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C $Header: /u/gcmpack/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.32 2015/02/26 16:45:24 mlosch 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, tempV, 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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CEOP |
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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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iMin = 2-OLx |
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iMax = sNx+OLx-1 |
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jMin = 2-OLy |
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jMax = sNy+OLy-1 |
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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 |
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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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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 |
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ENDDO |
328 |
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 |
334 |
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 |
341 |
ENDDO |
342 |
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) = MIN(GGL90mixingLength(i,j,k), |
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& mxLength_Dn(i,j,k)) |
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tmpmlx = SQRT( GGL90mixingLength(i,j,k)*mxLength_Dn(i,j,k) ) |
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tmpmlx = MAX( tmpmlx, GGL90mixingLengthMin) |
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rMixingLength(i,j,k) = 1. _d 0 / tmpmlx |
352 |
ENDDO |
353 |
ENDDO |
354 |
ENDDO |
355 |
|
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ELSE |
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STOP 'GGL90_CALC: Wrong mxlMaxFlag (mixing length limit)' |
358 |
ENDIF |
359 |
|
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C start "proper" k-loop (the code above was moved out and up to |
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C implemement various mixing parameters efficiently) |
362 |
DO k=2,Nr |
363 |
km1 = k-1 |
364 |
|
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#ifdef ALLOW_GGL90_HORIZDIFF |
366 |
IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
367 |
C horizontal diffusion of TKE (requires an exchange in |
368 |
C do_fields_blocking_exchanges) |
369 |
C common factors |
370 |
DO j=1-OLy,sNy+OLy |
371 |
DO i=1-OLx,sNx+OLx |
372 |
xA(i,j) = _dyG(i,j,bi,bj)*drC(k)* |
373 |
& (min(.5 _d 0,_hFacW(i,j,k-1,bi,bj) ) + |
374 |
& min(.5 _d 0,_hFacW(i,j,k ,bi,bj) ) ) |
375 |
yA(i,j) = _dxG(i,j,bi,bj)*drC(k)* |
376 |
& (min(.5 _d 0,_hFacS(i,j,k-1,bi,bj) ) + |
377 |
& min(.5 _d 0,_hFacS(i,j,k ,bi,bj) ) ) |
378 |
ENDDO |
379 |
ENDDO |
380 |
C Compute diffusive fluxes |
381 |
C ... across x-faces |
382 |
DO j=1-OLy,sNy+OLy |
383 |
dfx(1-OLx,j)=0. _d 0 |
384 |
DO i=1-OLx+1,sNx+OLx |
