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jmc |
1.22 |
C $Header: /u/gcmpack/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.21 2012/06/27 22:39:09 jmc Exp $ |
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mlosch |
1.1 |
C $Name: $ |
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#include "GGL90_OPTIONS.h" |
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CBOP |
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C !ROUTINE: GGL90_CALC |
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C !INTERFACE: ====================================================== |
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jmc |
1.19 |
SUBROUTINE GGL90_CALC( |
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jmc |
1.21 |
I bi, bj, sigmaR, myTime, myIter, myThid ) |
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mlosch |
1.1 |
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C !DESCRIPTION: \bv |
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jmc |
1.12 |
C *==========================================================* |
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mlosch |
1.1 |
C | SUBROUTINE GGL90_CALC | |
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C | o Compute all GGL90 fields defined in GGL90.h | |
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jmc |
1.12 |
C *==========================================================* |
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mlosch |
1.1 |
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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jmc |
1.12 |
C *==========================================================* |
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mlosch |
1.1 |
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C global parameters updated by ggl90_calc |
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jmc |
1.12 |
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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mlosch |
1.1 |
C \ev |
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C !USES: ============================================================ |
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jmc |
1.12 |
IMPLICIT NONE |
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mlosch |
1.1 |
#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 "GGL90.h" |
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#include "FFIELDS.h" |
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#include "GRID.h" |
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C !INPUT PARAMETERS: =================================================== |
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jmc |
1.12 |
C Routine arguments |
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jmc |
1.21 |
C bi, bj :: Current tile indices |
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C sigmaR :: Vertical gradient of iso-neutral density |
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jmc |
1.12 |
C myTime :: Current time in simulation |
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jmc |
1.19 |
C myIter :: Current time-step number |
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jmc |
1.12 |
C myThid :: My Thread Id number |
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mlosch |
1.1 |
INTEGER bi, bj |
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jmc |
1.21 |
_RL sigmaR(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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jmc |
1.12 |
_RL myTime |
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jmc |
1.19 |
INTEGER myIter |
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mlosch |
1.1 |
INTEGER myThid |
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jmc |
1.12 |
CEOP |
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mlosch |
1.1 |
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#ifdef ALLOW_GGL90 |
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C !LOCAL VARIABLES: ==================================================== |
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jmc |
1.12 |
C Local constants |
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jmc |
1.19 |
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 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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mlosch |
1.1 |
INTEGER iMin ,iMax ,jMin ,jMax |
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jmc |
1.19 |
INTEGER i, j, k, kp1, km1, kSurf, kBottom |
