL ldf_c1d( 'DYN', ahmt(:,:,1), ahmf(:,:,1), ahmt, ahmf ) ! reduction with depth ! CASE( 31 ) !== time varying 3D field ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity = F( latitude, longitude, depth , time )' IF(lwp) WRITE(numout,*) ' proportional to the local velocity : 1/2 |u|e (lap) or 1/12 |u|e^3 (blp)' ! l_ldfdyn_time = .TRUE. ! will be calculated by call to ldf_dyn routine in step.F90 ! CASE( 32 ) !== time varying 3D field ==! IF(lwp) WRITE(numout,*) ' ==>>> eddy viscosity = F( latitude, longitude, depth , time )' IF(lwp) WRITE(numout,*) ' proportional to the local deformation rate and gridscale (Smagorinsky)' ! l_ldfdyn_time = .TRUE. ! will be calculated by call to ldf_dyn routine in step.F90 ! ! ! allocate arrays used in ldf_dyn. ALLOCATE( dtensq(jpi,jpj,jpk) , dshesq(jpi,jpj,jpk) , esqt(jpi,jpj) , esqf(jpi,jpj) , STAT=ierr ) IF( ierr /= 0 ) CALL ctl_stop( 'STOP', 'ldf_dyn_init: failed to allocate Smagorinsky arrays') ! DO_2D_11_11 esqt(ji,jj) = ( 2._wp * e1e2t(ji,jj) / ( e1t(ji,jj) + e2t(ji,jj) ) )**2 esqf(ji,jj) = ( 2._wp * e1e2f(ji,jj) / ( e1f(ji,jj) + e2f(ji,jj) ) )**2 END_2D ! CASE DEFAULT CALL ctl_stop('ldf_dyn_init: wrong choice for nn_ahm_ijk_t, the type of space-time variation of ahm') END SELECT ! IF( .NOT.l_ldfdyn_time ) THEN !* No time variation IF( ln_dynldf_lap ) THEN ! laplacian operator (mask only) ahmt(:,:,1:jpkm1) = ahmt(:,:,1:jpkm1) * tmask(:,:,1:jpkm1) ahmf(:,:,1:jpkm1) = ahmf(:,:,1:jpkm1) * fmask(:,:,1:jpkm1) ELSEIF( ln_dynldf_blp ) THEN ! bilaplacian operator (square root + mask) ahmt(:,:,1:jpkm1) = SQRT( ahmt(:,:,1:jpkm1) ) * tmask(:,:,1:jpkm1) ahmf(:,:,1:jpkm1) = SQRT( ahmf(:,:,1:jpkm1) ) * fmask(:,:,1:jpkm1) ENDIF ENDIF ! ENDIF ! END SUBROUTINE ldf_dyn_init SUBROUTINE ldf_dyn( kt, Kbb ) !!---------------------------------------------------------------------- !! *** ROUTINE ldf_dyn *** !! !! ** Purpose : update at kt the momentum lateral mixing coeff. (ahmt and ahmf) !! !! ** Method : time varying eddy viscosity coefficients: !! !! nn_ahm_ijk_t = 31 ahmt, ahmf = F(i,j,k,t) = F(local velocity) !! ( |u|e /12 or |u|e^3/12 for laplacian or bilaplacian operator ) !! !! nn_ahm_ijk_t = 32 ahmt, ahmf = F(i,j,k,t) = F(local deformation rate and gridscale) (D and L) (Smagorinsky) !! ( L^2|D| or L^4|D|/8 for laplacian or bilaplacian operator ) !! !! ** note : in BLP cases the sqrt of the eddy coef is returned, since bilaplacian is en re-entrant laplacian !! ** action : ahmt, ahmf updated at each time step !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! time step index INTEGER, INTENT(in) :: Kbb ! ocean time level indices ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zu2pv2_ij_p1, zu2pv2_ij, zu2pv2_ij_m1, zemax ! local scalar (option 31) REAL(wp) :: zcmsmag, zstabf_lo, zstabf_up, zdelta, zdb ! local scalar (option 32) !!