11 |
I bi, bj, myTime, myThid ) |
I bi, bj, myTime, myThid ) |
12 |
|
|
13 |
C !DESCRIPTION: \bv |
C !DESCRIPTION: \bv |
14 |
C /==========================================================\ |
C *==========================================================* |
15 |
C | SUBROUTINE GGL90_CALC | |
C | SUBROUTINE GGL90_CALC | |
16 |
C | o Compute all GGL90 fields defined in GGL90.h | |
C | o Compute all GGL90 fields defined in GGL90.h | |
17 |
C |==========================================================| |
C *==========================================================* |
18 |
C | Equation numbers refer to | |
C | Equation numbers refer to | |
19 |
C | Gaspar et al. (1990), JGR 95 (C9), pp 16,179 | |
C | Gaspar et al. (1990), JGR 95 (C9), pp 16,179 | |
20 |
C | Some parts of the implementation follow Blanke and | |
C | Some parts of the implementation follow Blanke and | |
21 |
C | Delecuse (1993), JPO, and OPA code, in particular the | |
C | Delecuse (1993), JPO, and OPA code, in particular the | |
22 |
C | computation of the | |
C | computation of the | |
23 |
C | mixing length = max(min(lk,depth),lkmin) | |
C | mixing length = max(min(lk,depth),lkmin) | |
24 |
C \==========================================================/ |
C *==========================================================* |
|
IMPLICIT NONE |
|
|
C |
|
|
C-------------------------------------------------------------------- |
|
25 |
|
|
26 |
C global parameters updated by ggl90_calc |
C global parameters updated by ggl90_calc |
27 |
C GGL90TKE - sub-grid turbulent kinetic energy (m^2/s^2) |
C GGL90TKE :: sub-grid turbulent kinetic energy (m^2/s^2) |
28 |
C GGL90viscAz - GGL90 eddy viscosity coefficient (m^2/s) |
C GGL90viscAz :: GGL90 eddy viscosity coefficient (m^2/s) |
29 |
C GGL90diffKzT - GGL90 diffusion coefficient for temperature (m^2/s) |
C GGL90diffKzT :: GGL90 diffusion coefficient for temperature (m^2/s) |
|
C |
|
30 |
C \ev |
C \ev |
31 |
|
|
32 |
C !USES: ============================================================ |
C !USES: ============================================================ |
33 |
|
IMPLICIT NONE |
34 |
#include "SIZE.h" |
#include "SIZE.h" |
35 |
#include "EEPARAMS.h" |
#include "EEPARAMS.h" |
36 |
#include "PARAMS.h" |
#include "PARAMS.h" |
40 |
#include "GRID.h" |
#include "GRID.h" |
41 |
|
|
42 |
C !INPUT PARAMETERS: =================================================== |
C !INPUT PARAMETERS: =================================================== |
43 |
c Routine arguments |
C Routine arguments |
44 |
c bi, bj - array indices on which to apply calculations |
C bi, bj :: array indices on which to apply calculations |
45 |
c myTime - Current time in simulation |
C myTime :: Current time in simulation |
46 |
|
C myThid :: My Thread Id number |
47 |
INTEGER bi, bj |
INTEGER bi, bj |
|