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_RL explDissFac, implDissFac |
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mlosch |
1.1 |
_RL uStarSquare |
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_RL verticalShear |
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_RL KappaM, KappaH |
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dfer |
1.11 |
c _RL Nsquare |
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_RL Nsquare(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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mlosch |
1.1 |
_RL deltaTggl90 |
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dfer |
1.11 |
c _RL SQRTTKE |
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_RL SQRTTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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mlosch |
1.1 |
_RL RiNumber |
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_RL TKEdissipation |
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_RL tempU, tempV, prTemp |
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gforget |
1.16 |
_RL MaxLength, tmpmlx, tmpVisc |
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mlosch |
1.1 |
_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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dfer |
1.13 |
_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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mlosch |
1.1 |
_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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gforget |
1.16 |
_RL GGL90visctmp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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dfer |
1.13 |
C- tri-diagonal matrix |
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jmc |
1.20 |
_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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dfer |
1.15 |
INTEGER errCode |
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mlosch |
1.2 |
#ifdef ALLOW_GGL90_HORIZDIFF |
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jmc |
1.19 |
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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mlosch |
1.2 |
_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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jmc |
1.19 |
_RL gTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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mlosch |
1.2 |
#endif /* ALLOW_GGL90_HORIZDIFF */ |
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dfer |
1.11 |
#ifdef ALLOW_GGL90_SMOOTH |
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gforget |
1.16 |
_RL p4, p8, p16 |
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dfer |
1.11 |
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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mlosch |
1.1 |
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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C set separate time step (should be deltaTtracer) |
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jmc |
1.4 |
deltaTggl90 = dTtracerLev(1) |
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jmc |
1.12 |
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mlosch |
1.1 |
kSurf = 1 |
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jmc |
1.19 |
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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mlosch |
1.1 |
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C Initialize local fields |
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jmc |
1.19 |
DO k = 1, Nr |
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jmc |
1.21 |
DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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jmc |
1.19 |
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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jmc |
1.20 |
#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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mlosch |
1.1 |
ENDDO |
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jmc |
1.8 |
ENDDO |
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mlosch |
1.1 |
ENDDO |
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jmc |
1.21 |
DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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jmc |
1.19 |
totalDepth(i,j) = Ro_surf(i,j,bi,bj) - R_low(i,j,bi,bj) |
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jmc |
