--- MITgcm/pkg/ggl90/ggl90_calc.F 2010/08/11 03:32:29 1.18 +++ MITgcm/pkg/ggl90/ggl90_calc.F 2010/08/19 23:52:37 1.19 @@ -1,4 +1,4 @@ -C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.18 2010/08/11 03:32:29 gforget Exp $ +C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.19 2010/08/19 23:52:37 jmc Exp $ C $Name: $ #include "GGL90_OPTIONS.h" @@ -7,8 +7,8 @@ C !ROUTINE: GGL90_CALC C !INTERFACE: ====================================================== - subroutine GGL90_CALC( - I bi, bj, myTime, myThid ) + SUBROUTINE GGL90_CALC( + I bi, bj, myTime, myIter, myThid ) C !DESCRIPTION: \bv C *==========================================================* @@ -43,9 +43,11 @@ C Routine arguments C bi, bj :: array indices on which to apply calculations C myTime :: Current time in simulation +C myIter :: Current time-step number C myThid :: My Thread Id number INTEGER bi, bj _RL myTime + INTEGER myIter INTEGER myThid CEOP @@ -53,26 +55,27 @@ C !LOCAL VARIABLES: ==================================================== C Local constants -C iMin, iMax, jMin, jMax, I, J - array computation indices -C K, Kp1, km1, kSurf, kBottom - vertical loop indices -C ab15, ab05 - weights for implicit timestepping -C uStarSquare - square of friction velocity -C verticalShear - (squared) vertical shear of horizontal velocity -C Nsquare - squared buoyancy freqency -C RiNumber - local Richardson number -C KappaM - (local) viscosity parameter (eq.10) -C KappaH - (local) diffusivity parameter for temperature (eq.11) -C KappaE - (local) diffusivity parameter for TKE (eq.15) -C TKEdissipation - dissipation of TKE -C GGL90mixingLength- mixing length of scheme following Banke+Delecuse -C rMixingLength- inverse of mixing length -C totalDepth - thickness of water column (inverse of recip_Rcol) -C TKEPrandtlNumber - here, an empirical function of the Richardson number -C rhoK, rhoKm1 - density at layer K and Km1 (relative to K) -C gTKE - right hand side of implicit equation +C iMin,iMax,jMin,jMax :: index boundaries of computation domain +C i, j, k, kp1,km1 :: array computation indices +C kSurf, kBottom :: vertical indices of domain boundaries +C explDissFac :: explicit Dissipation Factor (in [0-1]) +C implDissFac :: implicit Dissipation Factor (in [0-1]) +C uStarSquare :: square of friction velocity +C verticalShear :: (squared) vertical shear of horizontal velocity +C Nsquare :: squared buoyancy freqency +C RiNumber :: local Richardson number +C KappaM :: (local) viscosity parameter (eq.10) +C KappaH :: (local) diffusivity parameter for temperature (eq.11) +C KappaE :: (local) diffusivity parameter for TKE (eq.15) +C TKEdissipation :: dissipation of TKE +C GGL90mixingLength:: mixing length of scheme following Banke+Delecuse +C rMixingLength:: inverse of mixing length +C totalDepth :: thickness of water column (inverse of recip_Rcol) +C TKEPrandtlNumber :: here, an empirical function of the Richardson number +C rhoK, rhoKm1 :: density at layer k and km1 (relative to k) INTEGER iMin ,iMax ,jMin ,jMax - INTEGER I, J, K, Kp1, Km1, kSurf, kBottom - _RL ab15, ab05 + INTEGER i, j, k, kp1, km1, kSurf, kBottom + _RL explDissFac, implDissFac _RL uStarSquare _RL verticalShear _RL KappaM, KappaH @@ -93,7 +96,6 @@ _RL rhoK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL rhoKm1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL totalDepth (1-OLx:sNx+OLx,1-OLy:sNy+OLy) - _RL gTKE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL GGL90visctmp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) C- tri-diagonal matrix _RL a(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) @@ -101,12 +103,14 @@ _RL c(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) INTEGER errCode #ifdef ALLOW_GGL90_HORIZDIFF -C- xA, yA - area of lateral faces -C- dfx, dfy - diffusive flux across lateral faces +C xA, yA :: area of lateral faces +C dfx, dfy :: diffusive flux across lateral faces +C gTKE :: right hand side of diffusion equation _RL xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL dfx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL dfy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) + _RL gTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) #endif /* ALLOW_GGL90_HORIZDIFF */ #ifdef ALLOW_GGL90_SMOOTH _RL p4, p8, p16 @@ -123,72 +127,69 @@ deltaTggl90 = dTtracerLev(1) kSurf = 1 -C implicit timestepping weights for dissipation - ab15 = 1.5 _d 0 - ab05 = -0.5 _d 0 - ab15 = 1. _d 0 - ab05 = 0. _d 0 +C explicit/implicit timestepping weights for dissipation + explDissFac = 0. _d 0 + implDissFac = 1. _d 0 - explDissFac C Initialize local fields - DO K = 1, Nr - DO J=1-Oly,sNy+Oly - DO I=1-Olx,sNx+Olx - gTKE(I,J,K) = 0. _d 0 - KappaE(I,J,K) = 0. _d 0 - TKEPrandtlNumber(I,J,K) = 1. _d 0 - GGL90mixingLength(I,J,K) = GGL90mixingLengthMin - GGL90visctmp(I,J,K) = 0. _d 0 + DO k = 1, Nr + DO j=1-Oly,sNy+Oly + DO i=1-Olx,sNx+Olx + KappaE(i,j,k) = 0. _d 0 + TKEPrandtlNumber(i,j,k) = 1. _d 0 + GGL90mixingLength(i,j,k) = GGL90mixingLengthMin + GGL90visctmp(i,j,k) = 0. _d 0 ENDDO ENDDO ENDDO - DO J=1-Oly,sNy+Oly - DO I=1-Olx,sNx+Olx - rhoK(I,J) = 0. _d 0 - rhoKm1(I,J) = 0. _d 0 - totalDepth(I,J) = Ro_surf(i,j,bi,bj) - R_low(i,j,bi,bj) + DO j=1-Oly,sNy+Oly + DO i=1-Olx,sNx+Olx + rhoK(i,j) = 0. _d 0 + rhoKm1(i,j) = 0. _d 0 + totalDepth(i,j) = Ro_surf(i,j,bi,bj) - R_low(i,j,bi,bj) rMixingLength(i,j,1) = 0. _d 0 - mxLength_Dn(I,J,1) = GGL90mixingLengthMin + mxLength_Dn(i,j,1) = GGL90mixingLengthMin SQRTTKE(i,j,1) = SQRT( GGL90TKE(i,j,1,bi,bj) ) ENDDO ENDDO C start k-loop - DO K = 2, Nr - Km1 = K-1 -c Kp1 = MIN(Nr,K+1) + DO k = 2, Nr + km1 = k-1 +c kp1 = MIN(Nr,k+1) CALL FIND_RHO_2D( - I