385 |
dfx(i,j) = -GGL90diffTKEh*xA(i,j) |
386 |
& *_recip_dxC(i,j,bi,bj) |
387 |
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i-1,j,k,bi,bj)) |
388 |
#ifdef ISOTROPIC_COS_SCALING |
389 |
& *CosFacU(j,bi,bj) |
390 |
#endif /* ISOTROPIC_COS_SCALING */ |
391 |
ENDDO |
392 |
ENDDO |
393 |
C ... across y-faces |
394 |
DO i=1-OLx,sNx+OLx |
395 |
dfy(i,1-OLy)=0. _d 0 |
396 |
ENDDO |
397 |
DO j=1-OLy+1,sNy+OLy |
398 |
DO i=1-OLx,sNx+OLx |
399 |
dfy(i,j) = -GGL90diffTKEh*yA(i,j) |
400 |
& *_recip_dyC(i,j,bi,bj) |
401 |
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i,j-1,k,bi,bj)) |
402 |
#ifdef ISOTROPIC_COS_SCALING |
403 |
& *CosFacV(j,bi,bj) |
404 |
#endif /* ISOTROPIC_COS_SCALING */ |
405 |
ENDDO |
406 |
ENDDO |
407 |
C Compute divergence of fluxes |
408 |
DO j=1-OLy,sNy+OLy-1 |
409 |
DO i=1-OLx,sNx+OLx-1 |
410 |
gTKE(i,j) = -recip_drC(k)*recip_rA(i,j,bi,bj) |
411 |
& *recip_hFacI(i,j,k) |
412 |
& *((dfx(i+1,j)-dfx(i,j)) |
413 |
& + (dfy(i,j+1)-dfy(i,j)) ) |
414 |
ENDDO |
415 |
ENDDO |
416 |
C end if GGL90diffTKEh .eq. 0. |
417 |
ENDIF |
418 |
#endif /* ALLOW_GGL90_HORIZDIFF */ |
419 |
|
420 |
C viscosity and diffusivity |
421 |
DO j=jMin,jMax |
422 |
DO i=iMin,iMax |
423 |
KappaM(i,j) = GGL90ck*GGL90mixingLength(i,j,k)*SQRTTKE(i,j,k) |
424 |
GGL90visctmp(i,j,k) = MAX(KappaM(i,j),diffKrNrS(k)) |
425 |
& * maskC(i,j,k,bi,bj) |
426 |
C note: storing GGL90visctmp like this, and using it later to compute |
427 |
C GGL9rdiffKr etc. is robust in case of smoothing (e.g. see OPA) |
428 |
KappaM(i,j) = MAX(KappaM(i,j),viscArNr(k)) * maskC(i,j,k,bi,bj) |
429 |
ENDDO |
430 |
ENDDO |
431 |
|
432 |
C compute Prandtl number (always greater than 0) |
433 |
#ifdef ALLOW_GGL90_IDEMIX |
434 |
IF ( useIDEMIX ) THEN |
435 |
DO j=jMin,jMax |
436 |
DO i=iMin,iMax |
437 |
C vertical shear term (dU/dz)^2+(dV/dz)^2 |
438 |
tempU= .5 _d 0*( uVel(i,j,km1,bi,bj)+uVel(i+1,j,km1,bi,bj) |
439 |
& -( uVel(i,j,k ,bi,bj)+uVel(i+1,j,k ,bi,bj)) ) |
440 |
& *recip_drC(k)*recip_hFacI(i,j,k) |
441 |
tempV= .5 _d 0*( vVel(i,j,km1,bi,bj)+vVel(i,j+1,km1,bi,bj) |
442 |
& -( vVel(i,j,k ,bi,bj)+vVel(i,j+1,k ,bi,bj)) ) |
443 |
& *recip_drC(k)*recip_hFacI(i,j,k) |
444 |
verticalShear(i,j) = tempU*tempU + tempV*tempV |
445 |
RiNumber = MAX(Nsquare(i,j,k),0. _d 0) |
446 |
& /(verticalShear(i,j)+GGL90eps) |
447 |
CML IDEMIX_RiNumber = 1./GGL90eps |
448 |
IDEMIX_RiNumber = MAX( KappaM(i,j)*Nsquare(i,j,k), 0. _d 0)/ |
449 |
& (GGL90eps+IDEMIX_tau_d(i,j,k,bi,bj)*IDEMIX_E(i,j,k,bi,bj)**2) |
450 |
prTemp = MIN(5.*RiNumber, 6.6 _d 0*IDEMIX_RiNumber) |
451 |
TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) |
452 |
TKEPrandtlNumber(i,j,k) = MAX( 1. _d 0,TKEPrandtlNumber(i,j,k)) |
453 |
ENDDO |
454 |
ENDDO |
455 |
ELSE |
456 |
#else /* ndef ALLOW_GGL90_IDEMIX */ |
457 |
IF (.TRUE.) THEN |
458 |
#endif /* ALLOW_GGL90_IDEMIX */ |
459 |
DO j=jMin,jMax |
460 |
DO i=iMin,iMax |
461 |
tempU= .5 _d 0*( uVel(i,j,km1,bi,bj)+uVel(i+1,j,km1,bi,bj) |
462 |
& -( uVel(i,j,k ,bi,bj)+uVel(i+1,j,k ,bi,bj)) ) |
463 |
& *recip_drC(k) |