1.14 |
rMixingLength(i,j,1) = 0. _d 0 |
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jmc |
1.19 |
mxLength_Dn(i,j,1) = GGL90mixingLengthMin |
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jmc |
1.14 |
SQRTTKE(i,j,1) = SQRT( GGL90TKE(i,j,1,bi,bj) ) |
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mlosch |
1.1 |
ENDDO |
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ENDDO |
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C start k-loop |
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jmc |
1.19 |
DO k = 2, Nr |
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jmc |
1.22 |
c km1 = k-1 |
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jmc |
1.19 |
c kp1 = MIN(Nr,k+1) |
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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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jmc |
1.14 |
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mlosch |
1.1 |
C buoyancy frequency |
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jmc |
1.21 |
Nsquare(i,j,k) = gravity*gravitySign*recip_rhoConst |
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& * sigmaR(i,j,k) |
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dfer |
1.11 |
cC vertical shear term (dU/dz)^2+(dV/dz)^2 |
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jmc |
1.19 |
c tempU= .5 _d 0*( uVel(i,j,km1,bi,bj)+uVel(i+1,j,km1,bi,bj) |
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c & -( uVel(i,j,k ,bi,bj)+uVel(i+1,j,k ,bi,bj)) ) |
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c & *recip_drC(k) |
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c tempV= .5 _d 0*( vVel(i,j,km1,bi,bj)+vVel(i,j+1,km1,bi,bj) |
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c & -( vVel(i,j,k ,bi,bj)+vVel(i,j+1,k ,bi,bj)) ) |
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c & *recip_drC(k) |
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dfer |
1.11 |
c verticalShear = tempU*tempU + tempV*tempV |
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c RiNumber = MAX(Nsquare(i,j,k),0. _d 0)/(verticalShear+GGL90eps) |
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cC compute Prandtl number (always greater than 0) |
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c prTemp = 1. _d 0 |
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c IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber |
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jmc |
1.19 |
c TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) |
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dfer |
1.11 |
C mixing length |
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jmc |
1.19 |
GGL90mixingLength(i,j,k) = SQRTTWO * |
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dfer |
1.11 |
& 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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dfer |
1.13 |
C- Impose upper and lower bound for mixing length |
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dfer |
1.11 |
IF ( mxlMaxFlag .EQ. 0 ) THEN |
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jmc |
1.21 |
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dfer |
1.11 |
DO k=2,Nr |
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jmc |
1.19 |
DO j=jMin,jMax |
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DO i=iMin,iMax |
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MaxLength=totalDepth(i,j) |
| 197 |
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GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
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dfer |
1.13 |
& MaxLength) |
| 199 |
dfer |
1.11 |
ENDDO |
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ENDDO |
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ENDDO |
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dfer |
1.13 |
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DO k=2,Nr |
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jmc |
1.19 |
DO j=jMin,jMax |
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DO i=iMin,iMax |
| 206 |
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GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), |
| 207 |
dfer |
1.13 |
& GGL90mixingLengthMin) |
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jmc |
1.19 |
rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) |
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dfer |
1.13 |
ENDDO |
