17 |
C harmonic viscosity= |
C harmonic viscosity= |
18 |
C viscAh (or viscAhD on div pts and viscAhZ on zeta pts) |
C viscAh (or viscAhD on div pts and viscAhZ on zeta pts) |
19 |
C +0.25*L**2*viscAhGrid/deltaT |
C +0.25*L**2*viscAhGrid/deltaT |
20 |
C +sqrt(viscC2leith**2*grad(Vort3)**2 |
C +sqrt((viscC2leith/pi)**6*grad(Vort3)**2 |
21 |
C +viscC2leithD**2*grad(hDiv)**2)*L**3 |
C +(viscC2leithD/pi)**6*grad(hDiv)**2)*L**3 |
22 |
C +(viscC2smag/pi)**2*L**2*sqrt(Tension**2+Strain**2) |
C +(viscC2smag/pi)**2*L**2*sqrt(Tension**2+Strain**2) |
23 |
C |
C |
24 |
C biharmonic viscosity= |
C biharmonic viscosity= |
25 |
C viscA4 (or viscA4D on div pts and viscA4Z on zeta pts) |
C viscA4 (or viscA4D on div pts and viscA4Z on zeta pts) |
26 |
C +0.25*0.125*L**4*viscA4Grid/deltaT (approx) |
C +0.25*0.125*L**4*viscA4Grid/deltaT (approx) |
27 |
C +0.125*L**5*sqrt(viscC4leith**2*grad(Vort3)**2 |
C +0.125*L**5*sqrt((viscC4leith/pi)**6*grad(Vort3)**2 |
28 |
C +viscC4leithD**2*grad(hDiv)**2) |
C +(viscC4leithD/pi)**6*grad(hDiv)**2) |
29 |
C +0.125*L**4*(viscC4smag/pi)**2*sqrt(Tension**2+Strain**2) |
C +0.125*L**4*(viscC4smag/pi)**2*sqrt(Tension**2+Strain**2) |
30 |
C |
C |
31 |
C Note that often 0.125*L**2 is the scale between harmonic and |
C Note that often 0.125*L**2 is the scale between harmonic and |
51 |
C biharmonic viscosity>viscA4gridmax*L**4/32/deltaT (approx) |
C biharmonic viscosity>viscA4gridmax*L**4/32/deltaT (approx) |
52 |
C |
C |
53 |
C RECOMMENDED VALUES |
C RECOMMENDED VALUES |
54 |
C viscC2Leith=? |
C viscC2Leith=1-3 |
55 |
C viscC2LeithD=? |
C viscC2LeithD=1-3 |
56 |
C viscC4Leith=? |
C viscC4Leith=1-3 |
57 |
C viscC4LeithD=? |
C viscC4LeithD=1.5-3 |
58 |
C viscC2smag=2.2-4 (Griffies and Hallberg,2000) |
C viscC2smag=2.2-4 (Griffies and Hallberg,2000) |
59 |
C 0.2-0.9 (Smagorinsky,1993) |
C 0.2-0.9 (Smagorinsky,1993) |
60 |
C viscC4smag=2.2-4 (Griffies and Hallberg,2000) |
C viscC4smag=2.2-4 (Griffies and Hallberg,2000) |
91 |
C == Local variables == |
C == Local variables == |
92 |
INTEGER I,J |
INTEGER I,J |
93 |
_RL smag2fac, smag4fac |
_RL smag2fac, smag4fac |
94 |
|
_RL leith2fac, leith4fac |
95 |
|
_RL leithD2fac, leithD4fac |
96 |
_RL viscAhRe_max, viscA4Re_max |
_RL viscAhRe_max, viscA4Re_max |
97 |
_RL Alin,grdVrt,grdDiv, keZpt |
_RL Alin,grdVrt,grdDiv, keZpt |
98 |
_RL recip_dt,L2,L3,L4,L5,L2rdt,L4rdt |
_RL recip_dt,L2,L3,L4,L5,L2rdt,L4rdt |
99 |
_RL Uscl,U4scl |
_RL Uscl,U4scl |
100 |
|
_RL divDx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
101 |
|
_RL divDy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
102 |
_RL viscAh_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
_RL viscAh_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
103 |
_RL viscAh_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