INTEGER myThid |
|
48 |
_RL myTime |
_RL myTime |
49 |
|
INTEGER myThid |
50 |
|
CEOP |
51 |
|
|
52 |
#ifdef ALLOW_GGL90 |
#ifdef ALLOW_GGL90 |
53 |
|
|
54 |
C !LOCAL VARIABLES: ==================================================== |
C !LOCAL VARIABLES: ==================================================== |
55 |
c Local constants |
C Local constants |
56 |
C iMin, iMax, jMin, jMax, I, J - array computation indices |
C iMin, iMax, jMin, jMax, I, J - array computation indices |
57 |
C K, Kp1, km1, kSurf, kBottom - vertical loop indices |
C K, Kp1, km1, kSurf, kBottom - vertical loop indices |
58 |
C ab15, ab05 - weights for implicit timestepping |
C ab15, ab05 - weights for implicit timestepping |
59 |
C uStarSquare - square of friction velocity |
C uStarSquare - square of friction velocity |
60 |
C verticalShear - (squared) vertical shear of horizontal velocity |
C verticalShear - (squared) vertical shear of horizontal velocity |
61 |
C Nsquare - squared buoyancy freqency |
C Nsquare - squared buoyancy freqency |
62 |
C RiNumber - local Richardson number |
C RiNumber - local Richardson number |
63 |
C KappaM - (local) viscosity parameter (eq.10) |
C KappaM - (local) viscosity parameter (eq.10) |
64 |
C KappaH - (local) diffusivity parameter for temperature (eq.11) |
C KappaH - (local) diffusivity parameter for temperature (eq.11) |
65 |
C KappaE - (local) diffusivity parameter for TKE (eq.15) |
C KappaE - (local) diffusivity parameter for TKE (eq.15) |
|
C buoyFreq - buoyancy freqency |
|
66 |
C TKEdissipation - dissipation of TKE |
C TKEdissipation - dissipation of TKE |
67 |
C GGL90mixingLength- mixing length of scheme following Banke+Delecuse |
C GGL90mixingLength- mixing length of scheme following Banke+Delecuse |
68 |
|
C rMixingLength- inverse of mixing length |
69 |
C totalDepth - thickness of water column (inverse of recip_Rcol) |
C totalDepth - thickness of water column (inverse of recip_Rcol) |
70 |
C TKEPrandtlNumber - here, an empirical function of the Richardson number |
C TKEPrandtlNumber - here, an empirical function of the Richardson number |
71 |
C rhoK, rhoKm1 - density at layer K and Km1 (relative to K) |
C rhoK, rhoKm1 - density at layer K and Km1 (relative to K) |
76 |
_RL uStarSquare |
_RL uStarSquare |
77 |
_RL verticalShear |
_RL verticalShear |
78 |
_RL KappaM, KappaH |
_RL KappaM, KappaH |
79 |
_RL Nsquare |
c _RL Nsquare |
80 |
|
_RL Nsquare(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
81 |
_RL deltaTggl90 |
_RL deltaTggl90 |
82 |
_RL SQRTTKE |
c _RL SQRTTKE |
83 |
|
_RL SQRTTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
84 |
_RL RiNumber |
_RL RiNumber |
85 |
_RL TKEdissipation |
_RL TKEdissipation |
86 |
_RL tempU, tempV, prTemp |
_RL tempU, tempV, prTemp |
87 |
|
_RL MaxLength, tmpmlx |
88 |