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ENDDO |
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ENDDO |
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dfer |
1.11 |
ELSEIF ( mxlMaxFlag .EQ. 1 ) THEN |
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jmc |
1.21 |
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dfer |
1.11 |
DO k=2,Nr |
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jmc |
1.19 |
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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dfer |
1.11 |
c MaxLength=MAX(MaxLength,20. _d 0) |
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jmc |
1.19 |
GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
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dfer |
1.13 |
& MaxLength) |
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ENDDO |
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ENDDO |
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ENDDO |
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DO k=2,Nr |
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jmc |
1.19 |
DO j=jMin,jMax |
| 228 |
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DO i=iMin,iMax |
| 229 |
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GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), |
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dfer |
1.13 |
& GGL90mixingLengthMin) |
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jmc |
1.19 |
rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) |
| 232 |
dfer |
1.11 |
ENDDO |
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ENDDO |
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ENDDO |
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dfer |
1.13 |
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| 236 |
dfer |
1.11 |
ELSEIF ( mxlMaxFlag .EQ. 2 ) THEN |
| 237 |
jmc |
1.21 |
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| 238 |
gforget |
1.16 |
cgf ensure mixing between first and second level |
| 239 |
jmc |
1.19 |
c DO j=jMin,jMax |
| 240 |
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c DO i=iMin,iMax |
| 241 |
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c GGL90mixingLength(i,j,2)=drF(1) |
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gforget |
1.16 |
c ENDDO |
| 243 |
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c ENDDO |
| 244 |
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cgf |
| 245 |
dfer |
1.11 |
DO k=2,Nr |
| 246 |
jmc |
1.19 |
DO j=jMin,jMax |
| 247 |
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DO i=iMin,iMax |
| 248 |
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GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
| 249 |
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& GGL90mixingLength(i,j,k-1)+drF(k-1)) |
| 250 |
dfer |
1.11 |
ENDDO |
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ENDDO |
| 252 |
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ENDDO |
| 253 |
jmc |
1.19 |
DO j=jMin,jMax |
| 254 |
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DO i=iMin,iMax |
| 255 |
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GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr), |
| 256 |
dfer |
1.11 |
& GGL90mixingLengthMin+drF(Nr)) |
| 257 |
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ENDDO |
| 258 |
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ENDDO |
| 259 |
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DO k=Nr-1,2,-1 |
| 260 |
jmc |
1.19 |
DO j=jMin,jMax |
| 261 |
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DO i=iMin,iMax |
| 262 |
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GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
| 263 |
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& GGL90mixingLength(i,j,k+1)+drF(k)) |
| 264 |
jmc |
1.12 |
ENDDO |
| 265 |
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ENDDO |
| 266 |
dfer |
1.11 |
ENDDO |
| 267 |
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| 268 |
dfer |
1.13 |
DO k=2,Nr |
| 269 |
jmc |
1.19 |
DO j=jMin,jMax |
| 270 |
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DO i=iMin,iMax |
| 271 |
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GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), |
| 272 |
dfer |
1.13 |
& GGL90mixingLengthMin) |
| 273 |
jmc |
1.19 |
rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) |
| 274 |
dfer |
1.13 |
ENDDO |
| 275 |
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ENDDO |
| 276 |