iMin, iMax, jMin, jMax, K, - I theta(1-OLx,1-OLy,Km1,bi,bj), salt(1-OLx,1-OLy,Km1,bi,bj), + I iMin, iMax, jMin, jMax, k, + I theta(1-OLx,1-OLy,km1,bi,bj), salt(1-OLx,1-OLy,km1,bi,bj), O rhoKm1, - I Km1, bi, bj, myThid ) + I km1, bi, bj, myThid ) CALL FIND_RHO_2D( - I iMin, iMax, jMin, jMax, K, - I theta(1-OLx,1-OLy,K,bi,bj), salt(1-OLx,1-OLy,K,bi,bj), + I iMin, iMax, jMin, jMax, k, + I theta(1-OLx,1-OLy,k,bi,bj), salt(1-OLx,1-OLy,k,bi,bj), O rhoK, - I K, bi, bj, myThid ) - DO J=jMin,jMax - DO I=iMin,iMax - SQRTTKE(i,j,k)=SQRT( GGL90TKE(I,J,K,bi,bj) ) + I k, bi, bj, myThid ) + DO j=jMin,jMax + DO i=iMin,iMax + SQRTTKE(i,j,k)=SQRT( GGL90TKE(i,j,k,bi,bj) ) C buoyancy frequency - Nsquare(i,j,k) = - gravity*recip_rhoConst*recip_drC(K) - & * ( rhoKm1(I,J) - rhoK(I,J) )*maskC(I,J,K,bi,bj) + Nsquare(i,j,k) = - gravity*recip_rhoConst*recip_drC(k) + & * ( rhoKm1(i,j) - rhoK(i,j) )*maskC(i,j,k,bi,bj) cC vertical shear term (dU/dz)^2+(dV/dz)^2 -c tempU= .5 _d 0*( uVel(I,J,Km1,bi,bj)+uVel(I+1,J,Km1,bi,bj) -c & -( uVel(I,J,K ,bi,bj)+uVel(I+1,J,K ,bi,bj)) ) -c & *recip_drC(K) -c tempV= .5 _d 0*( vVel(I,J,Km1,bi,bj)+vVel(I,J+1,Km1,bi,bj) -c & -( vVel(I,J,K ,bi,bj)+vVel(I,J+1,K ,bi,bj)) ) -c & *recip_drC(K) +c tempU= .5 _d 0*( uVel(i,j,km1,bi,bj)+uVel(i+1,j,km1,bi,bj) +c & -( uVel(i,j,k ,bi,bj)+uVel(i+1,j,k ,bi,bj)) ) +c & *recip_drC(k) +c tempV= .5 _d 0*( vVel(i,j,km1,bi,bj)+vVel(i,j+1,km1,bi,bj) +c & -( vVel(i,j,k ,bi,bj)+vVel(i,j+1,k ,bi,bj)) ) +c & *recip_drC(k) c verticalShear = tempU*tempU + tempV*tempV c RiNumber = MAX(Nsquare(i,j,k),0. _d 0)/(verticalShear+GGL90eps) cC compute Prandtl number (always greater than 0) c prTemp = 1. _d 0 c IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber -c TKEPrandtlNumber(I,J,K) = MIN(10. _d 0,prTemp) +c TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) C mixing length - GGL90mixingLength(I,J,K) = SQRTTWO * + GGL90mixingLength(i,j,k) = SQRTTWO * & SQRTTKE(i,j,k)/SQRT( MAX(Nsquare(i,j,k),GGL90eps) ) ENDDO ENDDO @@ -198,21 +199,21 @@ IF ( mxlMaxFlag .EQ. 0 ) THEN C- DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - MaxLength=totalDepth(I,J) - GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), + DO j=jMin,jMax + DO i=iMin,iMax + MaxLength=totalDepth(i,j) + GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), & MaxLength) ENDDO ENDDO ENDDO DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), & GGL90mixingLengthMin) - rMixingLength(I,J,K) = 1. _d 0 / GGL90mixingLength(I,J,K) + rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) ENDDO ENDDO ENDDO @@ -220,22 +221,22 @@ ELSEIF ( mxlMaxFlag .EQ. 1 ) THEN C- DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - MaxLength=MIN(Ro_surf(I,J,bi,bj)-rF(k),rF(k)-R_low(I,J,bi,bj)) + DO j=jMin,jMax + DO i=iMin,iMax + MaxLength=MIN(Ro_surf(i,j,bi,bj)-rF(k),rF(k)-R_low(i,j,bi,bj)) c