464 |
tempV= .5 _d 0*( vVel(i,j,km1,bi,bj)+vVel(i,j+1,km1,bi,bj) |
465 |
& -( vVel(i,j,k ,bi,bj)+vVel(i,j+1,k ,bi,bj)) ) |
466 |
& *recip_drC(k) |
467 |
verticalShear(i,j) = tempU*tempU + tempV*tempV |
468 |
RiNumber = MAX(Nsquare(i,j,k),0. _d 0) |
469 |
& /(verticalShear(i,j)+GGL90eps) |
470 |
prTemp = 1. _d 0 |
471 |
IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber |
472 |
TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) |
473 |
ENDDO |
474 |
ENDDO |
475 |
ENDIF |
476 |
|
477 |
DO j=jMin,jMax |
478 |
DO i=iMin,iMax |
479 |
C diffusivity |
480 |
KappaH = KappaM(i,j)/TKEPrandtlNumber(i,j,k) |
481 |
KappaE(i,j,k) = GGL90alpha * KappaM(i,j) * maskC(i,j,k,bi,bj) |
482 |
|
483 |
C dissipation term |
484 |
TKEdissipation = explDissFac*GGL90ceps |
485 |
& *SQRTTKE(i,j,k)*rMixingLength(i,j,k) |
486 |
& *GGL90TKE(i,j,k,bi,bj) |
487 |
C partial update with sum of explicit contributions |
488 |
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
489 |
& + deltaTggl90*( |
490 |
& + KappaM(i,j)*verticalShear(i,j) |
491 |
& - KappaH*Nsquare(i,j,k) |
492 |
& - TKEdissipation |
493 |
& ) |
494 |
ENDDO |
495 |
ENDDO |
496 |
|
497 |
#ifdef ALLOW_GGL90_IDEMIX |
498 |
IF ( useIDEMIX ) THEN |
499 |
C add IDEMIX contribution to the turbulent kinetic energy |
500 |
DO j=jMin,jMax |
501 |
DO i=iMin,iMax |
502 |
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
503 |
& + deltaTggl90*( |
504 |
& + IDEMIX_tau_d(i,j,k,bi,bj)*IDEMIX_E(i,j,k,bi,bj)**2 |
505 |
& ) |
506 |
ENDDO |
507 |
ENDDO |
508 |
ENDIF |
509 |
#endif /* ALLOW_GGL90_IDEMIX */ |
510 |
|
511 |
#ifdef ALLOW_GGL90_HORIZDIFF |
512 |
IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
513 |
C-- Add horiz. diffusion tendency |
514 |
DO j=jMin,jMax |
515 |
DO i=iMin,iMax |
516 |
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
517 |
& + gTKE(i,j)*deltaTggl90 |
518 |
ENDDO |
519 |
ENDDO |
520 |
ENDIF |
521 |
#endif /* ALLOW_GGL90_HORIZDIFF */ |
522 |
|
523 |
C-- end of k loop |
524 |
ENDDO |
525 |
|
526 |
C ============================================ |
527 |
C Implicit time step to update TKE for k=1,Nr; |
528 |
C TKE(Nr+1)=0 by default |
529 |
C ============================================ |
530 |
C set up matrix |
531 |
C-- Lower diagonal |
532 |
DO j=jMin,jMax |
533 |
DO i=iMin,iMax |
534 |
a3d(i,j,1) = 0. _d 0 |
535 |
ENDDO |
536 |
ENDDO |
537 |
DO k=2,Nr |
538 |
km1=MAX(2,k-1) |
539 |
DO j=jMin,jMax |
540 |
DO i=iMin,iMax |
541 |
C- We keep recip_hFacC in the diffusive flux calculation, |
542 |
C- but no hFacC in TKE volume control |
543 |
C- No need for maskC(k-1) with recip_hFacC(k-1) |
544 |
a3d(i,j,k) = -deltaTggl90 |
545 |
& *recip_drF(k-1)*recip_hFacC(i,j,k-1,bi,bj) |
546 |
& *.5 _d 0*(KappaE(i,j, k )+KappaE(i,j,km1)) |
547 |
& *recip_drC(k)*maskC(i,j,k,bi,bj) |
548 |
ENDDO |
549 |
ENDDO |
550 |
ENDDO |
551 |
C-- Upper diagonal |
552 |
DO j=jMin,jMax |
553 |
DO i=iMin,iMax |
554 |
c3d(i,j,1) = 0. _d 0 |
555 |
ENDDO |
556 |
ENDDO |
557 |
DO k=2,Nr |
558 |
DO j=jMin,jMax |
559 |
DO i=iMin,iMax |