_RL viscAh_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
104 |
_RL viscA4_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
_RL viscA4_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
185 |
smag4fac=0. _d 0 |
smag4fac=0. _d 0 |
186 |
ENDIF |
ENDIF |
187 |
|
|
188 |
|
IF (calcleith) THEN |
189 |
|
IF (useFullLeith) THEN |
190 |
|
leith2fac =(viscC2leith /pi)**6 |
191 |
|
leithD2fac=(viscC2leithD/pi)**6 |
192 |
|
leith4fac =0.015625 _d 0*(viscC4leith /pi)**6 |
193 |
|
leithD4fac=0.015625 _d 0*(viscC4leithD/pi)**6 |
194 |
|
ELSE |
195 |
|
leith2fac =(viscC2leith /pi)**3 |
196 |
|
leithD2fac=(viscC2leithD/pi)**3 |
197 |
|
leith4fac =0.125 _d 0*(viscC4leith /pi)**3 |
198 |
|
leithD4fac=0.125 _d 0*(viscC4leithD/pi)**3 |
199 |
|
ENDIF |
200 |
|
ELSE |
201 |
|
leith2fac=0. _d 0 |
202 |
|
leith4fac=0. _d 0 |
203 |
|
leithD2fac=0. _d 0 |
204 |
|
leithD4fac=0. _d 0 |
205 |
|
ENDIF |
206 |
|
|
207 |
C - Viscosity |
C - Viscosity |
208 |
IF (useVariableViscosity) THEN |
IF (useVariableViscosity) THEN |
209 |
|
|
210 |
|
C horizontal gradient of horizontal divergence: |
211 |
|
DO j=1-Oly,sNy+Oly |
212 |
|
DO i=1-Olx,sNx+Olx |
213 |
|
divDx(i,j) = 0. |
214 |
|
divDy(i,j) = 0. |
215 |
|
ENDDO |
216 |
|
ENDDO |
217 |
|
IF (calcleith) THEN |
218 |
|
C- gradient in x direction: |
219 |
|
#ifndef ALLOW_AUTODIFF_TAMC |
220 |
|
IF (useCubedSphereExchange) THEN |
221 |
|
C to compute d/dx(hDiv), fill corners with appropriate values: |
222 |
|
CALL FILL_CS_CORNER_TR_RL( .TRUE., hDiv, bi,bj, myThid ) |
223 |
|
ENDIF |
224 |
|
#endif |
225 |
|
DO j=2-Oly,sNy+Oly-1 |
226 |
|
DO i=2-Olx,sNx+Olx-1 |
227 |
|
divDx(i,j) = (hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj) |
228 |
|
ENDDO |
229 |
|
ENDDO |
230 |
|
|
231 |
|
C- gradient in y direction: |
232 |
|
#ifndef ALLOW_AUTODIFF_TAMC |
233 |
|
IF (useCubedSphereExchange) THEN |
234 |
|
C to compute d/dy(hDiv), fill corners with appropriate values: |
235 |
|
CALL FILL_CS_CORNER_TR_RL(.FALSE., hDiv, bi,bj, myThid ) |
236 |
|
ENDIF |
237 |
|
#endif |
238 |
|
DO j=2-Oly,sNy+Oly-1 |
239 |
|
DO i=2-Olx,sNx+Olx-1 |
240 |
|
divDy(i,j) = (hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj) |
241 |
|
ENDDO |
242 |
|
ENDDO |
243 |
|
ENDIF |
244 |
|
|
245 |
DO j=2-Oly,sNy+Oly-1 |
DO j=2-Oly,sNy+Oly-1 |
246 |
DO i=2-Olx,sNx+Olx-1 |
DO i=2-Olx,sNx+Olx-1 |
247 |
CCCCCCCCCCCCCCC Divergence Point CalculationsCCCCCCCCCCCCCCCCCCCC |
CCCCCCCCCCCCCCC Divergence Point CalculationsCCCCCCCCCCCCCCCCCCCC |
291 |
|
|
292 |
C This is the vector magnitude of grad (div.v) squared |
C This is the vector magnitude of grad (div.v) squared |
293 |
C Using it in Leith serves to damp instabilities in w. |
C Using it in Leith serves to damp instabilities in w. |
294 |
grdDiv=0.25 _d 0*( |