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ENDDO |
| 277 |
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| 278 |
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ELSEIF ( mxlMaxFlag .EQ. 3 ) THEN |
| 279 |
jmc |
1.21 |
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| 280 |
dfer |
1.13 |
DO k=2,Nr |
| 281 |
jmc |
1.19 |
DO j=jMin,jMax |
| 282 |
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DO i=iMin,iMax |
| 283 |
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mxLength_Dn(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
| 284 |
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& mxLength_Dn(i,j,k-1)+drF(k-1)) |
| 285 |
dfer |
1.13 |
ENDDO |
| 286 |
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ENDDO |
| 287 |
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ENDDO |
| 288 |
jmc |
1.19 |
DO j=jMin,jMax |
| 289 |
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DO i=iMin,iMax |
| 290 |
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|
GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr), |
| 291 |
dfer |
1.13 |
& GGL90mixingLengthMin+drF(Nr)) |
| 292 |
|
|
ENDDO |
| 293 |
|
|
ENDDO |
| 294 |
|
|
DO k=Nr-1,2,-1 |
| 295 |
jmc |
1.19 |
DO j=jMin,jMax |
| 296 |
|
|
DO i=iMin,iMax |
| 297 |
|
|
GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
| 298 |
|
|
& GGL90mixingLength(i,j,k+1)+drF(k)) |
| 299 |
dfer |
1.13 |
ENDDO |
| 300 |
dfer |
1.11 |
ENDDO |
| 301 |
|
|
ENDDO |
| 302 |
dfer |
1.13 |
|
| 303 |
|
|
DO k=2,Nr |
| 304 |
jmc |
1.19 |
DO j=jMin,jMax |
| 305 |
|
|
DO i=iMin,iMax |
| 306 |
|
|
GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), |
| 307 |
|
|
& mxLength_Dn(i,j,k)) |
| 308 |
|
|
tmpmlx = SQRT( GGL90mixingLength(i,j,k)*mxLength_Dn(i,j,k) ) |
| 309 |
dfer |
1.13 |
tmpmlx = MAX( tmpmlx, GGL90mixingLengthMin) |
| 310 |
jmc |
1.19 |
rMixingLength(i,j,k) = 1. _d 0 / tmpmlx |
| 311 |
dfer |
1.13 |
ENDDO |
| 312 |
|
|
ENDDO |
| 313 |
|
|
ENDDO |
| 314 |
|
|
|
| 315 |
|
|
ELSE |
| 316 |
|
|
STOP 'GGL90_CALC: Wrong mxlMaxFlag (mixing length limit)' |
| 317 |
|
|
ENDIF |
| 318 |
|
|
|
| 319 |
|
|
C- Impose minimum mixing length (to avoid division by zero) |
| 320 |
|
|
c DO k=2,Nr |
| 321 |
jmc |
1.19 |
c DO j=jMin,jMax |
| 322 |
|
|
c DO i=iMin,iMax |
| 323 |
|
|
c GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), |
| 324 |
dfer |
1.13 |
c & GGL90mixingLengthMin) |
| 325 |
jmc |
1.19 |
c rMixingLength(i,j,k) = 1. _d 0 /GGL90mixingLength(i,j,k) |
| 326 |
dfer |
1.13 |
c ENDDO |
| 327 |
|
|
c ENDDO |
| 328 |
|
|
c ENDDO |
| 329 |
dfer |
1.11 |
|
| 330 |
|
|
DO k=2,Nr |
| 331 |
jmc |
1.19 |
km1 = k-1 |
| 332 |
dfer |
1.11 |
|
| 333 |
jmc |
1.19 |
#ifdef ALLOW_GGL90_HORIZDIFF |
| 334 |
|
|
IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
| 335 |
jmc |
1.8 |
C horizontal diffusion of TKE (requires an exchange in |
| 336 |
|
|
C do_fields_blocking_exchanges) |
| 337 |
mlosch |
1.2 |
C common factors |
| 338 |
jmc |
1.21 |
DO j=1-OLy,sNy+OLy |
| 339 |
|
|
DO i=1-OLx,sNx+OLx |
| 340 |
mlosch |
1.2 |
xA(i,j) = _dyG(i,j,bi,bj) |
| 341 |
|
|
& *drF(k)*_hFacW(i,j,k,bi,bj) |
| 342 |
|
|
yA(i,j) = _dxG(i,j,bi,bj) |
| 343 |
|
|
& *drF(k)*_hFacS(i,j,k,bi,bj) |
| 344 |
|
|
ENDDO |
| 345 |
jmc |
1.8 |
ENDDO |
| 346 |
mlosch |
1.2 |
C Compute diffusive fluxes |
| 347 |
|
|
C ... across x-faces |
| 348 |
jmc |
1.21 |
DO j=1-OLy,sNy+OLy |
| 349 |
|
|
dfx(1-OLx,j)=0. _d 0 |
| 350 |
|
|
DO i=1-OLx+1,sNx+OLx |
| 351 |
mlosch |
1.2 |
dfx(i,j) = -GGL90diffTKEh*xA(i,j) |
| 352 |
|
|
& *_recip_dxC(i,j,bi,bj) |
| 353 |
|
|
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i-1,j,k,bi,bj)) |
| 354 |
|
|
& *CosFacU(j,bi,bj) |
| 355 |
|
|
ENDDO |
| 356 |
|
|
ENDDO |
| 357 |
|
|
C ... across y-faces |
| 358 |
jmc |
1.21 |
DO i=1-OLx,sNx+OLx |
| 359 |
|
|
dfy(i,1-OLy)=0. _d 0 |
| 360 |
mlosch |
1.2 |
ENDDO |
| 361 |
jmc |
1.21 |
DO j=1-OLy+1,sNy+OLy |
| 362 |
|
|
DO i=1-OLx,sNx+OLx |
| 363 |
mlosch |
1.2 |
dfy(i,j) = -GGL90diffTKEh*yA(i,j) |
| 364 |
|
|
& *_recip_dyC(i,j,bi,bj) |
| 365 |
|
|
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i,j-1,k,bi,bj)) |
| 366 |
|
|
#ifdef ISOTROPIC_COS_SCALING |
| 367 |
|
|
& *CosFacV(j,bi,bj) |
| 368 |
|
|
#endif /* ISOTROPIC_COS_SCALING */ |
| 369 |
|
|
ENDDO |
| 370 |
jmc |
1.8 |
ENDDO |
| 371 |
mlosch |
1.2 |
C Compute divergence of fluxes |
| 372 |
jmc |
1.21 |
DO j=1-OLy,sNy+OLy-1 |
| 373 |
|
|
DO i=1-OLx,sNx+OLx-1 |
| 374 |
jmc |
1.19 |
gTKE(i,j) = |
| 375 |
|
|
& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)*recip_rA(i,j,bi,bj) |