_RL TKEPrandtlNumber (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
_RL TKEPrandtlNumber (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
89 |
_RL GGL90mixingLength(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
_RL GGL90mixingLength(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
90 |
|
_RL rMixingLength (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
91 |
|
_RL mxLength_Dn (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
92 |
_RL KappaE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
_RL KappaE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
93 |
_RL rhoK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
_RL rhoK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
94 |
_RL rhoKm1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
_RL rhoKm1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
95 |
_RL totalDepth (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
_RL totalDepth (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
96 |
_RL gTKE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
_RL gTKE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
97 |
C tri-diagonal matrix |
C- tri-diagonal matrix |
98 |
_RL a(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
_RL a(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
99 |
_RL b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
_RL b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
100 |
_RL c(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
_RL c(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
101 |
CEOP |
INTEGER errCode |
102 |
|
#ifdef ALLOW_GGL90_HORIZDIFF |
103 |
|
C- xA, yA - area of lateral faces |
104 |
|
C- dfx, dfy - diffusive flux across lateral faces |
105 |
|
_RL xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
106 |
|
_RL yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
107 |
|
_RL dfx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
108 |
|
_RL dfy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
109 |
|
#endif /* ALLOW_GGL90_HORIZDIFF */ |
110 |
|
#ifdef ALLOW_GGL90_SMOOTH |
111 |
|
_RL p4, p8, p16, tmpdiffKrS |
112 |
|
p4=0.25 _d 0 |
113 |
|
p8=0.125 _d 0 |
114 |
|
p16=0.0625 _d 0 |
115 |
|
#endif |
116 |
iMin = 2-OLx |
iMin = 2-OLx |
117 |
iMax = sNx+OLx-1 |
iMax = sNx+OLx-1 |
118 |
jMin = 2-OLy |
jMin = 2-OLy |
119 |
jMax = sNy+OLy-1 |
jMax = sNy+OLy-1 |
120 |
|
|
121 |
C set separate time step (should be deltaTtracer) |
C set separate time step (should be deltaTtracer) |
122 |
deltaTggl90 = deltaTtracer |
deltaTggl90 = dTtracerLev(1) |
123 |
C |
|
124 |
kSurf = 1 |
kSurf = 1 |
125 |
C implicit timestepping weights for dissipation |
C implicit timestepping weights for dissipation |
126 |
ab15 = 1.5 _d 0 |
ab15 = 1.5 _d 0 |
134 |
DO I=1-Olx,sNx+Olx |
DO I=1-Olx,sNx+Olx |
135 |
gTKE(I,J,K) = 0. _d 0 |
gTKE(I,J,K) = 0. _d 0 |
