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C $Header: /u/gcmpack/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.34 2016/01/14 17:50:25 jmc Exp $ |
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C $Name: $ |
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|
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#include "GGL90_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: GGL90_CALC |
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|
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C !INTERFACE: ====================================================== |
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SUBROUTINE GGL90_CALC( |
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I bi, bj, sigmaR, myTime, myIter, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE GGL90_CALC | |
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C | o Compute all GGL90 fields defined in GGL90.h | |
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C *==========================================================* |
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C | Equation numbers refer to | |
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C | Gaspar et al. (1990), JGR 95 (C9), pp 16,179 | |
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C | Some parts of the implementation follow Blanke and | |
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C | Delecuse (1993), JPO, and OPA code, in particular the | |
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C | computation of the | |
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C | mixing length = max(min(lk,depth),lkmin) | |
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C *==========================================================* |
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|
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C global parameters updated by ggl90_calc |
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C GGL90TKE :: sub-grid turbulent kinetic energy (m^2/s^2) |
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C GGL90viscAz :: GGL90 eddy viscosity coefficient (m^2/s) |
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C GGL90diffKzT :: GGL90 diffusion coefficient for temperature (m^2/s) |
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C \ev |
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|
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C !USES: ============================================================ |
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IMPLICIT NONE |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "DYNVARS.h" |
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#include "FFIELDS.h" |
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#include "GRID.h" |
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#include "GGL90.h" |
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|
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C !INPUT PARAMETERS: =================================================== |
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C Routine arguments |
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C bi, bj :: Current tile indices |
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C sigmaR :: Vertical gradient of iso-neutral density |
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C myTime :: Current time in simulation |
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C myIter :: Current time-step number |
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C myThid :: My Thread Id number |
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INTEGER bi, bj |
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_RL sigmaR(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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|
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#ifdef ALLOW_GGL90 |
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|
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C !LOCAL VARIABLES: ==================================================== |
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C Local constants |
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C iMin,iMax,jMin,jMax :: index boundaries of computation domain |
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C i, j, k, kp1,km1 :: array computation indices |
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C kSurf, kBottom :: vertical indices of domain boundaries |
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C hFac/hFacI :: fractional thickness of W-cell |
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C explDissFac :: explicit Dissipation Factor (in [0-1]) |
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C implDissFac :: implicit Dissipation Factor (in [0-1]) |