| 376 |
mlosch |
1.2 |
& *( (dfx(i+1,j)-dfx(i,j)) |
| 377 |
jmc |
1.8 |
& +(dfy(i,j+1)-dfy(i,j)) |
| 378 |
jmc |
1.19 |
& ) |
| 379 |
jmc |
1.8 |
ENDDO |
| 380 |
mlosch |
1.2 |
ENDDO |
| 381 |
jmc |
1.19 |
C end if GGL90diffTKEh .eq. 0. |
| 382 |
|
|
ENDIF |
| 383 |
|
|
#endif /* ALLOW_GGL90_HORIZDIFF */ |
| 384 |
|
|
|
| 385 |
|
|
DO j=jMin,jMax |
| 386 |
|
|
DO i=iMin,iMax |
| 387 |
|
|
C vertical shear term (dU/dz)^2+(dV/dz)^2 |
| 388 |
|
|
tempU= .5 _d 0*( uVel(i,j,km1,bi,bj)+uVel(i+1,j,km1,bi,bj) |
| 389 |
|
|
& -( uVel(i,j,k ,bi,bj)+uVel(i+1,j,k ,bi,bj)) ) |
| 390 |
|
|
& *recip_drC(k) |
| 391 |
|
|
tempV= .5 _d 0*( vVel(i,j,km1,bi,bj)+vVel(i,j+1,km1,bi,bj) |
| 392 |
|
|
& -( vVel(i,j,k ,bi,bj)+vVel(i,j+1,k ,bi,bj)) ) |
| 393 |
|
|
& *recip_drC(k) |
| 394 |
|
|
verticalShear = tempU*tempU + tempV*tempV |
| 395 |
|
|
RiNumber = MAX(Nsquare(i,j,k),0. _d 0)/(verticalShear+GGL90eps) |
| 396 |
|
|
C compute Prandtl number (always greater than 0) |
| 397 |
|
|
prTemp = 1. _d 0 |
| 398 |
|
|
IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber |
| 399 |
|
|
TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) |
| 400 |
|
|
c TKEPrandtlNumber(i,j,k) = 1. _d 0 |
| 401 |
|
|
|
| 402 |
|
|
C viscosity and diffusivity |
| 403 |
|
|
KappaM = GGL90ck*GGL90mixingLength(i,j,k)*SQRTTKE(i,j,k) |
| 404 |
|
|
GGL90visctmp(i,j,k) = MAX(KappaM,diffKrNrT(k)) |
| 405 |
|
|
& * maskC(i,j,k,bi,bj) |
| 406 |
|
|
c note: storing GGL90visctmp like this, and using it later to compute |
| 407 |
|
|
c GGL9rdiffKr etc. is robust in case of smoothing (e.g. see OPA) |
| 408 |
|
|
KappaM = MAX(KappaM,viscArNr(k)) * maskC(i,j,k,bi,bj) |
| 409 |
|
|
KappaH = KappaM/TKEPrandtlNumber(i,j,k) |
| 410 |
|
|
KappaE(i,j,k) = GGL90alpha * KappaM * maskC(i,j,k,bi,bj) |
| 411 |
|
|
|
| 412 |
|
|
C dissipation term |
| 413 |
|
|
TKEdissipation = explDissFac*GGL90ceps |
| 414 |
|
|
& *SQRTTKE(i,j,k)*rMixingLength(i,j,k) |
| 415 |
|
|
& *GGL90TKE(i,j,k,bi,bj) |
| 416 |
|
|
C partial update with sum of explicit contributions |
| 417 |
|
|
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
| 418 |
|
|
& + deltaTggl90*( |
| 419 |
|
|
& + KappaM*verticalShear |
| 420 |
|
|
& - KappaH*Nsquare(i,j,k) |
| 421 |
|
|
& - TKEdissipation |
| 422 |
|
|
& ) |
| 423 |
|
|
ENDDO |
| 424 |
mlosch |
1.2 |
ENDDO |
| 425 |
jmc |
1.19 |
|
| 426 |
|
|
#ifdef ALLOW_GGL90_HORIZDIFF |
| 427 |
|
|
IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
| 428 |
|
|
C-- Add horiz. diffusion tendency |
| 429 |
|
|
DO j=jMin,jMax |
| 430 |
|
|
DO i=iMin,iMax |
| 431 |
|
|
GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) |
| 432 |
|
|
& + gTKE(i,j)*deltaTggl90 |
| 433 |
|
|
ENDDO |
| 434 |
|
|
ENDDO |
| 435 |
|
|
ENDIF |
| 436 |
mlosch |
1.2 |
#endif /* ALLOW_GGL90_HORIZDIFF */ |
| 437 |
|
|
|
| 438 |
jmc |
1.19 |
C-- end of k loop |
| 439 |
|
|
ENDDO |
| 440 |
|
|
|
| 441 |
mlosch |
1.2 |
C ============================================ |
| 442 |
|
|
C Implicit time step to update TKE for k=1,Nr; |
| 443 |
|
|
C TKE(Nr+1)=0 by default |
| 444 |
|
|
C ============================================ |
| 445 |
mlosch |
1.1 |
C set up matrix |
| 446 |
mlosch |
1.2 |
C-- Lower diagonal |
| 447 |
mlosch |
1.1 |
DO j=jMin,jMax |
| 448 |
|
|
DO i=iMin,iMax |
| 449 |
jmc |
1.20 |
a3d(i,j,1) = 0. _d 0 |
| 450 |
mlosch |
1.1 |
ENDDO |
| 451 |
|
|
ENDDO |
| 452 |
|
|
DO k=2,Nr |
| 453 |
dfer |
1.15 |
km1=MAX(2,k-1) |
| 454 |
mlosch |
1.1 |
DO j=jMin,jMax |
| 455 |
|
|
DO i=iMin,iMax |
| 456 |
dfer |
1.15 |
C- We keep recip_hFacC in the diffusive flux calculation, |
| 457 |
|
|
C- but no hFacC in TKE volume control |
| 458 |
|
|
C- No need for maskC(k-1) with recip_hFacC(k-1) |
| 459 |
jmc |
1.20 |
a3d(i,j,k) = -deltaTggl90 |
| 460 |
dfer |
1.11 |
& *recip_drF(k-1)*recip_hFacC(i,j,k-1,bi,bj) |
| 461 |
dfer |
1.10 |
& *.5 _d 0*(KappaE(i,j, k )+KappaE(i,j,km1)) |
| 462 |
dfer |
1.15 |
& *recip_drC(k)*maskC(i,j,k,bi,bj) |
| 463 |
mlosch |
1.1 |
ENDDO |
| 464 |
|
|
ENDDO |
| 465 |
|
|
ENDDO |
| 466 |
mlosch |
1.2 |
C-- Upper diagonal |
| 467 |
mlosch |
1.1 |
DO j=jMin,jMax |
| 468 |
|
|
DO i=iMin,iMax |
| 469 |
jmc |
1.20 |
c3d(i,j,1) = 0. _d 0 |
| 470 |
mlosch |
1.1 |
ENDDO |
| 471 |
|
|
ENDDO |
| 472 |
dfer |
1.11 |
DO k=2,Nr |
| 473 |
mlosch |
1.1 |
DO j=jMin,jMax |
| 474 |
|
|
DO i=iMin,iMax |
| 475 |
dfer |
1.15 |
kp1=MAX(1,MIN(klowC(i,j,bi,bj),k+1)) |
| 476 |
|
|
C- We keep recip_hFacC in the diffusive flux calculation, |
| 477 |
|
|
C- but no hFacC in TKE volume control |
| 478 |
|
|