136 |
KappaE(I,J,K) = 0. _d 0 |
KappaE(I,J,K) = 0. _d 0 |
137 |
TKEPrandtlNumber(I,J,K) = 0. _d 0 |
TKEPrandtlNumber(I,J,K) = 1. _d 0 |
138 |
GGL90mixingLength(I,J,K) = 0. _d 0 |
GGL90mixingLength(I,J,K) = GGL90mixingLengthMin |
139 |
ENDDO |
ENDDO |
140 |
ENDDO |
ENDDO |
141 |
ENDDO |
ENDDO |
142 |
DO J=1-Oly,sNy+Oly |
DO J=1-Oly,sNy+Oly |
143 |
DO I=1-Olx,sNx+Olx |
DO I=1-Olx,sNx+Olx |
144 |
rhoK (I,J) = 0. _d 0 |
rhoK(I,J) = 0. _d 0 |
145 |
rhoKm1 (I,J) = 0. _d 0 |
rhoKm1(I,J) = 0. _d 0 |
146 |
totalDepth(I,J) = 0. _d 0 |
totalDepth(I,J) = Ro_surf(i,j,bi,bj) - R_low(i,j,bi,bj) |
147 |
IF ( recip_Rcol(I,J,bi,bj) .NE. 0. ) |
rMixingLength(i,j,1) = 0. _d 0 |
148 |
& totalDepth(I,J) = 1./recip_Rcol(I,J,bi,bj) |
mxLength_Dn(I,J,1) = GGL90mixingLengthMin |
149 |
|
SQRTTKE(i,j,1) = SQRT( GGL90TKE(i,j,1,bi,bj) ) |
150 |
ENDDO |
ENDDO |
151 |
ENDDO |
ENDDO |
152 |
|
|
153 |
C start k-loop |
C start k-loop |
154 |
DO K = 2, Nr |
DO K = 2, Nr |
155 |
Km1 = K-1 |
Km1 = K-1 |
156 |
Kp1 = MIN(Nr,K+1) |
c Kp1 = MIN(Nr,K+1) |
157 |
CALL FIND_RHO( |
CALL FIND_RHO_2D( |
158 |
I bi, bj, iMin, iMax, jMin, jMax, Km1, K, |
I iMin, iMax, jMin, jMax, K, |
159 |
I theta, salt, |
I theta(1-OLx,1-OLy,Km1,bi,bj), salt(1-OLx,1-OLy,Km1,bi,bj), |
160 |
O rhoKm1, |
O rhoKm1, |
161 |
I myThid ) |
I Km1, bi, bj, myThid ) |
162 |
CALL FIND_RHO( |
|
163 |
I bi, bj, iMin, iMax, jMin, jMax, K, K, |
CALL FIND_RHO_2D( |
164 |
I theta, salt, |
I iMin, iMax, jMin, jMax, K, |
165 |
|
I theta(1-OLx,1-OLy,K,bi,bj), salt(1-OLx,1-OLy,K,bi,bj), |
166 |
O rhoK, |
O rhoK, |
167 |
I myThid ) |
I K, bi, bj, myThid ) |
168 |
DO J=jMin,jMax |
DO J=jMin,jMax |
169 |
DO I=iMin,iMax |
DO I=iMin,iMax |
170 |
SQRTTKE=SQRT( GGL90TKE(I,J,K,bi,bj) ) |
SQRTTKE(i,j,k)=SQRT( GGL90TKE(I,J,K,bi,bj) ) |
171 |
C |
|
172 |
C buoyancy frequency |
C buoyancy frequency |
173 |
C |
Nsquare(i,j,k) = - gravity*recip_rhoConst*recip_drC(K) |
|
Nsquare = - gravity*recip_rhoConst*recip_drC(K) |
|
174 |
& * ( rhoKm1(I,J) - rhoK(I,J) )*maskC(I,J,K,bi,bj) |
& * ( rhoKm1(I,J) - rhoK(I,J) )*maskC(I,J,K,bi,bj) |
175 |
|
cC vertical shear term (dU/dz)^2+(dV/dz)^2 |
176 |
|
c tempU= .5 _d 0*( uVel(I,J,Km1,bi,bj)+uVel(I+1,J,Km1,bi,bj) |
177 |
|
c & -( uVel(I,J,K ,bi,bj)+uVel(I+1,J,K ,bi,bj)) ) |
178 |
|
c & *recip_drC(K) |
179 |
|
c tempV= .5 _d 0*( vVel(I,J,Km1,bi,bj)+vVel(I,J+1,Km1,bi,bj) |
180 |
|
c & -( vVel(I,J,K ,bi,bj)+vVel(I,J+1,K ,bi,bj)) ) |
181 |
|
c & *recip_drC(K) |
182 |
|
c verticalShear = tempU*tempU + tempV*tempV |
183 |
|
c RiNumber = MAX(Nsquare(i,j,k),0. _d 0)/(verticalShear+GGL90eps) |
184 |
|
cC compute Prandtl number (always greater than 0) |
185 |
|
c prTemp = 1. _d 0 |
186 |
|
c IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber |
187 |
|
c TKEPrandtlNumber(I,J,K) = MIN(10. _d 0,prTemp) |
188 |
|
C mixing length |