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C uStarSquare :: square of friction velocity |
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C verticalShear :: (squared) vertical shear of horizontal velocity |
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C Nsquare :: squared buoyancy freqency |
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C RiNumber :: local Richardson number |
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C KappaM :: (local) viscosity parameter (eq.10) |
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C KappaH :: (local) diffusivity parameter for temperature (eq.11) |
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C KappaE :: (local) diffusivity parameter for TKE (eq.15) |
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C TKEdissipation :: dissipation of TKE |
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C GGL90mixingLength:: mixing length of scheme following Banke+Delecuse |
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C rMixingLength:: inverse of mixing length |
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C totalDepth :: thickness of water column (inverse of recip_Rcol) |
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C TKEPrandtlNumber :: here, an empirical function of the Richardson number |
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INTEGER iMin ,iMax ,jMin ,jMax |
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INTEGER i, j, k, kp1, km1, kSurf, kBottom |
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_RL explDissFac, implDissFac |
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_RL uStarSquare |
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_RL verticalShear(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL KappaM(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL KappaH |
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c _RL Nsquare |
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_RL Nsquare(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL deltaTggl90 |
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c _RL SQRTTKE |
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_RL SQRTTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL RiNumber |
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#ifdef ALLOW_GGL90_IDEMIX |
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_RL IDEMIX_RiNumber |
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#endif |
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_RL TKEdissipation |
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_RL tempU, tempUp, tempV, tempVp, prTemp |
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_RL MaxLength, tmpmlx, tmpVisc |
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_RL TKEPrandtlNumber (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL GGL90mixingLength(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL rMixingLength (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL mxLength_Dn (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL KappaE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL totalDepth (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL GGL90visctmp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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#ifdef ALLOW_DIAGNOSTICS |
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_RL surf_flx_tke (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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#endif /* ALLOW_DIAGNOSTICS */ |
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C hFac(I) :: fractional thickness of W-cell |
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_RL hFac |
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#ifdef ALLOW_GGL90_IDEMIX |
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_RL hFacI(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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#endif /* ALLOW_GGL90_IDEMIX */ |
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_RL recip_hFacI(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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C- tri-diagonal matrix |
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_RL a3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL b3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL c3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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INTEGER errCode |
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#ifdef ALLOW_GGL90_HORIZDIFF |
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C xA, yA :: area of lateral faces |
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C dfx, dfy :: diffusive flux across lateral faces |
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C gTKE :: right hand side of diffusion equation |