MaxLength=MAX(MaxLength,20. _d 0) - GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), + GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), & MaxLength) ENDDO ENDDO ENDDO DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), & GGL90mixingLengthMin) - rMixingLength(I,J,K) = 1. _d 0 / GGL90mixingLength(I,J,K) + rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) ENDDO ENDDO ENDDO @@ -243,41 +244,41 @@ ELSEIF ( mxlMaxFlag .EQ. 2 ) THEN C- cgf ensure mixing between first and second level -c DO J=jMin,jMax -c DO I=iMin,iMax -c GGL90mixingLength(I,J,2)=drF(1) +c DO j=jMin,jMax +c DO i=iMin,iMax +c GGL90mixingLength(i,j,2)=drF(1) c ENDDO c ENDDO cgf DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), - & GGL90mixingLength(I,J,K-1)+drF(k-1)) + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), + & GGL90mixingLength(i,j,k-1)+drF(k-1)) ENDDO ENDDO ENDDO - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,Nr) = MIN(GGL90mixingLength(I,J,Nr), + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr), & GGL90mixingLengthMin+drF(Nr)) ENDDO ENDDO DO k=Nr-1,2,-1 - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), - & GGL90mixingLength(I,J,K+1)+drF(k)) + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), + & GGL90mixingLength(i,j,k+1)+drF(k)) ENDDO ENDDO ENDDO DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), & GGL90mixingLengthMin) - rMixingLength(I,J,K) = 1. _d 0 / GGL90mixingLength(I,J,K) + rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) ENDDO ENDDO ENDDO @@ -285,36 +286,36 @@ ELSEIF ( mxlMaxFlag .EQ. 3 ) THEN C- DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - mxLength_Dn(I,J,K) = MIN(GGL90mixingLength(I,J,K), - & mxLength_Dn(I,J,K-1)+drF(k-1)) + DO j=jMin,jMax + DO i=iMin,iMax + mxLength_Dn(i,j,k) = MIN(GGL90mixingLength(i,j,k), + & mxLength_Dn(i,j,k-1)+drF(k-1)) ENDDO ENDDO ENDDO - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,Nr) = MIN(GGL90mixingLength(I,J,Nr), + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr), & GGL90mixingLengthMin+drF(Nr)) ENDDO ENDDO DO k=Nr-1,2,-1 - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), - & GGL90mixingLength(I,J,K+1)+drF(k)) + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), + & GGL90mixingLength(i,j,k+1)+drF(k)) ENDDO ENDDO ENDDO DO k=2,Nr - DO J=jMin,jMax - DO I=iMin,iMax - GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), - & mxLength_Dn(I,J,K)) - tmpmlx = SQRT( GGL90mixingLength(I,J,K)*mxLength_Dn(I,J,K) ) + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k), + & mxLength_Dn(i,j,k)) + tmpmlx = SQRT( GGL90mixingLength(i,j,k)*mxLength_Dn(i,j,k) ) tmpmlx = MAX( tmpmlx, GGL90mixingLengthMin) - rMixingLength(I,J,K) = 1. _d 0 / tmpmlx + rMixingLength(i,j,k) = 1. _d 0 / tmpmlx ENDDO ENDDO ENDDO @@ -325,65 +326,22 @@ C- Impose minimum mixing length (to avoid