grdDiv=0.25 _d 0*( (divDx(i+1,j)*divDx(i+1,j) |
295 |
& ((hDiv(i+1,j)-hDiv(i,j))*recip_DXC(i+1,j,bi,bj))**2 |
& + divDx(i,j)*divDx(i,j) ) |
296 |
& +((hDiv(i,j+1)-hDiv(i,j))*recip_DYC(i,j+1,bi,bj))**2 |
& + (divDy(i,j+1)*divDy(i,j+1) |
297 |
& +((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))**2 |
& + divDy(i,j)*divDy(i,j) ) ) |
|
& +((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))**2) |
|
298 |
|
|
299 |
viscAh_DLth(i,j)= |
viscAh_DLth(i,j)= |
300 |
& sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
& sqrt(leith2fac*grdVrt+leithD2fac*grdDiv)*L3 |
301 |
viscA4_DLth(i,j)=0.125 _d 0* |
viscA4_DLth(i,j)= |
302 |
& sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
& sqrt(leith4fac*grdVrt+leithD4fac*grdDiv)*L5 |
303 |
viscAh_DLthd(i,j)= |
viscAh_DLthd(i,j)= |
304 |
& sqrt(viscC2leithD**2*grdDiv)*L3 |
& sqrt(leithD2fac*grdDiv)*L3 |
305 |
viscA4_DLthd(i,j)=0.125 _d 0* |
viscA4_DLthd(i,j)= |
306 |
& sqrt(viscC4leithD**2*grdDiv)*L5 |
& sqrt(leithD4fac*grdDiv)*L5 |
307 |
ELSEIF (calcleith) THEN |
ELSEIF (calcleith) THEN |
308 |
C but this approximation will work on cube |
C but this approximation will work on cube |
309 |
c (and differs by as much as 4X) |
c (and differs by as much as 4X) |
315 |
grdVrt=max(grdVrt, |
grdVrt=max(grdVrt, |
316 |
& abs((vort3(i+1,j+1)-vort3(i+1,j))*recip_DYG(i+1,j,bi,bj))) |
& abs((vort3(i+1,j+1)-vort3(i+1,j))*recip_DYG(i+1,j,bi,bj))) |
317 |
|
|
318 |
grdDiv=abs((hDiv(i+1,j)-hDiv(i,j))*recip_DXC(i+1,j,bi,bj)) |
grdDiv=max( abs(divDx(i+1,j)), abs(divDx(i,j)) ) |
319 |
grdDiv=max(grdDiv, |
grdDiv=max( grdDiv, abs(divDy(i,j+1)) ) |
320 |
& abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYC(i,j+1,bi,bj))) |
grdDiv=max( grdDiv, abs(divDy(i,j)) ) |
|
grdDiv=max(grdDiv, |
|
|
& abs((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))) |
|
|
grdDiv=max(grdDiv, |
|
|
& abs((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))) |
|
321 |
|
|
322 |
c This approximation is good to the same order as above... |
c This approximation is good to the same order as above... |
323 |
viscAh_Dlth(i,j)= |
viscAh_Dlth(i,j)=(leith2fac*grdVrt+(leithD2fac*grdDiv))*L3 |
324 |
& (viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 |
viscA4_Dlth(i,j)=(leith4fac*grdVrt+(leithD4fac*grdDiv))*L5 |
325 |
viscA4_Dlth(i,j)=0.125 _d 0* |
viscAh_DlthD(i,j)=((leithD2fac*grdDiv))*L3 |
326 |
& (viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 |
viscA4_DlthD(i,j)=((leithD4fac*grdDiv))*L5 |
|
viscAh_DlthD(i,j)= |
|
|
& ((viscC2leithD*grdDiv))*L3 |
|
|
viscA4_DlthD(i,j)=0.125 _d 0* |
|
|
& ((viscC4leithD*grdDiv))*L5 |
|
327 |
ELSE |
ELSE |
328 |
viscAh_Dlth(i,j)=0. _d 0 |
viscAh_Dlth(i,j)=0. _d 0 |
329 |
viscA4_Dlth(i,j)=0. _d 0 |
viscA4_Dlth(i,j)=0. _d 0 |
405 |
& +((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))**2) |
