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C $Header: /u/gcmpack/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.8 2008/08/11 22:28:06 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, myTime, 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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IMPLICIT NONE |
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C |
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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 |
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C \ev |
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|
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C !USES: ============================================================ |
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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 "GGL90.h" |
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#include "FFIELDS.h" |
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#include "GRID.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 - array indices on which to apply calculations |
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c myTime - Current time in simulation |
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|
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INTEGER bi, bj |
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INTEGER myThid |
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_RL myTime |
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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, I, J - array computation indices |
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C K, Kp1, km1, kSurf, kBottom - vertical loop indices |
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C ab15, ab05 - weights for implicit timestepping |
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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 buoyFreq - buoyancy freqency |
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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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C rhoK, rhoKm1 - density at layer K and Km1 (relative to K) |
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C gTKE - right hand side of implicit equation |
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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 ab15, ab05 |
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_RL uStarSquare |
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_RL verticalShear |
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_RL KappaM, KappaH |
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_RL Nsquare |
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_RL deltaTggl90 |
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_RL SQRTTKE |
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_RL RiNumber |
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_RL TKEdissipation |
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_RL tempU, tempV, prTemp |
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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 KappaE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL rhoK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL rhoKm1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL totalDepth (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL gTKE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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C tri-diagonal matrix |
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_RL a(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL c(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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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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_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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#endif /* ALLOW_GGL90_HORIZDIFF */ |
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CEOP |
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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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C |
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kSurf = 1 |
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C implicit timestepping weights for dissipation |
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ab15 = 1.5 _d 0 |
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ab05 = -0.5 _d 0 |
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ab15 = 1. _d 0 |
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ab05 = 0. _d 0 |
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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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gTKE(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) = 0. _d 0 |
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GGL90mixingLength(I,J,K) = GGL90mixingLengthMin |
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rMixingLength(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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rhoK (I,J) = 0. _d 0 |
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rhoKm1 (I,J) = 0. _d 0 |
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totalDepth(I,J) = 0. _d 0 |
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IF ( recip_Rcol(I,J,bi,bj) .NE. 0. ) |
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& totalDepth(I,J) = 1./recip_Rcol(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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|
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C start k-loop |
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DO K = 2, Nr |
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Km1 = K-1 |
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Kp1 = MIN(Nr,K+1) |
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CALL FIND_RHO_2D( |
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I iMin, iMax, jMin, jMax, K, |
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I theta(1-OLx,1-OLy,Km1,bi,bj), salt(1-OLx,1-OLy,Km1,bi,bj), |
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O rhoKm1, |
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I Km1, bi, bj, myThid ) |
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|
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CALL FIND_RHO_2D( |
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I iMin, iMax, jMin, jMax, K, |
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I theta(1-OLx,1-OLy,K,bi,bj), salt(1-OLx,1-OLy,K,bi,bj), |
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O rhoK, |
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I K, bi, bj, myThid ) |
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DO J=jMin,jMax |
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DO I=iMin,iMax |
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SQRTTKE=SQRT( GGL90TKE(I,J,K,bi,bj) ) |
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C |
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C buoyancy frequency |
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C |
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Nsquare = - gravity*recip_rhoConst*recip_drC(K) |