560 |
kp1=MAX(1,MIN(klowC(i,j,bi,bj),k+1)) |
561 |
C- We keep recip_hFacC in the diffusive flux calculation, |
562 |
C- but no hFacC in TKE volume control |
563 |
C- No need for maskC(k) with recip_hFacC(k) |
564 |
c3d(i,j,k) = -deltaTggl90 |
565 |
& *recip_drF( k ) * recip_hFacC(i,j,k,bi,bj) |
566 |
& *.5 _d 0*(KappaE(i,j,k)+KappaE(i,j,kp1)) |
567 |
& *recip_drC(k)*maskC(i,j,k-1,bi,bj) |
568 |
ENDDO |
569 |
ENDDO |
570 |
ENDDO |
571 |
|
572 |
#ifdef ALLOW_GGL90_IDEMIX |
573 |
IF ( useIDEMIX ) THEN |
574 |
DO k=2,Nr |
575 |
DO j=jMin,jMax |
576 |
DO i=iMin,iMax |
577 |
a3d(i,j,k) = a3d(i,j,k)*recip_hFacI(i,j,k) |
578 |
c3d(i,j,k) = c3d(i,j,k)*recip_hFacI(i,j,k) |
579 |
ENDDO |
580 |
ENDDO |
581 |
ENDDO |
582 |
ENDIF |
583 |
#endif /* ALLOW_GGL90_IDEMIX */ |
584 |
|
585 |
IF (.NOT.GGL90_dirichlet) THEN |
586 |
C Neumann bottom boundary condition for TKE: no flux from bottom |
587 |
DO j=jMin,jMax |
588 |
DO i=iMin,iMax |
589 |
kBottom = MAX(kLowC(i,j,bi,bj),1) |
590 |
c3d(i,j,kBottom) = 0. _d 0 |
591 |
ENDDO |
592 |
ENDDO |
593 |
ENDIF |
594 |
|
595 |
C-- Center diagonal |
596 |
DO k=1,Nr |
597 |
km1 = MAX(k-1,1) |
598 |
DO j=jMin,jMax |
599 |
DO i=iMin,iMax |
600 |
b3d(i,j,k) = 1. _d 0 - c3d(i,j,k) - a3d(i,j,k) |
601 |
& + implDissFac*deltaTggl90*GGL90ceps*SQRTTKE(i,j,k) |
602 |
& * rMixingLength(i,j,k) |
603 |
& * maskC(i,j,k,bi,bj)*maskC(i,j,km1,bi,bj) |
604 |
ENDDO |
605 |
ENDDO |
606 |
ENDDO |
607 |
C end set up matrix |
608 |
|
609 |
C Apply boundary condition |
610 |
kp1 = MIN(Nr,kSurf+1) |
611 |
DO j=jMin,jMax |
612 |
DO i=iMin,iMax |
613 |
C estimate friction velocity uStar from surface forcing |
614 |
uStarSquare = SQRT( |
615 |
& ( .5 _d 0*( surfaceForcingU(i, j, bi,bj) |
616 |
& + surfaceForcingU(i+1,j, bi,bj) ) )**2 |
617 |
& + ( .5 _d 0*( surfaceForcingV(i, j, bi,bj) |
618 |
& + surfaceForcingV(i, j+1,bi,bj) ) )**2 |
619 |
& ) |
620 |
C Dirichlet surface boundary condition for TKE |
621 |
GGL90TKE(i,j,kSurf,bi,bj) = maskC(i,j,kSurf,bi,bj) |
622 |
& *MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare) |
623 |
GGL90TKE(i,j,kp1,bi,bj) = GGL90TKE(i,j,kp1,bi,bj) |
624 |
& - a3d(i,j,kp1)*GGL90TKE(i,j,kSurf,bi,bj) |
625 |
a3d(i,j,kp1) = 0. _d 0 |
626 |
ENDDO |
627 |
ENDDO |
628 |
|
629 |
IF (GGL90_dirichlet) THEN |
630 |
C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom |
631 |
DO j=jMin,jMax |
632 |
DO i=iMin,iMax |
633 |
kBottom = MAX(kLowC(i,j,bi,bj),1) |
634 |
GGL90TKE(i,j,kBottom,bi,bj) = GGL90TKE(i,j,kBottom,bi,bj) |
635 |
& - GGL90TKEbottom*c3d(i,j,kBottom) |
636 |
c3d(i,j,kBottom) = 0. _d 0 |
637 |
ENDDO |
638 |
ENDDO |
639 |
ENDIF |
640 |
|
641 |
C solve tri-diagonal system |
642 |
CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
643 |
I a3d, b3d, c3d, |
644 |
U GGL90TKE(1-OLx,1-OLy,1,bi,bj), |
645 |
O errCode, |
646 |
I bi, bj, myThid ) |
647 |
|
648 |
DO k=1,Nr |
649 |
DO j=jMin,jMax |
650 |
DO i=iMin,iMax |
651 |
C impose minimum TKE to avoid numerical undershoots below zero |
652 |
GGL90TKE(i,j,k,bi,bj) = maskC(i,j,k,bi,bj) |
653 |