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_RL xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL dfx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL dfy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL gTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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#endif /* ALLOW_GGL90_HORIZDIFF */ |
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#ifdef ALLOW_GGL90_SMOOTH |
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_RL p4, p8, p16 |
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#endif |
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CEOP |
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|
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PARAMETER( iMin = 2-OLx, iMax = sNx+OLx-1 ) |
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PARAMETER( jMin = 2-OLy, jMax = sNy+OLy-1 ) |
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#ifdef ALLOW_GGL90_SMOOTH |
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p4 = 0.25 _d 0 |
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p8 = 0.125 _d 0 |
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p16 = 0.0625 _d 0 |
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#endif |
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|
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C set separate time step (should be deltaTtracer) |
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deltaTggl90 = dTtracerLev(1) |
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|
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kSurf = 1 |
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C explicit/implicit timestepping weights for dissipation |
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explDissFac = 0. _d 0 |
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implDissFac = 1. _d 0 - explDissFac |
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|
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C For nonlinear free surface and especially with r*-coordinates, the |
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C hFacs change every timestep, so we need to update them here in the |
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C case of using IDEMIX. |
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DO K=1,Nr |
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Km1 = MAX(K-1,1) |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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hFac = |
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& MIN(.5 _d 0,_hFacC(i,j,km1,bi,bj) ) + |
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& MIN(.5 _d 0,_hFacC(i,j,k ,bi,bj) ) |
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recip_hFacI(I,J,K)=0. _d 0 |
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IF ( hFac .NE. 0. _d 0 ) |
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& recip_hFacI(I,J,K)=1. _d 0/hFac |
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#ifdef ALLOW_GGL90_IDEMIX |
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hFacI(i,j,k) = hFac |
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#endif /* ALLOW_GGL90_IDEMIX */ |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C Initialize local fields |
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DO k = 1, Nr |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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rMixingLength(i,j,k) = 0. _d 0 |
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mxLength_Dn(i,j,k) = 0. _d 0 |
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GGL90visctmp(i,j,k) = 0. _d 0 |
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KappaE(i,j,k) = 0. _d 0 |
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TKEPrandtlNumber(i,j,k) = 1. _d 0 |
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GGL90mixingLength(i,j,k) = GGL90mixingLengthMin |
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GGL90visctmp(i,j,k) = 0. _d 0 |
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#ifndef SOLVE_DIAGONAL_LOWMEMORY |
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a3d(i,j,k) = 0. _d 0 |
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b3d(i,j,k) = 1. _d 0 |
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c3d(i,j,k) = 0. _d 0 |
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#endif |
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Nsquare(i,j,k) = 0. _d 0 |
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SQRTTKE(i,j,k) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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KappaM(i,j) = 0. _d 0 |
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verticalShear(i,j) = 0. _d 0 |
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totalDepth(i,j) = Ro_surf(i,j,bi,bj) - R_low(i,j,bi,bj) |