189 |
|
GGL90mixingLength(I,J,K) = SQRTTWO * |
190 |
|
& SQRTTKE(i,j,k)/SQRT( MAX(Nsquare(i,j,k),GGL90eps) ) |
191 |
|
ENDDO |
192 |
|
ENDDO |
193 |
|
ENDDO |
194 |
|
|
195 |
|
C- Impose upper and lower bound for mixing length |
196 |
|
IF ( mxlMaxFlag .EQ. 0 ) THEN |
197 |
|
C- |
198 |
|
DO k=2,Nr |
199 |
|
DO J=jMin,jMax |
200 |
|
DO I=iMin,iMax |
201 |
|
MaxLength=totalDepth(I,J) |
202 |
|
GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
203 |
|
& MaxLength) |
204 |
|
ENDDO |
205 |
|
ENDDO |
206 |
|
ENDDO |
207 |
|
|
208 |
|
DO k=2,Nr |
209 |
|
DO J=jMin,jMax |
210 |
|
DO I=iMin,iMax |
211 |
|
GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), |
212 |
|
& GGL90mixingLengthMin) |
213 |
|
rMixingLength(I,J,K) = 1. _d 0 / GGL90mixingLength(I,J,K) |
214 |
|
ENDDO |
215 |
|
ENDDO |
216 |
|
ENDDO |
217 |
|
|
218 |
|
ELSEIF ( mxlMaxFlag .EQ. 1 ) THEN |
219 |
|
C- |
220 |
|
DO k=2,Nr |
221 |
|
DO J=jMin,jMax |
222 |
|
DO I=iMin,iMax |
223 |
|
MaxLength=MIN(Ro_surf(I,J,bi,bj)-rF(k),rF(k)-R_low(I,J,bi,bj)) |
224 |
|
c MaxLength=MAX(MaxLength,20. _d 0) |
225 |
|
GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
226 |
|
& MaxLength) |
227 |
|
ENDDO |
228 |
|
ENDDO |
229 |
|
ENDDO |
230 |
|
|
231 |
|
DO k=2,Nr |
232 |
|
DO J=jMin,jMax |
233 |
|
DO I=iMin,iMax |
234 |
|
GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), |
235 |
|
& GGL90mixingLengthMin) |
236 |
|
rMixingLength(I,J,K) = 1. _d 0 / GGL90mixingLength(I,J,K) |
237 |
|
ENDDO |
238 |
|
ENDDO |
239 |
|
ENDDO |
240 |
|
|
241 |
|
ELSEIF ( mxlMaxFlag .EQ. 2 ) THEN |
242 |
|
C- |
243 |
|
DO k=2,Nr |
244 |
|
DO J=jMin,jMax |
245 |
|
DO I=iMin,iMax |
246 |
|
GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
247 |
|
& GGL90mixingLength(I,J,K-1)+drF(k-1)) |
248 |
|
ENDDO |
249 |
|
ENDDO |
250 |
|
ENDDO |
251 |
|
DO J=jMin,jMax |
252 |
|
DO I=iMin,iMax |
253 |
|
GGL90mixingLength(I,J,Nr) = MIN(GGL90mixingLength(I,J,Nr), |
254 |
|
& GGL90mixingLengthMin+drF(Nr)) |
255 |
|
ENDDO |
256 |
|
ENDDO |
257 |
|
DO k=Nr-1,2,-1 |
258 |
|
DO J=jMin,jMax |
259 |
|
DO I=iMin,iMax |
260 |
|
GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
261 |
|
& GGL90mixingLength(I,J,K+1)+drF(k)) |
262 |
|
ENDDO |
263 |
|
ENDDO |
264 |
|
ENDDO |
265 |
|
|
266 |
|
DO k=2,Nr |
267 |
|
DO J=jMin,jMax |
268 |
|
DO I=iMin,iMax |
269 |
|
GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), |
270 |
|
& GGL90mixingLengthMin) |
271 |
|
rMixingLength(I,J,K) = 1. _d 0 / GGL90mixingLength(I,J,K) |
272 |
|
ENDDO |
273 |
|
ENDDO |
274 |
|
ENDDO |
275 |
|
|
276 |
|
ELSEIF ( mxlMaxFlag .EQ. 3 ) THEN |
277 |
|
C- |
278 |
|
DO k=2,Nr |
279 |
|
DO J=jMin,jMax |
280 |
|
DO I=iMin,iMax |
281 |
|
mxLength_Dn(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
282 |
|
& mxLength_Dn(I,J,K-1)+drF(k-1)) |
283 |
|
ENDDO |
284 |
|
ENDDO |
