--- MITgcm/pkg/ggl90/ggl90_calc.F 2009/10/08 20:07:18 1.12 +++ MITgcm/pkg/ggl90/ggl90_calc.F 2012/08/08 22:22:42 1.23 @@ -1,4 +1,4 @@ -C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.12 2009/10/08 20:07:18 jmc Exp $ +C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.23 2012/08/08 22:22:42 gforget Exp $ C $Name: $ #include "GGL90_OPTIONS.h" @@ -7,8 +7,9 @@ C !ROUTINE: GGL90_CALC C !INTERFACE: ====================================================== - subroutine GGL90_CALC( - I bi, bj, myTime, myThid ) + SUBROUTINE GGL90_CALC( + I bi, bj, sigmaR, myTime, myIter, myThid ) + C !DESCRIPTION: \bv C *==========================================================* @@ -27,7 +28,6 @@ C GGL90TKE :: sub-grid turbulent kinetic energy (m^2/s^2) C GGL90viscAz :: GGL90 eddy viscosity coefficient (m^2/s) C GGL90diffKzT :: GGL90 diffusion coefficient for temperature (m^2/s) -C C \ev C !USES: ============================================================ @@ -42,11 +42,15 @@ C !INPUT PARAMETERS: =================================================== C Routine arguments -C bi, bj :: array indices on which to apply calculations +C bi, bj :: Current tile indices +C sigmaR :: Vertical gradient of iso-neutral density C myTime :: Current time in simulation +C myIter :: Current time-step number C myThid :: My Thread Id number INTEGER bi, bj + _RL sigmaR(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL myTime + INTEGER myIter INTEGER myThid CEOP @@ -54,26 +58,26 @@ 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 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 @@ -85,29 +89,31 @@ _RL RiNumber _RL TKEdissipation _RL tempU, tempV, prTemp - _RL MaxLength + _RL MaxLength, tmpmlx, tmpVisc _RL TKEPrandtlNumber (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL GGL90mixingLength(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) - _RL rMixingLength(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) + _RL rMixingLength (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) + _RL mxLength_Dn (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL KappaE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) - _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) -C tri-diagonal matrix - _RL a(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) - _RL b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) - _RL c(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 a3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) + _RL b3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) + _RL c3d(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, tmpdiffKrS + _RL p4, p8, p16 p4=0.25 _d 0 p8=0.125 _d 0 p16=0.0625 _d 0 @@ -121,191 +127,218 @@ 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) = 0. _d 0 - GGL90mixingLength(I,J,K) = GGL90mixingLengthMin - rMixingLength(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 +#ifndef SOLVE_DIAGONAL_LOWMEMORY + a3d(i,j,k) = 0. _d 0 + b3d(i,j,k) = 1. _d 0 + c3d(i,j,k) = 0. _d 0 +#endif 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 + 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 + 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) - 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), - O rhoKm1, - 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), - 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) ) -C + DO k = 2, Nr +c km1 = k-1 +c kp1 = MIN(Nr,k+1) + DO j=jMin,jMax + DO i=iMin,iMax + SQRTTKE(i,j,k)=SQRT( GGL90TKE(i,j,k,bi,bj) ) + C buoyancy frequency -C - 