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rMixingLength(i,j,1) = 0. _d 0 |
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mxLength_Dn(i,j,1) = GGL90mixingLengthMin |
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SQRTTKE(i,j,1) = SQRT( GGL90TKE(i,j,1,bi,bj) ) |
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#ifdef ALLOW_GGL90_HORIZDIFF |
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xA(i,j) = 0. _d 0 |
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yA(i,j) = 0. _d 0 |
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dfx(i,j) = 0. _d 0 |
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dfy(i,j) = 0. _d 0 |
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gTKE(i,j) = 0. _d 0 |
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#endif /* ALLOW_GGL90_HORIZDIFF */ |
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ENDDO |
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ENDDO |
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|
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#ifdef ALLOW_GGL90_IDEMIX |
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IF ( useIDEMIX) CALL GGL90_IDEMIX( |
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& bi, bj, hFacI, recip_hFacI, sigmaR, myTime, myIter, myThid ) |
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#endif /* ALLOW_GGL90_IDEMIX */ |
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|
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DO k = 2, Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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SQRTTKE(i,j,k)=SQRT( GGL90TKE(i,j,k,bi,bj) ) |
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|
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C buoyancy frequency |
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Nsquare(i,j,k) = gravity*gravitySign*recip_rhoConst |
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& * sigmaR(i,j,k) |
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C vertical shear term (dU/dz)^2+(dV/dz)^2 is computed later |
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C to save some memory |
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C mixing length |
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GGL90mixingLength(i,j,k) = SQRTTWO * |
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& SQRTTKE(i,j,k)/SQRT( MAX(Nsquare(i,j,k),GGL90eps) ) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C- ensure mixing between first and second level |
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IF (mxlSurfFlag) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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GGL90mixingLength(i,j,2)=drF(1) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C-- Impose upper and lower bound for mixing length |
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C-- Impose minimum mixing length to avoid division by zero |
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IF ( mxlMaxFlag .EQ. 0 ) THEN |
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|
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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MaxLength=totalDepth(i,j) |
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GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
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& MaxLength) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), |
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& GGL90mixingLengthMin) |
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rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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ELSEIF ( mxlMaxFlag .EQ. 1 ) THEN |
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|
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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MaxLength=MIN(Ro_surf(i,j,bi,bj)-rF(k),rF(k)-R_low(i,j,bi,bj)) |
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c MaxLength=MAX(MaxLength,20. _d 0) |
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GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
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& MaxLength) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), |
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& GGL90mixingLengthMin) |
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rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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ELSEIF ( mxlMaxFlag .EQ. 2 ) THEN |
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|
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
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& GGL90mixingLength(i,j,k-1)+drF(k-1)) |
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ENDDO |
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ENDDO |