285 |
|
ENDDO |
286 |
|
DO J=jMin,jMax |
287 |
|
DO I=iMin,iMax |
288 |
|
GGL90mixingLength(I,J,Nr) = MIN(GGL90mixingLength(I,J,Nr), |
289 |
|
& GGL90mixingLengthMin+drF(Nr)) |
290 |
|
ENDDO |
291 |
|
ENDDO |
292 |
|
DO k=Nr-1,2,-1 |
293 |
|
DO J=jMin,jMax |
294 |
|
DO I=iMin,iMax |
295 |
|
GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
296 |
|
& GGL90mixingLength(I,J,K+1)+drF(k)) |
297 |
|
ENDDO |
298 |
|
ENDDO |
299 |
|
ENDDO |
300 |
|
|
301 |
|
DO k=2,Nr |
302 |
|
DO J=jMin,jMax |
303 |
|
DO I=iMin,iMax |
304 |
|
GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
305 |
|
& mxLength_Dn(I,J,K)) |
306 |
|
tmpmlx = SQRT( GGL90mixingLength(I,J,K)*mxLength_Dn(I,J,K) ) |
307 |
|
tmpmlx = MAX( tmpmlx, GGL90mixingLengthMin) |
308 |
|
rMixingLength(I,J,K) = 1. _d 0 / tmpmlx |
309 |
|
ENDDO |
310 |
|
ENDDO |
311 |
|
ENDDO |
312 |
|
|
313 |
|
ELSE |
314 |
|
STOP 'GGL90_CALC: Wrong mxlMaxFlag (mixing length limit)' |
315 |
|
ENDIF |
316 |
|
|
317 |
|
C- Impose minimum mixing length (to avoid division by zero) |
318 |
|
c DO k=2,Nr |
319 |
|
c DO J=jMin,jMax |
320 |
|
c DO I=iMin,iMax |
321 |
|
c GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), |
322 |
|
c & GGL90mixingLengthMin) |
323 |
|
c rMixingLength(I,J,K) = 1. _d 0 /GGL90mixingLength(I,J,K) |
324 |
|
c ENDDO |
325 |
|
c ENDDO |
326 |
|
c ENDDO |
327 |
|
|
328 |
|
DO k=2,Nr |
329 |
|
Km1 = K-1 |
330 |
|
DO J=jMin,jMax |
331 |
|
DO I=iMin,iMax |
332 |
C vertical shear term (dU/dz)^2+(dV/dz)^2 |
C vertical shear term (dU/dz)^2+(dV/dz)^2 |
333 |
tempu= .5*( uVel(I,J,Km1,bi,bj)+uVel(I+1,J,Km1,bi,bj) |
tempU= .5 _d 0*( uVel(I,J,Km1,bi,bj)+uVel(I+1,J,Km1,bi,bj) |
334 |
& - (uVel(I,J,K ,bi,bj)+uVel(I+1,J,K ,bi,bj)) ) |
& -( uVel(I,J,K ,bi,bj)+uVel(I+1,J,K ,bi,bj)) ) |
335 |
& *recip_drC(K) |
& *recip_drC(K) |
336 |
tempv= .5*( vVel(I,J,Km1,bi,bj)+vVel(I,J+1,Km1,bi,bj) |
tempV= .5 _d 0*( vVel(I,J,Km1,bi,bj)+vVel(I,J+1,Km1,bi,bj) |
337 |
& - (vVel(I,J,K ,bi,bj)+vVel(I,J+1,K ,bi,bj)) ) |
& -( vVel(I,J,K ,bi,bj)+vVel(I,J+1,K ,bi,bj)) ) |
338 |
& *recip_drC(K) |
& *recip_drC(K) |
339 |
verticalShear = tempU*tempU + tempV*tempV |
verticalShear = tempU*tempU + tempV*tempV |
340 |
RiNumber = MAX(Nsquare,0. _d 0)/(verticalShear+GGL90eps) |
RiNumber = MAX(Nsquare(i,j,k),0. _d 0)/(verticalShear+GGL90eps) |
341 |
C compute Prandtl number (always greater than 0) |
C compute Prandtl number (always greater than 0) |
342 |
prTemp = 1. _d 0 |
prTemp = 1. _d 0 |
343 |
IF ( RiNumber .GE. 0.2 ) prTemp = 5.0 * RiNumber |
IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber |
344 |
TKEPrandtlNumber(I,J,K) = MIN(10.,prTemp) |
TKEPrandtlNumber(I,J,K) = MIN(10. _d 0,prTemp) |
345 |
C mixing length |
c TKEPrandtlNumber(I,J,K) = 1. _d 0 |
346 |
GGL90mixingLength(I,J,K) = |
|
347 |
& SQRTTKE/SQRT( MAX(Nsquare,GGL90eps) ) |