C- No need for maskC(k) with recip_hFacC(k) |
| 479 |
jmc |
1.20 |
c3d(i,j,k) = -deltaTggl90 |
| 480 |
dfer |
1.11 |
& *recip_drF( k ) * recip_hFacC(i,j,k,bi,bj) |
| 481 |
|
|
& *.5 _d 0*(KappaE(i,j,k)+KappaE(i,j,kp1)) |
| 482 |
dfer |
1.15 |
& *recip_drC(k)*maskC(i,j,k-1,bi,bj) |
| 483 |
mlosch |
1.1 |
ENDDO |
| 484 |
|
|
ENDDO |
| 485 |
|
|
ENDDO |
| 486 |
mlosch |
1.2 |
C-- Center diagonal |
| 487 |
mlosch |
1.1 |
DO k=1,Nr |
| 488 |
dfer |
1.15 |
km1 = MAX(k-1,1) |
| 489 |
mlosch |
1.1 |
DO j=jMin,jMax |
| 490 |
|
|
DO i=iMin,iMax |
| 491 |
jmc |
1.20 |
b3d(i,j,k) = 1. _d 0 - c3d(i,j,k) - a3d(i,j,k) |
| 492 |
jmc |
1.19 |
& + implDissFac*deltaTggl90*GGL90ceps*SQRTTKE(i,j,k) |
| 493 |
|
|
& * rMixingLength(i,j,k) |
| 494 |
dfer |
1.15 |
& * maskC(i,j,k,bi,bj)*maskC(i,j,km1,bi,bj) |
| 495 |
mlosch |
1.1 |
ENDDO |
| 496 |
|
|
ENDDO |
| 497 |
|
|
ENDDO |
| 498 |
|
|
C end set up matrix |
| 499 |
|
|
|
| 500 |
|
|
C Apply boundary condition |
| 501 |
dfer |
1.15 |
kp1 = MIN(Nr,kSurf+1) |
| 502 |
jmc |
1.19 |
DO j=jMin,jMax |
| 503 |
|
|
DO i=iMin,iMax |
| 504 |
mlosch |
1.1 |
C estimate friction velocity uStar from surface forcing |
| 505 |
jmc |
1.8 |
uStarSquare = SQRT( |
| 506 |
jmc |
1.19 |
& ( .5 _d 0*( surfaceForcingU(i, j, bi,bj) |
| 507 |
|
|
& + surfaceForcingU(i+1,j, bi,bj) ) )**2 |
| 508 |
|
|
& + ( .5 _d 0*( surfaceForcingV(i, j, bi,bj) |
| 509 |
|
|
& + surfaceForcingV(i, j+1,bi,bj) ) )**2 |
| 510 |
mlosch |
1.1 |
& ) |
| 511 |
|
|
C Dirichlet surface boundary condition for TKE |
| 512 |
jmc |
1.19 |
GGL90TKE(i,j,kSurf,bi,bj) = maskC(i,j,kSurf,bi,bj) |
| 513 |
|
|
& *MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare) |
| 514 |
|
|
GGL90TKE(i,j,kp1,bi,bj) = GGL90TKE(i,j,kp1,bi,bj) |
| 515 |
jmc |
1.20 |
& - a3d(i,j,kp1)*GGL90TKE(i,j,kSurf,bi,bj) |
| 516 |
|
|
a3d(i,j,kp1) = 0. _d 0 |
| 517 |
mlosch |
1.1 |
C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom |
| 518 |
jmc |
1.19 |
kBottom = MAX(kLowC(i,j,bi,bj),1) |
| 519 |
|
|
GGL90TKE(i,j,kBottom,bi,bj) = GGL90TKE(i,j,kBottom,bi,bj) |
| 520 |
jmc |
1.20 |
& - GGL90TKEbottom*c3d(i,j,kBottom) |
| 521 |
|
|
c3d(i,j,kBottom) = 0. _d 0 |
| 522 |
mlosch |
1.1 |
ENDDO |
| 523 |
jmc |
1.8 |
ENDDO |
| 524 |
jmc |
1.14 |
|
| 525 |
jmc |
1.19 |
C solve tri-diagonal system |
| 526 |
dfer |
1.15 |
CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
| 527 |
jmc |
1.20 |
I a3d, b3d, c3d, |
| 528 |
jmc |
1.19 |
U GGL90TKE, |
| 529 |
dfer |
1.15 |
O errCode, |
| 530 |
jmc |
1.19 |
I bi, bj, myThid ) |
| 531 |
jmc |
1.14 |
|
| 532 |
jmc |
1.19 |
DO k=1,Nr |
| 533 |
|
|
DO j=jMin,jMax |
| 534 |
|
|
DO i=iMin,iMax |
| 535 |
mlosch |
1.1 |
C impose minimum TKE to avoid numerical undershoots below zero |
| 536 |
jmc |
1.19 |
GGL90TKE(i,j,k,bi,bj) = maskC(i,j,k,bi,bj) |
| 537 |
|
|
& *MAX( GGL90TKE(i,j,k,bi,bj), GGL90TKEmin ) |
| 538 |
mlosch |
1.1 |
ENDDO |
| 539 |
|
|
ENDDO |
| 540 |
jmc |
1.8 |
ENDDO |
| 541 |
dfer |
1.11 |
|
| 542 |
mlosch |
1.2 |
C end of time step |
| 543 |
|
|
C =============================== |
| 544 |
dfer |
1.11 |
|
| 545 |
jmc |
1.19 |
DO k=2,Nr |
| 546 |
|
|
DO j=1,sNy |
| 547 |
|
|
DO i=1,sNx |
| 548 |
gforget |
1.16 |
#ifdef ALLOW_GGL90_SMOOTH |
| 549 |
|
|
tmpVisc= |
| 550 |
dfer |
1.11 |
& ( |
| 551 |
gforget |
1.16 |
& p4 * GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) |
| 552 |
|
|
& +p8 *( GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj) |
| 553 |
|
|
& + GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj) |
| 554 |
|
|
& + GGL90visctmp(i+1,j ,k) * mskCor(i+1,j ,bi,bj) |
| 555 |
|
|
& + GGL90visctmp(i ,j+1,k) * mskCor(i ,j+1,bi,bj)) |
| 556 |
|
|
& +p16*( GGL90visctmp(i+1,j+1,k) * mskCor(i+1,j+1,bi,bj) |
| 557 |
|
|
& + GGL90visctmp(i+1,j-1,k) * mskCor(i+1,j-1,bi,bj) |
| 558 |
|
|
& + GGL90visctmp(i-1,j+1,k) * mskCor(i-1,j+1,bi,bj) |
| 559 |
|
|
& + GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj)) |
| 560 |
dfer |
1.11 |
& ) |
| 561 |
|
|
& /(p4 |
| 562 |
|
|
& +p8 *( maskC(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) |
| 563 |
|
|
& + maskC(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) |
| 564 |
|
|
& + maskC(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) |
| 565 |
|
|
& + maskC(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) |
| 566 |
|
|
& +p16*( maskC(i+1,j+1,k,bi,bj) * mskCor(i+1,j+1,bi,bj) |
| 567 |
|
|
& + maskC(i+1,j-1,k,bi,bj) * mskCor(i+1,j-1,bi,bj) |
| 568 |
|
|
& + maskC(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) |
| 569 |
|
|
& + maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj)) |