& *MAX( GGL90TKE(i,j,k,bi,bj), GGL90TKEmin ) |
654 |
ENDDO |
655 |
ENDDO |
656 |
ENDDO |
657 |
|
658 |
C end of time step |
659 |
C =============================== |
660 |
|
661 |
DO k=2,Nr |
662 |
DO j=1,sNy |
663 |
DO i=1,sNx |
664 |
#ifdef ALLOW_GGL90_SMOOTH |
665 |
tmpVisc= |
666 |
& ( |
667 |
& p4 * GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) |
668 |
& +p8 *( GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj) |
669 |
& + GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj) |
670 |
& + GGL90visctmp(i+1,j ,k) * mskCor(i+1,j ,bi,bj) |
671 |
& + GGL90visctmp(i ,j+1,k) * mskCor(i ,j+1,bi,bj)) |
672 |
& +p16*( GGL90visctmp(i+1,j+1,k) * mskCor(i+1,j+1,bi,bj) |
673 |
& + GGL90visctmp(i+1,j-1,k) * mskCor(i+1,j-1,bi,bj) |
674 |
& + GGL90visctmp(i-1,j+1,k) * mskCor(i-1,j+1,bi,bj) |
675 |
& + GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj)) |
676 |
& ) |
677 |
& /(p4 |
678 |
& +p8 *( maskC(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) |
679 |
& + maskC(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) |
680 |
& + maskC(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) |
681 |
& + maskC(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) |
682 |
& +p16*( maskC(i+1,j+1,k,bi,bj) * mskCor(i+1,j+1,bi,bj) |
683 |
& + maskC(i+1,j-1,k,bi,bj) * mskCor(i+1,j-1,bi,bj) |
684 |
& + maskC(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) |
685 |
& + maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj)) |
686 |
& )*maskC(i,j,k,bi,bj)*mskCor(i,j,bi,bj) |
687 |
#else |
688 |
tmpVisc = GGL90visctmp(i,j,k) |
689 |
#endif |
690 |
tmpVisc = MIN(tmpVisc/TKEPrandtlNumber(i,j,k),GGL90diffMax) |
691 |
GGL90diffKr(i,j,k,bi,bj)= MAX( tmpVisc , diffKrNrS(k) ) |
692 |
ENDDO |
693 |
ENDDO |
694 |
ENDDO |
695 |
|
696 |
DO k=2,Nr |
697 |
DO j=1,sNy |
698 |
DO i=1,sNx+1 |
699 |
#ifdef ALLOW_GGL90_SMOOTH |
700 |
tmpVisc = |
701 |
& ( |
702 |
& p4 *(GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) |
703 |
& +GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj)) |
704 |
& +p8 *(GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj) |
705 |
& +GGL90visctmp(i-1,j+1,k) * mskCor(i-1,j+1,bi,bj) |
706 |
& +GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj) |
707 |
& +GGL90visctmp(i ,j+1,k) * mskCor(i ,j+1,bi,bj)) |
708 |
& ) |
709 |
& /(p4 * 2. _d 0 |
710 |
& +p8 *( maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj) |
711 |
& + maskC(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) |
712 |
& + maskC(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) |
713 |
& + maskC(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) |
714 |
& ) |
715 |
& *maskC(i ,j,k,bi,bj)*mskCor(i ,j,bi,bj) |
716 |
& *maskC(i-1,j,k,bi,bj)*mskCor(i-1,j,bi,bj) |
717 |
#else |
718 |
tmpVisc = _maskW(i,j,k,bi,bj) * |
719 |
& (.5 _d 0*(GGL90visctmp(i,j,k) |
720 |
& +GGL90visctmp(i-1,j,k)) |
721 |
& ) |
722 |
#endif |
723 |
tmpVisc = MIN( tmpVisc , GGL90viscMax ) |
724 |
GGL90viscArU(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) |
725 |