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ENDDO |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr), |
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& GGL90mixingLengthMin+drF(Nr)) |
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ENDDO |
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ENDDO |
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DO k=Nr-1,2,-1 |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
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& GGL90mixingLength(i,j,k+1)+drF(k)) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), |
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& GGL90mixingLengthMin) |
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rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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ELSEIF ( mxlMaxFlag .EQ. 3 ) THEN |
| 321 |
|
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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mxLength_Dn(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
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& mxLength_Dn(i,j,k-1)+drF(k-1)) |
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ENDDO |
| 328 |
ENDDO |
| 329 |
ENDDO |
| 330 |
DO j=jMin,jMax |
| 331 |
DO i=iMin,iMax |
| 332 |
GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr), |
| 333 |
& GGL90mixingLengthMin+drF(Nr)) |
| 334 |
ENDDO |
| 335 |
ENDDO |
| 336 |
DO k=Nr-1,2,-1 |
| 337 |
DO j=jMin,jMax |
| 338 |
DO i=iMin,iMax |
| 339 |
GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
| 340 |
& GGL90mixingLength(i,j,k+1)+drF(k)) |
| 341 |
ENDDO |
| 342 |
ENDDO |
| 343 |
ENDDO |
| 344 |
|
| 345 |
DO k=2,Nr |
| 346 |
DO j=jMin,jMax |
| 347 |
DO i=iMin,iMax |
| 348 |
GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
| 349 |
& mxLength_Dn(i,j,k)) |
| 350 |
tmpmlx = SQRT( GGL90mixingLength(i,j,k)*mxLength_Dn(i,j,k) ) |
| 351 |
tmpmlx = MAX( tmpmlx, GGL90mixingLengthMin) |
| 352 |
rMixingLength(i,j,k) = 1. _d 0 / tmpmlx |
| 353 |
ENDDO |
| 354 |
ENDDO |
| 355 |
ENDDO |
| 356 |
|
| 357 |
ELSE |
| 358 |
STOP 'GGL90_CALC: Wrong mxlMaxFlag (mixing length limit)' |
| 359 |
ENDIF |
| 360 |
|
| 361 |
C start "proper" k-loop (the code above was moved out and up to |
| 362 |
C implemement various mixing parameters efficiently) |
| 363 |
DO k=2,Nr |
| 364 |
km1 = k-1 |
| 365 |
|
| 366 |
#ifdef ALLOW_GGL90_HORIZDIFF |
| 367 |
IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
| 368 |
C horizontal diffusion of TKE (requires an exchange in |
| 369 |
C do_fields_blocking_exchanges) |
| 370 |
C common factors |
| 371 |
DO j=1-OLy,sNy+OLy |
| 372 |
DO i=1-OLx,sNx+OLx |
| 373 |
xA(i,j) = _dyG(i,j,bi,bj)*drC(k)* |
| 374 |
& (min(.5 _d 0,_hFacW(i,j,k-1,bi,bj) ) + |
| 375 |
& min(.5 _d 0,_hFacW(i,j,k ,bi,bj) ) ) |
| 376 |
yA(i,j) = _dxG(i,j,bi,bj)*drC(k)* |
| 377 |
& (min(.5 _d 0,_hFacS(i,j,k-1,bi,bj) ) + |
| 378 |
& min(.5 _d 0,_hFacS(i,j,k ,bi,bj) ) ) |
| 379 |
ENDDO |
| 380 |
ENDDO |
| 381 |
C Compute diffusive fluxes |
| 382 |
C ... across x-faces |
| 383 |
DO j=1-OLy,sNy+OLy |
| 384 |
dfx(1-OLx,j)=0. _d 0 |
| 385 |
DO i=1-OLx+1,sNx+OLx |
| 386 |
dfx(i,j) = -GGL90diffTKEh*xA(i,j) |
| 387 |
& *_recip_dxC(i,j,bi,bj) |
| 388 |
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i-1,j,k,bi,bj)) |
| 389 |
#ifdef ISOTROPIC_COS_SCALING |
| 390 |
& *CosFacU(j,bi,bj) |
| 391 |
#endif /* ISOTROPIC_COS_SCALING */ |
| 392 |
ENDDO |
| 393 |
ENDDO |
| 394 |
C ... across y-faces |
| 395 |
DO i=1-OLx,sNx+OLx |
| 396 |
dfy(i,1-OLy)=0. _d 0 |
| 397 |
ENDDO |
| 398 |
DO j=1-OLy+1,sNy+OLy |
| 399 |
DO i=1-OLx,sNx+OLx |
| 400 |
dfy(i,j) = -GGL90diffTKEh*yA(i,j) |
| 401 |
& *_recip_dyC(i,j,bi,bj) |
| 402 |
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i,j-1,k,bi,bj)) |
| 403 |
#ifdef ISOTROPIC_COS_SCALING |
| 404 |
& *CosFacV(j,bi,bj) |
| 405 |
#endif /* ISOTROPIC_COS_SCALING */ |
| 406 |
ENDDO |
| 407 |
ENDDO |
| 408 |
C Compute divergence of fluxes |
| 409 |
DO j=1-OLy,sNy+OLy-1 |
| 410 |
DO i=1-OLx,sNx+OLx-1 |
| 411 |
gTKE(i,j) = -recip_drC(k)*recip_rA(i,j,bi,bj) |
| 412 |
& *recip_hFacI(i,j,k) |
| 413 |
& *((dfx(i+1,j)-dfx(i,j)) |
| 414 |
& + (dfy(i,j+1)-dfy(i,j)) ) |
| 415 |
ENDDO |
| 416 |
ENDDO |
| 417 |
C end if GGL90diffTKEh .eq. 0. |
| 418 |
ENDIF |
| 419 |
#endif /* ALLOW_GGL90_HORIZDIFF */ |
| 420 |
|
| 421 |
C viscosity and diffusivity |
| 422 |
DO j=jMin,jMax |
| 423 |
DO i=iMin,iMax |
| 424 |
KappaM(i,j) = GGL90ck*GGL90mixingLength(i,j,k)*SQRTTKE(i,j,k) |
| 425 |
GGL90visctmp(i,j,k) = MAX(KappaM(i,j),diffKrNrS(k)) |
| 426 |
& * maskC(i,j,k,bi,bj) |
| 427 |
C note: storing GGL90visctmp like this, and using it later to compute |
| 428 |
C GGL9rdiffKr etc. is robust in case of smoothing (e.g. see OPA) |
| 429 |
KappaM(i,j) = MAX(KappaM(i,j),viscArNr(k)) * maskC(i,j,k,bi,bj) |
| 430 |
ENDDO |
| 431 |
ENDDO |
| 432 |
|