| 570 |
|
|
& )*maskC(i,j,k,bi,bj)*mskCor(i,j,bi,bj) |
| 571 |
gforget |
1.16 |
#else |
| 572 |
jmc |
1.19 |
tmpVisc = GGL90visctmp(i,j,k) |
| 573 |
gforget |
1.16 |
#endif |
| 574 |
|
|
tmpVisc = MIN(tmpVisc/TKEPrandtlNumber(i,j,k),GGL90diffMax) |
| 575 |
jmc |
1.19 |
GGL90diffKr(i,j,k,bi,bj)= MAX( tmpVisc , diffKrNrT(k) ) |
| 576 |
dfer |
1.11 |
ENDDO |
| 577 |
|
|
ENDDO |
| 578 |
|
|
ENDDO |
| 579 |
gforget |
1.16 |
|
| 580 |
jmc |
1.19 |
DO k=2,Nr |
| 581 |
|
|
DO j=1,sNy |
| 582 |
|
|
DO i=1,sNx+1 |
| 583 |
gforget |
1.16 |
#ifdef ALLOW_GGL90_SMOOTH |
| 584 |
jmc |
1.19 |
tmpVisc = |
| 585 |
gforget |
1.16 |
& ( |
| 586 |
|
|
& p4 *(GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) |
| 587 |
|
|
& +GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj)) |
| 588 |
|
|
& +p8 *(GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj) |
| 589 |
|
|
& +GGL90visctmp(i-1,j+1,k) * mskCor(i-1,j+1,bi,bj) |
| 590 |
|
|
& +GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj) |
| 591 |
|
|
& +GGL90visctmp(i ,j+1,k) * mskCor(i ,j+1,bi,bj)) |
| 592 |
|
|
& ) |
| 593 |
|
|
& /(p4 * 2. _d 0 |
| 594 |
|
|
& +p8 *( maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj) |
| 595 |
|
|
& + maskC(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) |
| 596 |
|
|
& + maskC(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) |
| 597 |
|
|
& + maskC(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) |
| 598 |
|
|
& ) |
| 599 |
|
|
& *maskC(i ,j,k,bi,bj)*mskCor(i ,j,bi,bj) |
| 600 |
|
|
& *maskC(i-1,j,k,bi,bj)*mskCor(i-1,j,bi,bj) |
| 601 |
|
|
#else |
| 602 |
|
|
tmpVisc = _maskW(i,j,k,bi,bj) * |
| 603 |
|
|
& (.5 _d 0*(GGL90visctmp(i,j,k) |
| 604 |
|
|
& +GGL90visctmp(i-1,j,k)) |
| 605 |
|
|
& ) |
| 606 |
dfer |
1.11 |
#endif |
| 607 |
jmc |
1.19 |
tmpVisc = MIN( tmpVisc , GGL90viscMax ) |
| 608 |
|
|
GGL90viscArU(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) |
| 609 |
gforget |
1.16 |
ENDDO |
| 610 |
|
|
ENDDO |
| 611 |
|
|
ENDDO |
| 612 |
|
|
|
| 613 |
jmc |
1.19 |
DO k=2,Nr |
| 614 |
|
|
DO j=1,sNy+1 |
| 615 |
|
|
DO i=1,sNx |
| 616 |
gforget |
1.16 |
#ifdef ALLOW_GGL90_SMOOTH |
| 617 |
|
|
tmpVisc = |
| 618 |
|
|
& ( |
| 619 |
|
|
& p4 *(GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) |
| 620 |
|
|
& +GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj)) |
| 621 |
|
|
& +p8 *(GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj) |
| 622 |
|
|
& +GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj) |
| 623 |
|
|
& +GGL90visctmp(i+1,j ,k) * mskCor(i+1,j ,bi,bj) |
| 624 |
|
|
& +GGL90visctmp(i+1,j-1,k) * mskCor(i+1,j-1,bi,bj)) |
| 625 |
|
|
& ) |
| 626 |
|
|
& /(p4 * 2. _d 0 |
| 627 |
|
|
& +p8 *( maskC(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) |
| 628 |
|
|
& + maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj) |
| 629 |
|
|
& + maskC(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) |
| 630 |
|
|
& + maskC(i+1,j-1,k,bi,bj) * mskCor(i+1,j-1,bi,bj)) |
| 631 |
|
|
& ) |
| 632 |
|
|
& *maskC(i,j ,k,bi,bj)*mskCor(i,j ,bi,bj) |
| 633 |
|
|
& *maskC(i,j-1,k,bi,bj)*mskCor(i,j-1,bi,bj) |
| 634 |
|
|
#else |
| 635 |
|
|
tmpVisc = _maskS(i,j,k,bi,bj) * |
| 636 |
|
|
& (.5 _d 0*(GGL90visctmp(i,j,k) |
| 637 |
|
|
& +GGL90visctmp(i,j-1,k)) |
| 638 |
|
|
& ) |
| 639 |
|
|
|
| 640 |
|
|
#endif |
| 641 |
|
|
tmpVisc = MIN( tmpVisc , GGL90viscMax ) |
| 642 |
jmc |
1.19 |
GGL90viscArV(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) |
| 643 |
gforget |
1.16 |
ENDDO |
| 644 |
|
|
ENDDO |
| 645 |
|
|
ENDDO |
| 646 |
dfer |
1.10 |
|
| 647 |
|
|
#ifdef ALLOW_DIAGNOSTICS |
| 648 |
|
|
IF ( useDiagnostics ) THEN |
| 649 |
|
|
CALL DIAGNOSTICS_FILL( GGL90TKE ,'GGL90TKE', |
| 650 |
|
|
& 0,Nr, 1, bi, bj, myThid ) |
| 651 |
gforget |
1.16 |
CALL DIAGNOSTICS_FILL( GGL90viscArU,'GGL90ArU', |
| 652 |
|
|
& 0,Nr, 1, bi, bj, myThid ) |
| 653 |
|
|
CALL DIAGNOSTICS_FILL( GGL90viscArV,'GGL90ArV', |
| 654 |
dfer |
1.10 |
& 0,Nr, 1, bi, bj, myThid ) |
| 655 |
|
|
CALL DIAGNOSTICS_FILL( GGL90diffKr,'GGL90Kr ', |
| 656 |
|
|
& 0,Nr, 1, bi, bj, myThid ) |
| 657 |
|
|
CALL DIAGNOSTICS_FILL( TKEPrandtlNumber ,'GGL90Prl', |
| 658 |
|
|
& 0,Nr, 2, bi, bj, myThid ) |
| 659 |
|
|
CALL DIAGNOSTICS_FILL( GGL90mixingLength,'GGL90Lmx', |
| 660 |
|
|
& 0,Nr, 2, bi, bj, myThid ) |
| 661 |
|
|
ENDIF |
| 662 |
|
|
#endif |
| 663 |
mlosch |
1.1 |
|
| 664 |
|
|
#endif /* ALLOW_GGL90 */ |
| 665 |
|
|
|
| 666 |
|
|
RETURN |
| 667 |
|
|
END |
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