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& * ( rhoKm1(I,J) - rhoK(I,J) )*maskC(I,J,K,bi,bj) |
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C vertical shear term (dU/dz)^2+(dV/dz)^2 |
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tempu= .5*( uVel(I,J,Km1,bi,bj)+uVel(I+1,J,Km1,bi,bj) |
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& - (uVel(I,J,K ,bi,bj)+uVel(I+1,J,K ,bi,bj)) ) |
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& *recip_drC(K) |
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tempv= .5*( vVel(I,J,Km1,bi,bj)+vVel(I,J+1,Km1,bi,bj) |
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& - (vVel(I,J,K ,bi,bj)+vVel(I,J+1,K ,bi,bj)) ) |
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& *recip_drC(K) |
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verticalShear = tempU*tempU + tempV*tempV |
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RiNumber = MAX(Nsquare,0. _d 0)/(verticalShear+GGL90eps) |
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C compute Prandtl number (always greater than 0) |
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prTemp = 1. _d 0 |
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IF ( RiNumber .GE. 0.2 ) prTemp = 5.0 * RiNumber |
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TKEPrandtlNumber(I,J,K) = MIN(10.0 _d 0,prTemp) |
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C mixing length |
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GGL90mixingLength(I,J,K) = SQRTTWO * |
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& SQRTTKE/SQRT( MAX(Nsquare,GGL90eps) ) |
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C impose upper bound for mixing length (total depth) |
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GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
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& totalDepth(I,J)) |
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C impose minimum mixing length (to avoid division by zero) |
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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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C viscosity of last timestep |
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KappaM = GGL90ck*GGL90mixingLength(I,J,K)*SQRTTKE |
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KappaE(I,J,K) = KappaM*GGL90alpha |
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C dissipation term |
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TKEdissipation = ab05*GGL90ceps |
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& *SQRTTKE*rMixingLength(I,J,K) |
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& *GGL90TKE(I,J,K,bi,bj) |
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C sum up contributions to form the right hand side |
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gTKE(I,J,K) = GGL90TKE(I,J,K,bi,bj) |
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& + deltaTggl90*( |
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& + KappaM*verticalShear |
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& - KappaM*Nsquare/TKEPrandtlNumber(I,J,K) |
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& - TKEdissipation |
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& ) |
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ENDDO |
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ENDDO |
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ENDDO |
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C horizontal diffusion of TKE (requires an exchange in |
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C do_fields_blocking_exchanges) |
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#ifdef ALLOW_GGL90_HORIZDIFF |
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IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
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DO K=2,Nr |
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C common factors |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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xA(i,j) = _dyG(i,j,bi,bj) |
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& *drF(k)*_hFacW(i,j,k,bi,bj) |
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yA(i,j) = _dxG(i,j,bi,bj) |
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& *drF(k)*_hFacS(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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C Compute diffusive fluxes |
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C ... across x-faces |
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DO j=1-Oly,sNy+Oly |
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dfx(1-Olx,j)=0. |
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DO i=1-Olx+1,sNx+Olx |
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dfx(i,j) = -GGL90diffTKEh*xA(i,j) |
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& *_recip_dxC(i,j,bi,bj) |
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& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i-1,j,k,bi,bj)) |
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& *CosFacU(j,bi,bj) |
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ENDDO |
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ENDDO |
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C ... across y-faces |
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DO i=1-Olx,sNx+Olx |
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dfy(i,1-Oly)=0. |
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ENDDO |
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DO j=1-Oly+1,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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dfy(i,j) = -GGL90diffTKEh*yA(i,j) |
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& *_recip_dyC(i,j,bi,bj) |
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& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i,j-1,k,bi,bj)) |
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#ifdef ISOTROPIC_COS_SCALING |
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& *CosFacV(j,bi,bj) |
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#endif /* ISOTROPIC_COS_SCALING */ |
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ENDDO |
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ENDDO |
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C Compute divergence of fluxes |
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DO j=1-Oly,sNy+Oly-1 |
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DO i=1-Olx,sNx+Olx-1 |
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gTKE(i,j,k)=gTKE(i,j,k) |
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& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)*recip_rA(i,j,bi,bj) |
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& *( (dfx(i+1,j)-dfx(i,j)) |
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& +(dfy(i,j+1)-dfy(i,j)) |
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& ) |
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ENDDO |
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ENDDO |
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C end of k-loop |
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ENDDO |