division by zero) c DO k=2,Nr -c DO J=jMin,jMax -c DO I=iMin,iMax -c GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), +c DO j=jMin,jMax +c DO i=iMin,iMax +c GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k), c & GGL90mixingLengthMin) -c rMixingLength(I,J,K) = 1. _d 0 /GGL90mixingLength(I,J,K) +c rMixingLength(i,j,k) = 1. _d 0 /GGL90mixingLength(i,j,k) c ENDDO c ENDDO c ENDDO - DO k=2,Nr - Km1 = K-1 - DO J=jMin,jMax - DO I=iMin,iMax -C vertical shear term (dU/dz)^2+(dV/dz)^2 - tempU= .5 _d 0*( uVel(I,J,Km1,bi,bj)+uVel(I+1,J,Km1,bi,bj) - & -( uVel(I,J,K ,bi,bj)+uVel(I+1,J,K ,bi,bj)) ) - & *recip_drC(K) - tempV= .5 _d 0*( vVel(I,J,Km1,bi,bj)+vVel(I,J+1,Km1,bi,bj) - & -( vVel(I,J,K ,bi,bj)+vVel(I,J+1,K ,bi,bj)) ) - & *recip_drC(K) - verticalShear = tempU*tempU + tempV*tempV - RiNumber = MAX(Nsquare(i,j,k),0. _d 0)/(verticalShear+GGL90eps) -C compute Prandtl number (always greater than 0) - prTemp = 1. _d 0 - IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber - TKEPrandtlNumber(I,J,K) = MIN(10. _d 0,prTemp) -c TKEPrandtlNumber(I,J,K) = 1. _d 0 - -C viscosity and diffusivity - KappaM = GGL90ck*GGL90mixingLength(I,J,K)*SQRTTKE(i,j,k) - GGL90visctmp(I,J,K) = MAX(KappaM,diffKrNrT(k)) - & * maskC(I,J,K,bi,bj) -c note: storing GGL90visctmp like this, and using it later to compute -c GGL9rdiffKr etc. is robust in case of smoothing (e.g. see OPA) - KappaM = MAX(KappaM,viscArNr(k)) * maskC(I,J,K,bi,bj) - KappaH = KappaM/TKEPrandtlNumber(I,J,K) - KappaE(I,J,K) = GGL90alpha * KappaM * maskC(I,J,K,bi,bj) - -C dissipation term - TKEdissipation = ab05*GGL90ceps - & *SQRTTKE(i,j,k)*rMixingLength(I,J,K) - & *GGL90TKE(I,J,K,bi,bj) -C sum up contributions to form the right hand side - gTKE(I,J,K) = GGL90TKE(I,J,K,bi,bj) - & + deltaTggl90*( - & + KappaM*verticalShear - & - KappaH*Nsquare(i,j,k) - & - TKEdissipation - & ) - ENDDO - ENDDO - ENDDO + km1 = k-1 +#ifdef ALLOW_GGL90_HORIZDIFF + IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN C horizontal diffusion of TKE (requires an exchange in C do_fields_blocking_exchanges) -#ifdef ALLOW_GGL90_HORIZDIFF - IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN - DO K=2,Nr C common factors DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx @@ -421,19 +379,73 @@ C Compute divergence of fluxes DO j=1-Oly,sNy+Oly-1 DO i=1-Olx,sNx+Olx-1 - gTKE(i,j,k)=gTKE(i,j,k) - & -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)*recip_rA(i,j,bi,bj) + gTKE(i,j) = + & -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)*recip_rA(i,j,bi,bj) & *( (dfx(i+1,j)-dfx(i,j)) & +(dfy(i,j+1)-dfy(i,j)) - & )*deltaTggl90 + & ) ENDDO ENDDO -C end of k-loop +C end if GGL90diffTKEh .eq. 0. + ENDIF +#endif /* ALLOW_GGL90_HORIZDIFF */ + + DO j=jMin,jMax + DO i=iMin,iMax +C vertical shear term (dU/dz)^2+(dV/dz)^2 + tempU= .5 _d 