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*gravitySign*recip_rhoConst + & * sigmaR(i,j,k) 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 ENDDO -C- Impose upper bound for mixing length (total depth) +C- ensure mixing between first and second level + IF (mxlSurfFlag) THEN + DO j=jMin,jMax + DO i=iMin,iMax + GGL90mixingLength(i,j,2)=drF(1) + ENDDO + ENDDO + ENDIF + +C- Impose upper and lower bound for mixing length IF ( mxlMaxFlag .EQ. 0 ) THEN + + 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), + & MaxLength) + ENDDO + ENDDO + ENDDO + 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), - & MaxLength) + 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) ENDDO ENDDO ENDDO + ELSEIF ( mxlMaxFlag .EQ. 1 ) THEN + 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), - & MaxLength) + 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), + & GGL90mixingLengthMin) + rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k) ENDDO ENDDO ENDDO + ELSEIF ( mxlMaxFlag .EQ. 2 ) THEN + 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 - ELSE - STOP 'GGL90_CALC: Wrong mxlMaxFlag (mixing lenght limit)' - ENDIF -C- Impose minimum mixing length (to avoid division by zero) - DO k=2,Nr - 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) + DO k=2,Nr + 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) + ENDDO ENDDO ENDDO - 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) + ELSEIF ( mxlMaxFlag .EQ. 3 ) THEN -C viscosity and diffusivity - KappaM = GGL90ck*GGL90mixingLength(I,J,K)*SQRTTKE(i,j,k) - KappaH = KappaM/TKEPrandtlNumber(I,J,K) - -C Set a minium (= background) and maximum value - KappaM = MAX(KappaM,viscArNr(k)) - KappaH = MAX(KappaH,diffKrNrT(k)) - KappaM = MIN(KappaM,GGL90viscMax) - KappaH = MIN(KappaH,GGL90diffMax) - -C Mask land points and storage - GGL90viscAr(I,J,K,bi,bj) = KappaM * maskC(I,J,K,bi,bj) - GGL90diffKr(I,J,K,bi,bj) = KappaH * maskC(I,J,K,bi,bj) - KappaE(I,J,K) = GGL90alpha * GGL90viscAr(I,J,K,bi,bj) + 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)) + ENDDO + ENDDO + ENDDO + 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)) + ENDDO + ENDDO + ENDDO -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 - & ) + 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) ) + tmpmlx = MAX( tmpmlx, GGL90mixingLengthMin) + rMixingLength(i,j,k) = 1. _d 0 / tmpmlx + ENDDO ENDDO ENDDO - ENDDO + ELSE + STOP 'GGL90_CALC: Wrong mxlMaxFlag (mixing length limit)' + ENDIF + +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 & GGL90mixingLengthMin) +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 + +#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 + DO j=1-OLy,sNy+OLy + DO i=1-OLx,sNx+OLx xA(i,j) = _dyG(i,j,bi,bj) & *drF(k)*_hFacW(i,j,k,bi,bj) yA(i,j) = _dxG(i,j,bi,bj) @@ -314,9 +347,9 @@ ENDDO C Compute diffusive fluxes C ... across x-faces - DO j=1-Oly,sNy+Oly - dfx(1-Olx,j)=0. _d 0 - DO i=1-Olx+1,sNx+Olx + DO j=1-OLy,sNy+OLy + dfx(1-OLx,j)=0. _d 0 + DO i=1-OLx+1,sNx+OLx dfx(i,j) = -GGL90diffTKEh*xA(i,j) & *_recip_dxC(i,j,bi,bj) & *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i-1,j,k,bi,bj)) @@ -324,11 +357,11 @@ ENDDO ENDDO C ... across y-faces - DO i=1-Olx,sNx+Olx - dfy(i,1-Oly)=0. _d 0 + DO i=1-OLx,sNx+OLx + dfy(i,1-OLy)=0. _d 0 ENDDO - DO j=1-Oly+1,sNy+Oly - DO i=1-Olx,sNx+Olx + DO j=1-OLy+1,sNy+OLy + DO i=1-OLx,sNx+OLx dfy(i,j) = -GGL90diffTKEh*yA(i,j) & *_recip_dyC(i,j,bi,bj) & *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i,j-1,k,bi,bj)) @@ -338,21 +371,75 @@ ENDDO ENDDO 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) + DO j=1-OLy,sNy+OLy-1 + DO i=1-OLx,sNx+OLx-1 + 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)) - & ) + & ) 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 @@ -361,89 +448,95 @@ C-- Lower diagonal DO j=jMin,jMax DO i=iMin,iMax - a(i,j,1) = 0. _d 0 + a3d(i,j,1) = 0. _d 0 ENDDO ENDDO DO k=2,Nr - km1=max(2,k-1) + km1=MAX(2,k-1) DO j=jMin,jMax DO i=iMin,iMax - a(i,j,k) = -deltaTggl90 -c & *recip_drF(km1)*recip_hFacI(i,j,k,bi,bj) +C- We keep recip_hFacC in the diffusive flux calculation, +C- but no hFacC in TKE volume control +C- No need for maskC(k-1) with recip_hFacC(k-1) + a3d(i,j,k) = -deltaTggl90 & *recip_drF(k-1)*recip_hFacC(i,j,k-1,bi,bj) & *.5 _d 0*(KappaE(i,j, k )+KappaE(i,j,km1)) - & *recip_drC(k)*maskC(i,j,k,bi,bj)*maskC(i,j,k-1,bi,bj) + & *recip_drC(k)*maskC(i,j,k,bi,bj) ENDDO ENDDO ENDDO C-- Upper diagonal DO j=jMin,jMax DO i=iMin,iMax - c(i,j,1) = 0. _d 0 + c3d(i,j,1) = 0. _d 0 ENDDO ENDDO DO k=2,Nr DO j=jMin,jMax DO i=iMin,iMax - kp1=min(klowC(i,j,bi,bj),k+1) - c(i,j,k) = -deltaTggl90 -c & *recip_drF( k )*recip_hFacI(i,j,k,bi,bj) + kp1=MAX(1,MIN(klowC(i,j,bi,bj),k+1)) +C- We keep recip_hFacC in the diffusive flux calculation, +C- but no hFacC in TKE volume control +C- No need for maskC(k) with recip_hFacC(k) + c3d(i,j,k) = -deltaTggl90 & *recip_drF( k ) * recip_hFacC(i,j,k,bi,bj) & *.5 _d 0*(KappaE(i,j,k)+KappaE(i,j,kp1)) - & *recip_drC(k)*maskC(i,j,k,bi,bj)*maskC(i,j,k-1,bi,bj) + & *recip_drC(k)*maskC(i,j,k-1,bi,bj) ENDDO ENDDO ENDDO C-- Center diagonal DO k=1,Nr + km1 = MAX(k-1,1) 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*SQRT(GGL90TKE(I,J,K,bi,bj)) - & *rMixingLength(I,J,K)*maskC(i,j,k,bi,bj) + b3d(i,j,k) = 1. _d 0 - c3d(i,j,k) - a3d(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 ENDDO C end set up matrix -C C Apply boundary condition -C - DO J=jMin,jMax - DO I=iMin,iMax + kp1 = MIN(Nr,kSurf+1) + 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) + 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) + & - a3d(i,j,kp1)*GGL90TKE(i,j,kSurf,bi,bj) + a3d(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 - ENDDO - ENDDO -C -C solve tri-diagonal system, and store solution on gTKE (previously rhs) -C - CALL GGL90_SOLVE( bi, bj, iMin, iMax, jMin, jMax, - I a, b, c, - U gTKE, - I myThid ) -C -C now update TKE -C - DO K=1,Nr - DO J=jMin,jMax - DO I=iMin,iMax + kBottom = MAX(kLowC(i,j,bi,bj),1) + GGL90TKE(i,j,kBottom,bi,bj) = GGL90TKE(i,j,kBottom,bi,bj) + & - GGL90TKEbottom*c3d(i,j,kBottom) + c3d(i,j,kBottom) = 0. _d 0 + ENDDO + ENDDO + +C solve tri-diagonal system + CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, + I a3d, b3d, c3d, + U GGL90TKE, + O errCode, + I bi, bj, myThid ) + + 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 @@ -451,21 +544,21 @@ C end of time step C =============================== + DO k=2,Nr + DO j=1,sNy + DO i=1,sNx #ifdef ALLOW_GGL90_SMOOTH - DO K=1,Nr - DO J=jMin,jMax - DO I=iMin,iMax - tmpdiffKrS= + tmpVisc= & ( - & p4 * GGL90viscAr(i ,j ,k,bi,bj) * mskCor(i ,j ,bi,bj) - & +p8 *( GGL90viscAr(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) - & + GGL90viscAr(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) - & + GGL90viscAr(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) - & + GGL90viscAr(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) - & +p16*( GGL90viscAr(i+1,j+1,k,bi,bj) * mskCor(i+1,j+1,bi,bj) - & + GGL90viscAr(i+1,j-1,k,bi,bj) * mskCor(i+1,j-1,bi,bj) - & + GGL90viscAr(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) - & + GGL90viscAr(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj)) + & p4 * GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) + & +p8 *( GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj) + & + GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj) + & + GGL90visctmp(i+1,j ,k) * mskCor(i+1,j ,bi,bj) + & + GGL90visctmp(i ,j+1,k) * mskCor(i ,j+1,bi,bj)) + & +p16*( GGL90visctmp(i+1,j+1,k) * mskCor(i+1,j+1,bi,bj) + & + GGL90visctmp(i+1,j-1,k) * mskCor(i+1,j-1,bi,bj) + & + GGL90visctmp(i-1,j+1,k) * mskCor(i-1,j+1,bi,bj) + & + GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj)) & ) & /(p4 & +p8 *( maskC(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) @@ -477,18 +570,89 @@ & + maskC(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) & + 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) - & /TKEPrandtlNumber(i,j,k) - GGL90diffKrS(I,J,K,bi,bj)= MAX( tmpdiffKrS , diffKrNrT(k) ) +#else + tmpVisc = GGL90visctmp(i,j,k) +#endif + tmpVisc = MIN(tmpVisc/TKEPrandtlNumber(i,j,k),GGL90diffMax) + 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 +#ifdef ALLOW_GGL90_SMOOTH + tmpVisc = + & ( + & p4 *(GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) + & +GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj)) + & +p8 *(GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj) + & +GGL90visctmp(i-1,j+1,k) * mskCor(i-1,j+1,bi,bj) + & +GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj) + & +GGL90visctmp(i ,j+1,k) * mskCor(i ,j+1,bi,bj)) + & ) + & /(p4 * 2. _d 0 + & +p8 *( maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj) + & + maskC(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) + & + maskC(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) + & + maskC(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) + & ) + & *maskC(i ,j,k,bi,bj)*mskCor(i ,j,bi,bj) + & *maskC(i-1,j,k,bi,bj)*mskCor(i-1,j,bi,bj) +#else + tmpVisc = _maskW(i,j,k,bi,bj) * + & (.5 _d 0*(GGL90visctmp(i,j,k) + & +GGL90visctmp(i-1,j,k)) + & ) +#endif + 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 +#ifdef ALLOW_GGL90_SMOOTH + tmpVisc = + & ( + & p4 *(GGL90visctmp(i ,j ,k) * mskCor(i ,j ,bi,bj) + & +GGL90visctmp(i ,j-1,k) * mskCor(i ,j-1,bi,bj)) + & +p8 *(GGL90visctmp(i-1,j ,k) * mskCor(i-1,j ,bi,bj) + & +GGL90visctmp(i-1,j-1,k) * mskCor(i-1,j-1,bi,bj) + & +GGL90visctmp(i+1,j ,k) * mskCor(i+1,j ,bi,bj) + & +GGL90visctmp(i+1,j-1,k) * mskCor(i+1,j-1,bi,bj)) + & ) + & /(p4 * 2. _d 0 + & +p8 *( maskC(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) + & + maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj) + & + maskC(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) + & + 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) + & *maskC(i,j-1,k,bi,bj)*mskCor(i,j-1,bi,bj) +#else + tmpVisc = _maskS(i,j,k,bi,bj) * + & (.5 _d 0*(GGL90visctmp(i,j,k) + & +GGL90visctmp(i,j-1,k)) + & ) + #endif + tmpVisc = MIN( tmpVisc , GGL90viscMax ) + GGL90viscArV(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) ) + ENDDO + ENDDO + ENDDO #ifdef ALLOW_DIAGNOSTICS IF ( useDiagnostics ) THEN CALL DIAGNOSTICS_FILL( GGL90TKE ,'GGL90TKE', & 0,Nr, 1, bi, bj, myThid ) - CALL DIAGNOSTICS_FILL( GGL90viscAr,'GGL90Ar ', + CALL DIAGNOSTICS_FILL( GGL90viscArU,'GGL90ArU', + & 0,Nr, 1, bi, bj, myThid ) + CALL DIAGNOSTICS_FILL( GGL90viscArV,'GGL90ArV', & 0,Nr, 1, bi, bj, myThid ) CALL DIAGNOSTICS_FILL( GGL90diffKr,'GGL90Kr ', & 0,Nr, 1, bi, bj, myThid )