---------------------------------------------------------------------- ! IF( ln_timing ) CALL timing_start('ldf_dyn') ! SELECT CASE( nn_ahm_ijk_t ) !== Eddy vicosity coefficients ==! ! CASE( 31 ) !== time varying 3D field ==! = F( local velocity ) ! IF( ln_dynldf_lap ) THEN ! laplacian operator : |u| e /12 = |u/144| e DO jk = 1, jpkm1 DO_2D_00_00 zu2pv2_ij = uu(ji ,jj ,jk,Kbb) * uu(ji ,jj ,jk,Kbb) + vv(ji ,jj ,jk,Kbb) * vv(ji ,jj ,jk,Kbb) zu2pv2_ij_m1 = uu(ji-1,jj ,jk,Kbb) * uu(ji-1,jj ,jk,Kbb) + vv(ji ,jj-1,jk,Kbb) * vv(ji ,jj-1,jk,Kbb) zemax = MAX( e1t(ji,jj) , e2t(ji,jj) ) ahmt(ji,jj,jk) = SQRT( (zu2pv2_ij + zu2pv2_ij_m1) * r1_288 ) * zemax * tmask(ji,jj,jk) ! 288= 12*12 * 2 END_2D DO_2D_10_10 zu2pv2_ij_p1 = uu(ji ,jj+1,jk, Kbb) * uu(ji ,jj+1,jk, Kbb) + vv(ji+1,jj ,jk, Kbb) * vv(ji+1,jj ,jk, Kbb) zu2pv2_ij = uu(ji ,jj ,jk, Kbb) * uu(ji ,jj ,jk, Kbb) + vv(ji ,jj ,jk, Kbb) * vv(ji ,jj ,jk, Kbb) zemax = MAX( e1f(ji,jj) , e2f(ji,jj) ) ahmf(ji,jj,jk) = SQRT( (zu2pv2_ij + zu2pv2_ij_p1) * r1_288 ) * zemax * fmask(ji,jj,jk) ! 288= 12*12 * 2 END_2D END DO ELSEIF( ln_dynldf_blp ) THEN ! bilaplacian operator : sqrt( |u| e^3 /12 ) = sqrt( |u/144| e ) * e DO jk = 1, jpkm1 DO_2D_00_00 zu2pv2_ij = uu(ji ,jj ,jk,Kbb) * uu(ji ,jj ,jk,Kbb) + vv(ji ,jj ,jk,Kbb) * vv(ji ,jj ,jk,Kbb) zu2pv2_ij_m1 = uu(ji-1,jj ,jk,Kbb) * uu(ji-1,jj ,jk,Kbb) + vv(ji ,jj-1,jk,Kbb) * vv(ji ,jj-1,jk,Kbb) zemax = MAX( e1t(ji,jj) , e2t(ji,jj) ) ahmt(ji,jj,jk) = SQRT( SQRT( (zu2pv2_ij + zu2pv2_ij_m1) * r1_288 ) * zemax ) * zemax * tmask(ji,jj,jk) END_2D DO_2D_10_10 zu2pv2_ij_p1 = uu(ji ,jj+1,jk, Kbb) * uu(ji ,jj+1,jk, Kbb) + vv(ji+1,jj ,jk, Kbb) * vv(ji+1,jj ,jk, Kbb) zu2pv2_ij = uu(ji ,jj ,jk, Kbb) * uu(ji ,jj ,jk, Kbb) + vv(ji ,jj ,jk, Kbb) * vv(ji ,jj ,jk, Kbb) zemax = MAX( e1f(ji,jj) , e2f(ji,jj) ) ahmf(ji,jj,jk) = SQRT( SQRT( (zu2pv2_ij + zu2pv2_ij_p1) * r1_288 ) * zemax ) * zemax * fmask(ji,jj,jk) END_2D END DO ENDIF ! CALL lbc_lnk_multi( 'ldfdyn', ahmt, 'T', 1., ahmf, 'F', 1. ) ! ! CASE( 32 ) !== time varying 3D field ==! = F( local deformation rate and gridscale ) (Smagorinsky) ! IF( ln_dynldf_lap .OR. ln_dynldf_blp ) THEN ! laplacian operator : (C_smag/pi)^2 L^2 |D| ! zcmsmag = (rn_csmc/rpi)**2 ! (C_smag/pi)^2 zstabf_lo = rn_minfac * rn_minfac / ( 2._wp * 12._wp * 12._wp * zcmsmag ) ! lower limit stability factor scaling zstabf_up = rn_maxfac / ( 4._wp * zcmsmag * 2._wp * rn_Dt ) ! upper limit stability factor scaling IF( ln_dynldf_blp ) zstabf_lo = ( 16._wp / 9._wp ) * zstabf_lo ! provide |U|L^3/12 lower limit instead ! ! of |U|L^3/16 in blp case DO jk = 1, jpkm1 ! DO_2D_00_00 zdb = ( uu(ji,jj,jk,Kbb) * r1_e2u(ji,jj) - uu(ji-1,jj,jk,Kbb) * r1_e2u(ji-1,jj) ) & & * r1_e1t(ji,jj) * e2t(ji,jj) & & - ( vv(ji,jj,jk,Kbb) * r1_e1v(ji,jj) - vv(ji,jj-1,jk,Kbb) * r1_e1v(ji,jj-1) ) & & * r1_e2t(ji,jj) * e1t(ji,jj) dtensq(ji,jj,jk) = zdb * zdb * tmask(ji,jj,jk) END_2D ! DO_2D_10_10 zdb = ( uu(ji,jj+1,jk,Kbb) * r1_e1u(ji,jj+1) - uu(ji,jj,jk,Kbb) * r1_e1u(ji,jj) ) & & * r1_e2f(ji,jj) * e1f(ji,jj) & & + ( vv(ji+1,jj,jk,Kbb) * r1_e2v(ji+1,jj) - vv(ji,jj,jk,Kbb) * r1_e2v(ji,jj) ) & & * r1_e1f(ji,jj) * e2f(ji,jj) dshesq(ji,jj,jk) = zdb * zdb * fmask(ji,jj,jk) END_2D ! END DO ! CALL lbc_lnk_multi( 'ldfdyn', dtensq, 'T', 1. ) ! lbc_lnk on dshesq not needed ! DO jk = 1, jpkm1 ! DO_2D_00_00 ! zu2pv2_ij = uu(ji ,jj ,jk,Kbb) * uu(ji ,jj ,jk,Kbb) + vv(ji ,jj ,jk,Kbb) * vv(ji ,jj ,jk,Kbb) zu2pv2_ij_m1 = uu(ji-1,jj ,jk,Kbb) * uu(ji-1,jj ,jk,Kbb) + vv(ji ,jj-1,jk,Kbb) * vv(ji ,jj-1,jk,Kbb) ! zdelta = zcmsmag * esqt(ji,jj) ! L^2 * (C_smag/pi)^2 ahmt(ji,jj,jk) = zdelta * SQRT( dtensq(ji ,jj,jk) + & & r1_4 * ( dshesq(ji ,jj,jk) + dshesq(ji ,jj-1,jk) + & & dshesq(ji-1,jj,jk) + dshesq(ji-1,jj-1,jk) ) ) ahmt(ji,jj,jk) = MAX( ahmt(ji,jj,jk), SQRT( (zu2pv2_ij + zu2pv2_ij_m1) * zdelta * zstabf_lo ) ) ! Impose lower limit == minfac * |U|L/2 ahmt(ji,jj,jk) = MIN( ahmt(ji,jj,jk), zdelta * zstabf_up ) ! Impose upper limit == maxfac * L^2/(4*2dt) ! END_2D ! DO_2D_10_10 ! zu2pv2_ij_p1 = uu(ji ,jj+1,jk, kbb) * uu(ji ,jj+1,jk, kbb) + vv(ji+1,jj ,jk, kbb) * vv(ji+1,jj ,jk, kbb) zu2pv2_ij = uu(ji ,jj ,jk, kbb) * uu(ji ,jj ,jk, kbb) + vv(ji ,jj ,jk, kbb) * vv(ji ,jj ,jk, kbb) ! zdelta = zcmsmag * esqf(ji,jj) ! L^2 * (C_smag/pi)^2 ahmf(ji,jj,jk) = zdelta * SQRT( dshesq(ji ,jj,jk) + & & r1_4 * ( dtensq(ji ,jj,jk) + dtensq(ji ,jj+1,jk) + & & dtensq(ji+1,jj,jk) + dtensq(ji+1,jj+1,jk) ) ) ahmf(ji,jj,jk) = MAX( ahmf(ji,jj,jk), SQRT( (zu2pv2_ij + zu2pv2_ij_p1) * zdelta * zstabf_lo ) ) ! Impose lower limit == minfac * |U|L/2 ahmf(ji,jj,jk) = MIN( ahmf(ji,jj,jk), zdelta * zstabf_up ) ! Impose upper limit == maxfac * L^2/(4*2dt) ! END_2D ! END DO ! ENDIF ! IF( ln_dynldf_blp ) THEN ! bilaplacian operator : sqrt( (C_smag/pi)^2 L^4 |D|/8) ! ! = sqrt( A_lap_smag L^2/8 ) ! ! stability limits already applied to laplacian values ! ! effective default limits are 1/12 |U|L^3 < B_hm < 1//(32*2dt) L^4 DO jk = 1, jpkm1 DO_2D_00_00 ahmt(ji,jj,jk) = SQRT( r1_8 * esqt(ji,jj) * ahmt(ji,jj,jk) ) END_2D DO_2D_10_10 ahmf(ji,jj,jk) = SQRT( r1_8 * esqf(ji,jj) * ahmf(ji,jj,jk) ) END_2D END DO ! ENDIF ! CALL lbc_lnk_multi( 'ldfdyn', ahmt, 'T', 1. , ahmf, 'F', 1. ) ! END SELECT ! CALL iom_put( "ahmt_2d", ahmt(:,:,1) ) ! surface u-eddy diffusivity coeff. CALL iom_put( "ahmf_2d", ahmf(:,:,1) ) ! surface v-eddy diffusivity coeff. CALL iom_put( "ahmt_3d", ahmt(:,:,:) ) ! 3D u-eddy diffusivity coeff. CALL iom_put( "ahmf_3d", ahmf(:,:,:) ) ! 3D v-eddy diffusivity coeff. ! IF( ln_timing ) CALL timing_stop('ldf_dyn') ! END SUBROUTINE ldf_dyn !!====================================================================== END MODULE ldfdyn