| 433 |
C compute vertical shear (dU/dz)^2+(dV/dz)^2 |
| 434 |
IF ( calcMeanVertShear ) THEN |
| 435 |
C by averaging (@ grid-cell center) the 4 vertical shear compon @ U,V pos. |
| 436 |
DO j=jMin,jMax |
| 437 |
DO i=iMin,iMax |
| 438 |
tempU = ( uVel( i ,j,km1,bi,bj) - uVel( i ,j,k,bi,bj) ) |
| 439 |
tempUp = ( uVel(i+1,j,km1,bi,bj) - uVel(i+1,j,k,bi,bj) ) |
| 440 |
tempV = ( vVel(i, j ,km1,bi,bj) - vVel(i, j ,k,bi,bj) ) |
| 441 |
tempVp = ( vVel(i,j+1,km1,bi,bj) - vVel(i,j+1,k,bi,bj) ) |
| 442 |
verticalShear(i,j) = ( |
| 443 |
& ( tempU*tempU + tempUp*tempUp )*halfRL |
| 444 |
& + ( tempV*tempV + tempVp*tempVp )*halfRL |
| 445 |
& )*recip_drC(k)*recip_drC(k) |
| 446 |
ENDDO |
| 447 |
ENDDO |
| 448 |
ELSE |
| 449 |
C from the averaged flow at grid-cell center (2 compon x 2 pos.) |
| 450 |
DO j=jMin,jMax |
| 451 |
DO i=iMin,iMax |
| 452 |
tempU = ( ( uVel(i,j,km1,bi,bj) + uVel(i+1,j,km1,bi,bj) ) |
| 453 |
& -( uVel(i,j,k ,bi,bj) + uVel(i+1,j,k ,bi,bj) ) |
| 454 |
& )*halfRL*recip_drC(k) |
| 455 |
tempV = ( ( vVel(i,j,km1,bi,bj) + vVel(i,j+1,km1,bi,bj) ) |
| 456 |
& -( vVel(i,j,k ,bi,bj) + vVel(i,j+1,k ,bi,bj) ) |
| 457 |
& )*halfRL*recip_drC(k) |
| 458 |
verticalShear(i,j) = tempU*tempU + tempV*tempV |
| 459 |
ENDDO |
| 460 |
ENDDO |
| 461 |
ENDIF |
| 462 |
|
| 463 |
C compute Prandtl number (always greater than 0) |
| 464 |
#ifdef ALLOW_GGL90_IDEMIX |
| 465 |
IF ( useIDEMIX ) THEN |
| 466 |
DO j=jMin,jMax |
| 467 |
DO i=iMin,iMax |
| 468 |
C account for partical cell factor in vertical shear: |
| 469 |
verticalShear(i,j) = verticalShear(i,j) |
| 470 |
& * recip_hFacI(i,j,k)*recip_hFacI(i,j,k) |
| 471 |
RiNumber = MAX(Nsquare(i,j,k),0. _d 0) |
| 472 |
& /(verticalShear(i,j)+GGL90eps) |
| 473 |
CML IDEMIX_RiNumber = 1./GGL90eps |
| 474 |
IDEMIX_RiNumber = MAX( KappaM(i,j)*Nsquare(i,j,k), 0. _d 0)/ |
| 475 |
& (GGL90eps+IDEMIX_tau_d(i,j,k,bi,bj)*IDEMIX_E(i,j,k,bi,bj)**2) |
| 476 |
prTemp = MIN(5.*RiNumber, 6.6 _d 0*IDEMIX_RiNumber) |
| 477 |
TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) |
| 478 |
TKEPrandtlNumber(i,j,k) = MAX( 1. _d 0,TKEPrandtlNumber(i,j,k)) |
| 479 |
ENDDO |
| 480 |
ENDDO |
| 481 |
ELSE |
| 482 |
#else /* ndef ALLOW_GGL90_IDEMIX */ |
| 483 |
IF (.TRUE.) THEN |
| 484 |
#endif /* ALLOW_GGL90_IDEMIX */ |
| 485 |
DO j=jMin,jMax |
| 486 |
DO i=iMin,iMax |
| 487 |
RiNumber = MAX(Nsquare(i,j,k),0. _d 0) |
| 488 |
& /(verticalShear(i,j)+GGL90eps) |
| 489 |
prTemp = 1. _d 0 |
| 490 |
IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber |
| 491 |
TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) |
| 492 |
ENDDO |
| 493 |
ENDDO |
| 494 |
ENDIF |
| 495 |
|
| 496 |
DO j=jMin,jMax |
| 497 |
DO i=iMin,iMax |
| 498 |
C diffusivity |
| 499 |
KappaH = KappaM(i,j)/TKEPrandtlNumber(i,j,k) |
| 500 |
KappaE(i,j,k) = GGL90alpha * KappaM(i,j) * maskC(i,j,k,bi,bj) |
| 501 |
|
| 502 |
C dissipation term |
| 503 |
TKEdissipation = explDissFac*GGL90ceps |
| 504 |
& *SQRTTKE(i,j,k)*rMixingLength(i,j,k) |
| 505 |
& *GGL90TKE(i,j,k,bi,bj) |
| 506 |
C partial update with sum of explicit contributions |
| 507 |
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
| 508 |
& + deltaTggl90*( |
| 509 |
& + KappaM(i,j)*verticalShear(i,j) |
| 510 |
& - KappaH*Nsquare(i,j,k) |
| 511 |
& - TKEdissipation |
| 512 |
& ) |
| 513 |
ENDDO |
| 514 |
ENDDO |
| 515 |
|
| 516 |
#ifdef ALLOW_GGL90_IDEMIX |
| 517 |
IF ( useIDEMIX ) THEN |
| 518 |
C add IDEMIX contribution to the turbulent kinetic energy |
| 519 |
DO j=jMin,jMax |
| 520 |
DO i=iMin,iMax |
| 521 |
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
| 522 |
& + deltaTggl90*( |
| 523 |
& + IDEMIX_tau_d(i,j,k,bi,bj)*IDEMIX_E(i,j,k,bi,bj)**2 |
| 524 |
& ) |
| 525 |
ENDDO |
| 526 |
ENDDO |
| 527 |
ENDIF |
| 528 |
#endif /* ALLOW_GGL90_IDEMIX */ |
| 529 |
|
| 530 |
#ifdef ALLOW_GGL90_HORIZDIFF |
| 531 |
IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
| 532 |
C-- Add horiz. diffusion tendency |
| 533 |
DO j=jMin,jMax |
| 534 |
DO i=iMin,iMax |
| 535 |
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
| 536 |
& + gTKE(i,j)*deltaTggl90 |
| 537 |
ENDDO |
| 538 |
ENDDO |
| 539 |
ENDIF |
| 540 |
#endif /* ALLOW_GGL90_HORIZDIFF */ |
| 541 |
|
| 542 |
C-- end of k loop |
| 543 |
ENDDO |
| 544 |
|
| 545 |
C ============================================ |
| 546 |
C Implicit time step to update TKE for k=1,Nr; |
| 547 |
C TKE(Nr+1)=0 by default |
| 548 |
C ============================================ |
| 549 |
C set up matrix |
| 550 |
C-- Lower diagonal |
| 551 |
DO j=jMin,jMax |
| 552 |
DO i=iMin,iMax |
| 553 |
a3d(i,j,1) = 0. _d 0 |
| 554 |
ENDDO |
| 555 |
ENDDO |
| 556 |
DO k=2,Nr |
| 557 |
km1=MAX(2,k-1) |
| 558 |
DO j=jMin,jMax |
| 559 |
DO i=iMin,iMax |
| 560 |
C- We keep recip_hFacC in the diffusive flux calculation, |
| 561 |
C- but no hFacC in TKE volume control |
| 562 |
C- No need for maskC(k-1) with recip_hFacC(k-1) |