0*( uVel(i,j,km1,bi,bj)+uVel(i+1,j,km1,bi,bj) + & -( uVel(i,j,k ,bi,bj)+uVel(i+1,j,k ,bi,bj)) ) + & *recip_drC(k) + tempV= .5 _d 0*( vVel(i,j,km1,bi,bj)+vVel(i,j+1,km1,bi,bj) + & -( vVel(i,j,k ,bi,bj)+vVel(i,j+1,k ,bi,bj)) ) + & *recip_drC(k) + verticalShear = tempU*tempU + tempV*tempV + RiNumber = MAX(Nsquare(i,j,k),0. _d 0)/(verticalShear+GGL90eps) +C compute Prandtl number (always greater than 0) + prTemp = 1. _d 0 + IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber + TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp) +c TKEPrandtlNumber(i,j,k) = 1. _d 0 + +C viscosity and diffusivity + KappaM = GGL90ck*GGL90mixingLength(i,j,k)*SQRTTKE(i,j,k) + GGL90visctmp(i,j,k) = MAX(KappaM,diffKrNrT(k)) + & * maskC(i,j,k,bi,bj) +c note: storing GGL90visctmp like this, and using it later to compute +c GGL9rdiffKr etc. is robust in case of smoothing (e.g. see OPA) + KappaM = MAX(KappaM,viscArNr(k)) * maskC(i,j,k,bi,bj) + KappaH = KappaM/TKEPrandtlNumber(i,j,k) + KappaE(i,j,k) = GGL90alpha * KappaM * maskC(i,j,k,bi,bj) + +C dissipation term + TKEdissipation = explDissFac*GGL90ceps + & *SQRTTKE(i,j,k)*rMixingLength(i,j,k) + & *GGL90TKE(i,j,k,bi,bj) +C partial update with sum of explicit contributions + GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) + & + deltaTggl90*( + & + KappaM*verticalShear + & - KappaH*Nsquare(i,j,k) + & - TKEdissipation + & ) + ENDDO ENDDO -C end if GGL90diffTKEh .eq. 0. - ENDIF + +#ifdef ALLOW_GGL90_HORIZDIFF + IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN +C-- Add horiz. diffusion tendency + DO j=jMin,jMax + DO i=iMin,iMax + GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj) + & + gTKE(i,j)*deltaTggl90 + ENDDO + ENDDO + ENDIF #endif /* ALLOW_GGL90_HORIZDIFF */ +C-- end of k loop + ENDDO + C ============================================ C Implicit time step to update TKE for k=1,Nr; C TKE(Nr+1)=0 by default @@ -485,8 +497,8 @@ DO j=jMin,jMax DO i=iMin,iMax b(i,j,k) = 1. _d 0 - c(i,j,k) - a(i,j,k) - & + ab15*deltaTggl90*GGL90ceps*SQRTTKE(I,J,K) - & * rMixingLength(I,J,K) + & + implDissFac*deltaTggl90*GGL90ceps*SQRTTKE(i,j,k) + & * rMixingLength(i,j,k) & * maskC(i,j,k,bi,bj)*maskC(i,j,km1,bi,bj) ENDDO ENDDO @@ -495,43 +507,42 @@ C Apply boundary condition kp1 = MIN(Nr,kSurf+1) - DO J=jMin,jMax - DO I=iMin,iMax + DO j=jMin,jMax + DO i=iMin,iMax C estimate friction velocity uStar from surface forcing uStarSquare = SQRT( - & ( .5 _d 0*( surfaceForcingU(I, J, bi,bj) - & + surfaceForcingU(I+1,J, bi,bj) ) )**2 - & + ( .5 _d 0*( surfaceForcingV(I, J, bi,bj) - & + surfaceForcingV(I, J+1,bi,bj) ) )**2 + & ( .5 _d 0*( surfaceForcingU(i, j, bi,bj) + & + surfaceForcingU(i+1,j, bi,bj) ) )**2 + & + ( .5 _d 0*( surfaceForcingV(i, j, bi,bj) + & + surfaceForcingV(i, j+1,bi,bj) ) )**2 & ) C Dirichlet surface boundary condition for TKE - gTKE(I,J,kSurf) = MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare) - & *maskC(I,J,kSurf,bi,bj) - gTKE(i,j,kp1) = gTKE(i,j,kp1) - & - a(i,j,kp1)*gTKE(i,j,kSurf) + GGL90TKE(i,j,kSurf,bi,bj) = maskC(i,j,kSurf,bi,bj) + & *MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare) + GGL90TKE(i,j,kp1,bi,bj) = GGL90TKE(i,j,kp1,bi,bj) + & - a(i,j,kp1)*GGL90TKE(i,j,kSurf,bi,bj) a(i,j,kp1) = 0. _d 0 C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom - kBottom = MAX(kLowC(I,J,bi,bj),1) - gTKE(I,J,kBottom) = gTKE(I,J,kBottom) - & - GGL90TKEbottom*c(I,J,kBottom) - c(I,J,kBottom) = 0. _d 0 + kBottom = MAX(kLowC(i,j,bi,bj),1) + GGL90TKE(i,j,kBottom,bi,bj) = GGL90TKE(i,j,kBottom,bi,bj) + & - GGL90TKEbottom*c(i,j,kBottom) + c(i,j,kBottom) = 0. _d 0 ENDDO ENDDO -C solve tri-diagonal system, and store solution on gTKE (previously rhs) +C solve tri-diagonal system CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, I a, b, c, - U gTKE, + U GGL90TKE, O errCode, - I 1, 1, myThid ) + I bi, bj, myThid ) -C now update TKE - DO K=1,Nr - DO J=jMin,jMax - DO I=iMin,iMax + DO k=1,Nr + DO j=jMin,jMax + DO i=iMin,iMax C impose minimum TKE to avoid numerical undershoots below zero - GGL90TKE(I,J,K,bi,bj) = MAX( gTKE(I,J,K), GGL90TKEmin ) - & * maskC(I,J,K,bi,bj) + GGL90TKE(i,j,k,bi,bj) = maskC(i,j,k,bi,bj) + & *MAX( GGL90TKE(i,j,k,bi,bj), GGL90TKEmin ) ENDDO ENDDO ENDDO @@ -539,9 +550,9 @@ C end of time step C =============================== - DO K=2,Nr - DO J=1,sNy - DO I=1,sNx + DO k=2,Nr + DO j=1,sNy + DO i=1,sNx #ifdef ALLOW_GGL90_SMOOTH tmpVisc= & ( @@ -566,21 +577,19 @@ & + maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj)) & )*maskC(i,j,k,bi,bj)*mskCor(i,j,bi,bj) #else - tmpVisc = GGL90visctmp(I,J,K) + tmpVisc = GGL90visctmp(i,j,k) #endif tmpVisc = MIN(tmpVisc/TKEPrandtlNumber(i,j,k),GGL90diffMax) - GGL90diffKr(I,J,K,bi,bj)= MAX( tmpVisc , diffKrNrT(k) ) + GGL90diffKr(i,j,k,bi,bj)= MAX( tmpVisc , diffKrNrT(k) ) ENDDO ENDDO ENDDO - - - DO K=2,Nr - DO J=1,sNy - DO I=1,sNx+1 + DO k=2,Nr + DO j=1,sNy + DO i=1,sNx+1 #ifdef ALLOW_GGL90_SMOOTH - tmpVisc = + tmpVisc = & ( & p4 *(GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) & +GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj)) @@ -603,16 +612,15 @@ & +GGL90visctmp(i-1,j,k)) & ) #endif - tmpVisc = MIN( tmpVisc , GGL90viscMax ) - GGL90viscArU(i,j,k,bi,bj) = MAX( tmpVisc , viscArNr(k) ) + tmpVisc = MIN( tmpVisc , GGL90viscMax ) + GGL90viscArU(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) ENDDO ENDDO ENDDO - - DO K=2,Nr - DO J=1,sNy+1 - DO I=1,sNx + DO k=2,Nr + DO j=1,sNy+1 + DO i=1,sNx #ifdef ALLOW_GGL90_SMOOTH tmpVisc = & ( @@ -639,7 +647,7 @@ #endif tmpVisc = MIN( tmpVisc , GGL90viscMax ) - GGL90viscArV(i,j,k,bi,bj) = MAX( tmpVisc , viscArNr(k) ) + GGL90viscArV(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) ENDDO ENDDO ENDDO