& +((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))**2) |
406 |
|
|
407 |
C This is the vector magnitude of grad(div.v) squared |
C This is the vector magnitude of grad(div.v) squared |
408 |
grdDiv=0.25 _d 0*( |
grdDiv=0.25 _d 0*( (divDx(i,j-1)*divDx(i,j-1) |
409 |
& ((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))**2 |
& + divDx(i,j)*divDx(i,j) ) |
410 |
& +((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))**2 |
& + (divDy(i-1,j)*divDy(i-1,j) |
411 |
& +((hDiv(i,j-1)-hDiv(i-1,j-1))*recip_DXC(i,j-1,bi,bj))**2 |
& + divDy(i,j)*divDy(i,j) ) ) |
|
& +((hDiv(i-1,j)-hDiv(i-1,j-1))*recip_DYC(i-1,j,bi,bj))**2) |
|
412 |
|
|
413 |
viscAh_ZLth(i,j)= |
viscAh_ZLth(i,j)= |
414 |
& sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
& sqrt(leith2fac*grdVrt+leithD2fac*grdDiv)*L3 |
415 |
viscA4_ZLth(i,j)=0.125 _d 0* |
viscA4_ZLth(i,j)= |
416 |
& sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
& sqrt(leith4fac*grdVrt+leithD4fac*grdDiv)*L5 |
417 |
viscAh_ZLthD(i,j)= |
viscAh_ZLthD(i,j)= |
418 |
& sqrt(viscC2leithD**2*grdDiv)*L3 |
& sqrt(leithD2fac*grdDiv)*L3 |
419 |
viscA4_ZLthD(i,j)=0.125 _d 0* |
viscA4_ZLthD(i,j)= |
420 |
& sqrt(viscC4leithD**2*grdDiv)*L5 |
& sqrt(leithD4fac*grdDiv)*L5 |
421 |
|
|
422 |
ELSEIF (calcleith) THEN |
ELSEIF (calcleith) THEN |
423 |
C but this approximation will work on cube (and differs by 4X) |
C but this approximation will work on cube (and differs by 4X) |
429 |
grdVrt=max(grdVrt, |
grdVrt=max(grdVrt, |
430 |
& abs((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))) |
& abs((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))) |
431 |
|
|
432 |
grdDiv=abs((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj)) |
grdDiv=max( abs(divDx(i,j)), abs(divDx(i,j-1)) ) |
433 |
grdDiv=max(grdDiv, |
grdDiv=max( grdDiv, abs(divDy(i,j)) ) |
434 |
& abs((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))) |
grdDiv=max( grdDiv, abs(divDy(i-1,j)) ) |
435 |
grdDiv=max(grdDiv, |
|
436 |
& abs((hDiv(i,j-1)-hDiv(i-1,j-1))*recip_DXC(i,j-1,bi,bj))) |
viscAh_ZLth(i,j)=(leith2fac*grdVrt+(leithD2fac*grdDiv))*L3 |
437 |
grdDiv=max(grdDiv, |
viscA4_ZLth(i,j)=(leith4fac*grdVrt+(leithD4fac*grdDiv))*L5 |
438 |
& abs((hDiv(i-1,j)-hDiv(i-1,j-1))*recip_DYC(i-1,j,bi,bj))) |
viscAh_ZLthD(i,j)=(leithD2fac*grdDiv)*L3 |
439 |
|
viscA4_ZLthD(i,j)=(leithD4fac*grdDiv)*L5 |
|
viscAh_ZLth(i,j)=(viscC2leith*grdVrt |
|
|
& +(viscC2leithD*grdDiv))*L3 |
|
|
viscA4_ZLth(i,j)=0.125 _d 0*(viscC4leith*grdVrt |
|
|
& +(viscC4leithD*grdDiv))*L5 |
|
|
viscAh_ZLthD(i,j)=((viscC2leithD*grdDiv))*L3 |
|
|
viscA4_ZLthD(i,j)=0.125 _d 0*((viscC4leithD*grdDiv))*L5 |
|
440 |
ELSE |
ELSE |
441 |
viscAh_ZLth(i,j)=0. _d 0 |
viscAh_ZLth(i,j)=0. _d 0 |
442 |
viscA4_ZLth(i,j)=0. _d 0 |
viscA4_ZLth(i,j)=0. _d 0 |