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C end if GGL90diffTKEh .eq. 0. |
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ENDIF |
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#endif /* ALLOW_GGL90_HORIZDIFF */ |
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|
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C ============================================ |
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C Implicit time step to update TKE for k=1,Nr; |
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C TKE(Nr+1)=0 by default |
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C ============================================ |
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C set up matrix |
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C-- Lower diagonal |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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a(i,j,1) = 0. _d 0 |
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ENDDO |
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ENDDO |
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DO k=2,Nr |
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km1=MAX(1,k-1) |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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a(i,j,k) = -deltaTggl90 |
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& *recip_drF(km1)*recip_hFacI(i,j,k,bi,bj) |
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& *.5*(KappaE(i,j, k )+KappaE(i,j,km1)) |
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& *recip_drC(k) |
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IF (recip_hFacI(i,j,km1,bi,bj).EQ.0.) a(i,j,k)=0. |
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ENDDO |
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ENDDO |
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ENDDO |
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C-- Upper diagonal |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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c(i,j,1) = 0. _d 0 |
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c(i,j,Nr) = 0. _d 0 |
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ENDDO |
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ENDDO |
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CML DO k=1,Nr-1 |
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DO k=2,Nr-1 |
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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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c(i,j,k) = -deltaTggl90 |
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& *recip_drF( k )*recip_hFacI(i,j,k,bi,bj) |
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& *.5*(KappaE(i,j,k)+KappaE(i,j,kp1)) |
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& *recip_drC(k) |
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IF (recip_hFacI(i,j,kp1,bi,bj).EQ.0.) c(i,j,k)=0. |
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ENDDO |
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ENDDO |
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ENDDO |
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C-- Center diagonal |
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DO k=1,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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b(i,j,k) = 1. _d 0 - c(i,j,k) - a(i,j,k) |
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& + ab15*deltaTggl90*GGL90ceps*SQRT(GGL90TKE(I,J,K,bi,bj)) |
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& *rMixingLength(I,J,K) |
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ENDDO |
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ENDDO |
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ENDDO |
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C end set up matrix |
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|
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C |
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C Apply boundary condition |
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C |
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DO J=jMin,jMax |
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DO I=iMin,iMax |
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C estimate friction velocity uStar from surface forcing |
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uStarSquare = SQRT( |
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& ( .5*( surfaceForcingU(I, J, bi,bj) |
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& + surfaceForcingU(I+1,J, bi,bj) ) )**2 |
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& + ( .5*( surfaceForcingV(I, J, bi,bj) |
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& + surfaceForcingV(I, J+1,bi,bj) ) )**2 |
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& ) |
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C Dirichlet surface boundary condition for TKE |
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gTKE(I,J,kSurf) = MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare) |
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& *maskC(I,J,kSurf,bi,bj) |
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C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom |
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kBottom = MIN(MAX(kLowC(I,J,bi,bj),1),Nr) |
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gTKE(I,J,kBottom) = gTKE(I,J,kBottom) |
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& - GGL90TKEbottom*c(I,J,kBottom) |
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ENDDO |
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ENDDO |
| 340 |
C |
| 341 |
C solve tri-diagonal system, and store solution on gTKE (previously rhs) |
| 342 |
C |
| 343 |
CALL GGL90_SOLVE( bi, bj, iMin, iMax, jMin, jMax, |
| 344 |
I a, b, c, |
| 345 |
U gTKE, |
| 346 |
I myThid ) |
| 347 |
C |
| 348 |
C now update TKE |
| 349 |
C |
| 350 |
DO K=1,Nr |
| 351 |
DO J=jMin,jMax |
| 352 |
DO I=iMin,iMax |
| 353 |
C impose minimum TKE to avoid numerical undershoots below zero |
| 354 |
GGL90TKE(I,J,K,bi,bj) = MAX( gTKE(I,J,K), GGL90TKEmin ) |
| 355 |
& * maskC(I,J,K,bi,bj) |
| 356 |
ENDDO |
| 357 |
ENDDO |
| 358 |
ENDDO |
| 359 |
C |
| 360 |
C end of time step |
| 361 |
C =============================== |
| 362 |
C compute viscosity coefficients |
| 363 |
C |
| 364 |
DO K=2,Nr |
| 365 |
DO J=jMin,jMax |
| 366 |
DO I=iMin,iMax |
| 367 |
C Eq. (11), (18) and (21) |
| 368 |
KappaM = GGL90ck*GGL90mixingLength(I,J,K)* |
| 369 |
& SQRT( GGL90TKE(I,J,K,bi,bj) ) |
| 370 |
KappaH = KappaM/TKEPrandtlNumber(I,J,K) |
| 371 |
C Set a minium (= background) value |
| 372 |
KappaM = MAX(KappaM,viscAr) |
| 373 |
KappaH = MAX(KappaH,diffKrNrT(k)) |
| 374 |
C Set a maximum and mask land point |
| 375 |
GGL90viscAr(I,J,K,bi,bj) = MIN(KappaM,GGL90viscMax) |
| 376 |
& * maskC(I,J,K,bi,bj) |
| 377 |
GGL90diffKr(I,J,K,bi,bj) = MIN(KappaH,GGL90diffMax) |
| 378 |
& * maskC(I,J,K,bi,bj) |
| 379 |
ENDDO |
| 380 |
ENDDO |
| 381 |
C end third k-loop |
| 382 |
ENDDO |
| 383 |
|
| 384 |
#endif /* ALLOW_GGL90 */ |
| 385 |
|
| 386 |
RETURN |
| 387 |
END |
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