| 563 |
a3d(i,j,k) = -deltaTggl90 |
| 564 |
& *recip_drF(k-1)*recip_hFacC(i,j,k-1,bi,bj) |
| 565 |
& *.5 _d 0*(KappaE(i,j, k )+KappaE(i,j,km1)) |
| 566 |
& *recip_drC(k)*maskC(i,j,k,bi,bj) |
| 567 |
ENDDO |
| 568 |
ENDDO |
| 569 |
ENDDO |
| 570 |
C-- Upper diagonal |
| 571 |
DO j=jMin,jMax |
| 572 |
DO i=iMin,iMax |
| 573 |
c3d(i,j,1) = 0. _d 0 |
| 574 |
ENDDO |
| 575 |
ENDDO |
| 576 |
DO k=2,Nr |
| 577 |
DO j=jMin,jMax |
| 578 |
DO i=iMin,iMax |
| 579 |
kp1=MAX(1,MIN(klowC(i,j,bi,bj),k+1)) |
| 580 |
C- We keep recip_hFacC in the diffusive flux calculation, |
| 581 |
C- but no hFacC in TKE volume control |
| 582 |
C- No need for maskC(k) with recip_hFacC(k) |
| 583 |
c3d(i,j,k) = -deltaTggl90 |
| 584 |
& *recip_drF( k ) * recip_hFacC(i,j,k,bi,bj) |
| 585 |
& *.5 _d 0*(KappaE(i,j,k)+KappaE(i,j,kp1)) |
| 586 |
& *recip_drC(k)*maskC(i,j,k-1,bi,bj) |
| 587 |
ENDDO |
| 588 |
ENDDO |
| 589 |
ENDDO |
| 590 |
|
| 591 |
#ifdef ALLOW_GGL90_IDEMIX |
| 592 |
IF ( useIDEMIX ) THEN |
| 593 |
DO k=2,Nr |
| 594 |
DO j=jMin,jMax |
| 595 |
DO i=iMin,iMax |
| 596 |
a3d(i,j,k) = a3d(i,j,k)*recip_hFacI(i,j,k) |
| 597 |
c3d(i,j,k) = c3d(i,j,k)*recip_hFacI(i,j,k) |
| 598 |
ENDDO |
| 599 |
ENDDO |
| 600 |
ENDDO |
| 601 |
ENDIF |
| 602 |
#endif /* ALLOW_GGL90_IDEMIX */ |
| 603 |
|
| 604 |
IF (.NOT.GGL90_dirichlet) THEN |
| 605 |
C Neumann bottom boundary condition for TKE: no flux from bottom |
| 606 |
DO j=jMin,jMax |
| 607 |
DO i=iMin,iMax |
| 608 |
kBottom = MAX(kLowC(i,j,bi,bj),1) |
| 609 |
c3d(i,j,kBottom) = 0. _d 0 |
| 610 |
ENDDO |
| 611 |
ENDDO |
| 612 |
ENDIF |
| 613 |
|
| 614 |
C-- Center diagonal |
| 615 |
DO k=1,Nr |
| 616 |
km1 = MAX(k-1,1) |
| 617 |
DO j=jMin,jMax |
| 618 |
DO i=iMin,iMax |
| 619 |
b3d(i,j,k) = 1. _d 0 - c3d(i,j,k) - a3d(i,j,k) |
| 620 |
& + implDissFac*deltaTggl90*GGL90ceps*SQRTTKE(i,j,k) |
| 621 |
& * rMixingLength(i,j,k) |
| 622 |
& * maskC(i,j,k,bi,bj)*maskC(i,j,km1,bi,bj) |
| 623 |
ENDDO |
| 624 |
ENDDO |
| 625 |
ENDDO |
| 626 |
C end set up matrix |
| 627 |
|
| 628 |
C Apply boundary condition |
| 629 |
kp1 = MIN(Nr,kSurf+1) |
| 630 |
DO j=jMin,jMax |
| 631 |
DO i=iMin,iMax |
| 632 |
C estimate friction velocity uStar from surface forcing |
| 633 |
uStarSquare = SQRT( |
| 634 |
& ( .5 _d 0*( surfaceForcingU(i, j, bi,bj) |
| 635 |
& + surfaceForcingU(i+1,j, bi,bj) ) )**2 |
| 636 |
& + ( .5 _d 0*( surfaceForcingV(i, j, bi,bj) |
| 637 |
& + surfaceForcingV(i, j+1,bi,bj) ) )**2 |
| 638 |
& ) |
| 639 |
C Dirichlet surface boundary condition for TKE |
| 640 |
GGL90TKE(i,j,kSurf,bi,bj) = maskC(i,j,kSurf,bi,bj) |
| 641 |
& *MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare) |
| 642 |
GGL90TKE(i,j,kp1,bi,bj) = GGL90TKE(i,j,kp1,bi,bj) |
| 643 |
& - a3d(i,j,kp1)*GGL90TKE(i,j,kSurf,bi,bj) |
| 644 |
a3d(i,j,kp1) = 0. _d 0 |
| 645 |
ENDDO |
| 646 |
ENDDO |
| 647 |
|
| 648 |
IF (GGL90_dirichlet) THEN |
| 649 |
C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom |
| 650 |
DO j=jMin,jMax |
| 651 |
DO i=iMin,iMax |
| 652 |
kBottom = MAX(kLowC(i,j,bi,bj),1) |
| 653 |
GGL90TKE(i,j,kBottom,bi,bj) = GGL90TKE(i,j,kBottom,bi,bj) |
| 654 |
& - GGL90TKEbottom*c3d(i,j,kBottom) |
| 655 |
c3d(i,j,kBottom) = 0. _d 0 |
| 656 |
ENDDO |
| 657 |
ENDDO |
| 658 |
ENDIF |
| 659 |
|
| 660 |
C solve tri-diagonal system |
| 661 |
errCode = -1 |
| 662 |
CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
| 663 |
I a3d, b3d, c3d, |
| 664 |
U GGL90TKE(1-OLx,1-OLy,1,bi,bj), |
| 665 |
O errCode, |
| 666 |
I bi, bj, myThid ) |
| 667 |
|
| 668 |
DO k=1,Nr |
| 669 |
DO j=jMin,jMax |
| 670 |
DO i=iMin,iMax |
| 671 |
C impose minimum TKE to avoid numerical undershoots below zero |
| 672 |
GGL90TKE(i,j,k,bi,bj) = maskC(i,j,k,bi,bj) |
| 673 |
& *MAX( GGL90TKE(i,j,k,bi,bj), GGL90TKEmin ) |
| 674 |
ENDDO |
| 675 |
ENDDO |
| 676 |
ENDDO |
| 677 |
|
| 678 |
C end of time step |
| 679 |
C =============================== |
| 680 |
|
| 681 |
DO k=2,Nr |
| 682 |
DO j=1,sNy |
| 683 |
DO i=1,sNx |
| 684 |
#ifdef ALLOW_GGL90_SMOOTH |
| 685 |
tmpVisc = ( |
| 686 |
& p4 * GGL90visctmp(i ,j ,k)*mskCor(i ,j ,bi,bj) |
| 687 |
& +p8 *( ( GGL90visctmp(i-1,j ,k)*mskCor(i-1,j ,bi,bj) |
| 688 |
& + GGL90visctmp(i+1,j ,k)*mskCor(i+1,j ,bi,bj) ) |
| 689 |
& + ( GGL90visctmp(i ,j-1,k)*mskCor(i ,j-1,bi,bj) |
| 690 |
& + GGL90visctmp(i ,j+1,k)*mskCor(i ,j+1,bi,bj) ) ) |
| 691 |
& +p16*( ( GGL90visctmp(i+1,j+1,k)*mskCor(i+1,j+1,bi,bj) |
| 692 |
& + GGL90visctmp(i-1,j-1,k)*mskCor(i-1,j-1,bi,bj) ) |
| 693 |
& + ( GGL90visctmp(i+1,j-1,k)*mskCor(i+1,j-1,bi,bj) |
| 694 |
& + GGL90visctmp(i-1,j+1,k)*mskCor(i-1,j+1,bi,bj) ) ) |
| 695 |
& )/( |
| 696 |
& p4 |
| 697 |
& +p8 *( ( maskC(i-1,j ,k,bi,bj)*mskCor(i-1,j ,bi,bj) |
| 698 |
& + maskC(i+1,j ,k,bi,bj)*mskCor(i+1,j ,bi,bj) ) |
| 699 |
& + ( maskC(i ,j-1,k,bi,bj)*mskCor(i ,j-1,bi,bj) |
| 700 |
& + maskC(i ,j+1,k,bi,bj)*mskCor(i ,j+1,bi,bj) ) ) |
| 701 |