ENDDO |
726 |
ENDDO |
727 |
ENDDO |
728 |
|
729 |
DO k=2,Nr |
730 |
DO j=1,sNy+1 |
731 |
DO i=1,sNx |
732 |
#ifdef ALLOW_GGL90_SMOOTH |
733 |
tmpVisc = |
734 |
& ( |
735 |
& p4 *(GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) |
736 |
& +GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj)) |
737 |
& +p8 *(GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj) |
738 |
& +GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj) |
739 |
& +GGL90visctmp(i+1,j ,k) * mskCor(i+1,j ,bi,bj) |
740 |
& +GGL90visctmp(i+1,j-1,k) * mskCor(i+1,j-1,bi,bj)) |
741 |
& ) |
742 |
& /(p4 * 2. _d 0 |
743 |
& +p8 *( maskC(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) |
744 |
& + maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj) |
745 |
& + maskC(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) |
746 |
& + maskC(i+1,j-1,k,bi,bj) * mskCor(i+1,j-1,bi,bj)) |
747 |
& ) |
748 |
& *maskC(i,j ,k,bi,bj)*mskCor(i,j ,bi,bj) |
749 |
& *maskC(i,j-1,k,bi,bj)*mskCor(i,j-1,bi,bj) |
750 |
#else |
751 |
tmpVisc = _maskS(i,j,k,bi,bj) * |
752 |
& (.5 _d 0*(GGL90visctmp(i,j,k) |
753 |
& +GGL90visctmp(i,j-1,k)) |
754 |
& ) |
755 |
|
756 |
#endif |
757 |
tmpVisc = MIN( tmpVisc , GGL90viscMax ) |
758 |
GGL90viscArV(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) |
759 |
ENDDO |
760 |
ENDDO |
761 |
ENDDO |
762 |
|
763 |
#ifdef ALLOW_DIAGNOSTICS |
764 |
IF ( useDiagnostics ) THEN |
765 |
CALL DIAGNOSTICS_FILL( GGL90TKE ,'GGL90TKE', |
766 |
& 0,Nr, 1, bi, bj, myThid ) |
767 |
CALL DIAGNOSTICS_FILL( GGL90viscArU,'GGL90ArU', |
768 |
& 0,Nr, 1, bi, bj, myThid ) |
769 |
CALL DIAGNOSTICS_FILL( GGL90viscArV,'GGL90ArV', |
770 |
& 0,Nr, 1, bi, bj, myThid ) |
771 |
CALL DIAGNOSTICS_FILL( GGL90diffKr,'GGL90Kr ', |
772 |
& 0,Nr, 1, bi, bj, myThid ) |
773 |
CALL DIAGNOSTICS_FILL( TKEPrandtlNumber ,'GGL90Prl', |
774 |
& 0,Nr, 2, bi, bj, myThid ) |
775 |
CALL DIAGNOSTICS_FILL( GGL90mixingLength,'GGL90Lmx', |
776 |
& 0,Nr, 2, bi, bj, myThid ) |
777 |
|
778 |
kp1 = MIN(Nr,kSurf+1) |
779 |
DO j=jMin,jMax |
780 |
DO i=iMin,iMax |
781 |
C diagnose surface flux of TKE |
782 |
surf_flx_tke(i,j) =(GGL90TKE(i,j,kSurf,bi,bj)- |
783 |
& GGL90TKE(i,j,kp1,bi,bj)) |
784 |
& *recip_drF(kSurf)*recip_hFacC(i,j,kSurf,bi,bj) |
785 |
& *KappaE(i,j,kp1) |
786 |
ENDDO |
787 |
ENDDO |
788 |
CALL DIAGNOSTICS_FILL( surf_flx_tke,'GGL90flx', |
789 |
& 0, 1, 2, bi, bj, myThid ) |
790 |
|
791 |
k=kSurf |
792 |
DO j=jMin,jMax |
793 |
DO i=iMin,iMax |
794 |
C diagnose work done by the wind |
795 |
surf_flx_tke(i,j) = |
796 |
& halfRL*( surfaceForcingU(i, j,bi,bj)*uVel(i ,j,k,bi,bj) |
797 |
& +surfaceForcingU(i+1,j,bi,bj)*uVel(i+1,j,k,bi,bj)) |
798 |
& + halfRL*( surfaceForcingV(i,j, bi,bj)*vVel(i,j ,k,bi,bj) |
799 |
& +surfaceForcingV(i,j+1,bi,bj)*vVel(i,j+1,k,bi,bj)) |
800 |
ENDDO |
801 |
ENDDO |
802 |
CALL DIAGNOSTICS_FILL( surf_flx_tke,'GGL90tau', |
803 |
& 0, 1, 2, bi, bj, myThid ) |
804 |
|
805 |
ENDIF |
806 |
#endif /* ALLOW_DIAGNOSTICS */ |
807 |
|
808 |
#endif /* ALLOW_GGL90 */ |
809 |
|
810 |
RETURN |
811 |
END |