& +p16*( ( maskC(i+1,j+1,k,bi,bj)* mskCor(i+1,j+1,bi,bj) |
| 702 |
& + maskC(i-1,j-1,k,bi,bj)*mskCor(i-1,j-1,bi,bj) ) |
| 703 |
& + ( maskC(i+1,j-1,k,bi,bj)*mskCor(i+1,j-1,bi,bj) |
| 704 |
& + maskC(i-1,j+1,k,bi,bj)*mskCor(i-1,j+1,bi,bj) ) ) |
| 705 |
& )*maskC(i,j,k,bi,bj)*mskCor(i,j,bi,bj) |
| 706 |
#else |
| 707 |
tmpVisc = GGL90visctmp(i,j,k) |
| 708 |
#endif |
| 709 |
tmpVisc = MIN(tmpVisc/TKEPrandtlNumber(i,j,k),GGL90diffMax) |
| 710 |
GGL90diffKr(i,j,k,bi,bj)= MAX( tmpVisc , diffKrNrS(k) ) |
| 711 |
ENDDO |
| 712 |
ENDDO |
| 713 |
ENDDO |
| 714 |
|
| 715 |
DO k=2,Nr |
| 716 |
DO j=1,sNy |
| 717 |
DO i=1,sNx+1 |
| 718 |
#ifdef ALLOW_GGL90_SMOOTH |
| 719 |
tmpVisc = ( |
| 720 |
& p4 *( GGL90visctmp(i-1,j ,k)*mskCor(i-1,j ,bi,bj) |
| 721 |
& + GGL90visctmp(i ,j ,k)*mskCor(i ,j ,bi,bj) ) |
| 722 |
& +p8 *( ( GGL90visctmp(i-1,j-1,k)*mskCor(i-1,j-1,bi,bj) |
| 723 |
& + GGL90visctmp(i ,j-1,k)*mskCor(i ,j-1,bi,bj) ) |
| 724 |
& + ( GGL90visctmp(i-1,j+1,k)*mskCor(i-1,j+1,bi,bj) |
| 725 |
& + GGL90visctmp(i ,j+1,k)*mskCor(i ,j+1,bi,bj) ) ) |
| 726 |
& )/( |
| 727 |
& p4 * 2. _d 0 |
| 728 |
& +p8 *( ( maskC(i-1,j-1,k,bi,bj)*mskCor(i-1,j-1,bi,bj) |
| 729 |
& + maskC(i ,j-1,k,bi,bj)*mskCor(i ,j-1,bi,bj) ) |
| 730 |
& + ( maskC(i-1,j+1,k,bi,bj)*mskCor(i-1,j+1,bi,bj) |
| 731 |
& + maskC(i ,j+1,k,bi,bj)*mskCor(i ,j+1,bi,bj) ) ) |
| 732 |
& )*maskC(i-1,j,k,bi,bj)*mskCor(i-1,j,bi,bj) |
| 733 |
& *maskC(i ,j,k,bi,bj)*mskCor(i ,j,bi,bj) |
| 734 |
#else |
| 735 |
tmpVisc = _maskW(i,j,k,bi,bj) * halfRL |
| 736 |
& *( GGL90visctmp(i-1,j,k) |
| 737 |
& + GGL90visctmp(i,j,k) ) |
| 738 |
#endif |
| 739 |
tmpVisc = MIN( tmpVisc , GGL90viscMax ) |
| 740 |
GGL90viscArU(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) |
| 741 |
ENDDO |
| 742 |
ENDDO |
| 743 |
ENDDO |
| 744 |
|
| 745 |
DO k=2,Nr |
| 746 |
DO j=1,sNy+1 |
| 747 |
DO i=1,sNx |
| 748 |
#ifdef ALLOW_GGL90_SMOOTH |
| 749 |
tmpVisc = ( |
| 750 |
& p4 *( GGL90visctmp(i ,j-1,k)*mskCor(i ,j-1,bi,bj) |
| 751 |
& + GGL90visctmp(i ,j ,k)*mskCor(i ,j ,bi,bj) ) |
| 752 |
& +p8 *( ( GGL90visctmp(i-1,j-1,k)*mskCor(i-1,j-1,bi,bj) |
| 753 |
& + GGL90visctmp(i-1,j ,k)*mskCor(i-1,j ,bi,bj) ) |
| 754 |
& + ( GGL90visctmp(i+1,j-1,k)*mskCor(i+1,j-1,bi,bj) |
| 755 |
& + GGL90visctmp(i+1,j ,k)*mskCor(i+1,j ,bi,bj) ) ) |
| 756 |
& )/( |
| 757 |
& p4 * 2. _d 0 |
| 758 |
& +p8 *( ( maskC(i-1,j-1,k,bi,bj)*mskCor(i-1,j-1,bi,bj) |
| 759 |
& + maskC(i-1,j ,k,bi,bj)*mskCor(i-1,j ,bi,bj) ) |
| 760 |
& + ( maskC(i+1,j-1,k,bi,bj)*mskCor(i+1,j-1,bi,bj) |
| 761 |
& + maskC(i+1,j ,k,bi,bj)*mskCor(i+1,j ,bi,bj) ) ) |
| 762 |
& )*maskC(i,j-1,k,bi,bj)*mskCor(i,j-1,bi,bj) |
| 763 |
& *maskC(i,j ,k,bi,bj)*mskCor(i,j ,bi,bj) |
| 764 |
#else |
| 765 |
tmpVisc = _maskS(i,j,k,bi,bj) * halfRL |
| 766 |
& *( GGL90visctmp(i,j-1,k) |
| 767 |
& + GGL90visctmp(i,j,k) ) |
| 768 |
#endif |
| 769 |
tmpVisc = MIN( tmpVisc , GGL90viscMax ) |
| 770 |
GGL90viscArV(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) |
| 771 |
ENDDO |
| 772 |
ENDDO |
| 773 |
ENDDO |
| 774 |
|
| 775 |
#ifdef ALLOW_DIAGNOSTICS |
| 776 |
IF ( useDiagnostics ) THEN |
| 777 |
CALL DIAGNOSTICS_FILL( GGL90TKE ,'GGL90TKE', |
| 778 |
& 0,Nr, 1, bi, bj, myThid ) |
| 779 |
CALL DIAGNOSTICS_FILL( GGL90viscArU,'GGL90ArU', |
| 780 |
& 0,Nr, 1, bi, bj, myThid ) |
| 781 |
CALL DIAGNOSTICS_FILL( GGL90viscArV,'GGL90ArV', |
| 782 |
& 0,Nr, 1, bi, bj, myThid ) |
| 783 |
CALL DIAGNOSTICS_FILL( GGL90diffKr,'GGL90Kr ', |
| 784 |
& 0,Nr, 1, bi, bj, myThid ) |
| 785 |
CALL DIAGNOSTICS_FILL( TKEPrandtlNumber ,'GGL90Prl', |
| 786 |
& 0,Nr, 2, bi, bj, myThid ) |
| 787 |
CALL DIAGNOSTICS_FILL( GGL90mixingLength,'GGL90Lmx', |
| 788 |
& 0,Nr, 2, bi, bj, myThid ) |
| 789 |
|
| 790 |
kp1 = MIN(Nr,kSurf+1) |
| 791 |
DO j=jMin,jMax |
| 792 |
DO i=iMin,iMax |
| 793 |
C diagnose surface flux of TKE |
| 794 |
surf_flx_tke(i,j) =(GGL90TKE(i,j,kSurf,bi,bj)- |
| 795 |
& GGL90TKE(i,j,kp1,bi,bj)) |
| 796 |
& *recip_drF(kSurf)*recip_hFacC(i,j,kSurf,bi,bj) |
| 797 |
& *KappaE(i,j,kp1) |
| 798 |
ENDDO |
| 799 |
ENDDO |
| 800 |
CALL DIAGNOSTICS_FILL( surf_flx_tke,'GGL90flx', |
| 801 |
& 0, 1, 2, bi, bj, myThid ) |
| 802 |
|
| 803 |
k=kSurf |
| 804 |
DO j=jMin,jMax |
| 805 |
DO i=iMin,iMax |
| 806 |
C diagnose work done by the wind |
| 807 |
surf_flx_tke(i,j) = |
| 808 |
& halfRL*( surfaceForcingU(i, j,bi,bj)*uVel(i ,j,k,bi,bj) |
| 809 |
& +surfaceForcingU(i+1,j,bi,bj)*uVel(i+1,j,k,bi,bj)) |
| 810 |
& + halfRL*( surfaceForcingV(i,j, bi,bj)*vVel(i,j ,k,bi,bj) |
| 811 |
& +surfaceForcingV(i,j+1,bi,bj)*vVel(i,j+1,k,bi,bj)) |
| 812 |
ENDDO |
| 813 |
ENDDO |
| 814 |
CALL DIAGNOSTICS_FILL( surf_flx_tke,'GGL90tau', |
| 815 |
& 0, 1, 2, bi, bj, myThid ) |
| 816 |
|
| 817 |
ENDIF |
| 818 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 819 |
|
| 820 |
#endif /* ALLOW_GGL90 */ |
| 821 |
|
| 822 |
RETURN |
| 823 |
END |
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