C viscosity and diffusivity |
348 |
C impose upper bound for mixing length (total depth) |
KappaM = GGL90ck*GGL90mixingLength(I,J,K)*SQRTTKE(i,j,k) |
349 |
GGL90mixingLength(I,J,K) = MIN(GGL90mixingLength(I,J,K), |
KappaH = KappaM/TKEPrandtlNumber(I,J,K) |
350 |
& totalDepth(I,J)) |
|
351 |
C impose minimum mixing length (to avoid division by zero) |
C Set a minium (= background) and maximum value |
352 |
GGL90mixingLength(I,J,K) = MAX(GGL90mixingLength(I,J,K), |
KappaM = MAX(KappaM,viscArNr(k)) |
353 |
& GGL90mixingLengthMin) |
KappaH = MAX(KappaH,diffKrNrT(k)) |
354 |
C viscosity of last timestep |
KappaM = MIN(KappaM,GGL90viscMax) |
355 |
KappaM = GGL90ck*GGL90mixingLength(I,J,K)*SQRTTKE |
KappaH = MIN(KappaH,GGL90diffMax) |
356 |
KappaE(I,J,K) = KappaM*GGL90alpha |
|
357 |
|
C Mask land points and storage |
358 |
|
GGL90viscAr(I,J,K,bi,bj) = KappaM * maskC(I,J,K,bi,bj) |
359 |
|
GGL90diffKr(I,J,K,bi,bj) = KappaH * maskC(I,J,K,bi,bj) |
360 |
|
KappaE(I,J,K) = GGL90alpha * GGL90viscAr(I,J,K,bi,bj) |
361 |
|
|
362 |
C dissipation term |
C dissipation term |
363 |
TKEdissipation = ab05*GGL90ceps |
TKEdissipation = ab05*GGL90ceps |
364 |
& *SQRTTKE/GGL90mixingLength(I,J,K) |
& *SQRTTKE(i,j,k)*rMixingLength(I,J,K) |
365 |
& *GGL90TKE(I,J,K,bi,bj) |
& *GGL90TKE(I,J,K,bi,bj) |
366 |
C sum up contributions to form the right hand side |
C sum up contributions to form the right hand side |
367 |
gTKE(I,J,K) = GGL90TKE(I,J,K,bi,bj) |
gTKE(I,J,K) = GGL90TKE(I,J,K,bi,bj) |
368 |
& + deltaTggl90*( |
& + deltaTggl90*( |
369 |
& + KappaM*verticalShear |
& + KappaM*verticalShear |
370 |
& - KappaM*Nsquare/TKEPrandtlNumber(I,J,K) |
& - KappaH*Nsquare(i,j,k) |
371 |
& - TKEdissipation |
& - TKEdissipation |
372 |
& ) |
& ) |
373 |
ENDDO |
ENDDO |
374 |
ENDDO |
ENDDO |
375 |
ENDDO |
ENDDO |
376 |
C |
|
377 |
C Implicit time step to update TKE for k=1,Nr; TKE(Nr+1)=0 by default |
C horizontal diffusion of TKE (requires an exchange in |
378 |
C |
C do_fields_blocking_exchanges) |
379 |
|
#ifdef ALLOW_GGL90_HORIZDIFF |
380 |
|
IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN |
381 |
|
DO K=2,Nr |
382 |
|
C common factors |
383 |
|
DO j=1-Oly,sNy+Oly |
384 |
|
DO i=1-Olx,sNx+Olx |
385 |
|
xA(i,j) = _dyG(i,j,bi,bj) |
386 |
|
& *drF(k)*_hFacW(i,j,k,bi,bj) |
387 |
|
yA(i,j) = _dxG(i,j,bi,bj) |
388 |
|
& *drF(k)*_hFacS(i,j,k,bi,bj) |
389 |
|
ENDDO |
390 |
|
ENDDO |
391 |
|
C Compute diffusive fluxes |
392 |
|
C ... across x-faces |
393 |
|
DO j=1-Oly,sNy+Oly |
394 |
|
dfx(1-Olx,j)=0. _d 0 |
395 |
|
DO i=1-Olx+1,sNx+Olx |
396 |
|
dfx(i,j) = -GGL90diffTKEh*xA(i,j) |
397 |
|
& *_recip_dxC(i,j,bi,bj) |
398 |
|
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i-1,j,k,bi,bj)) |
399 |
|
& *CosFacU(j,bi,bj) |
400 |
|
ENDDO |
401 |
|
ENDDO |
402 |
|
C ... across y-faces |
403 |
|
DO i=1-Olx,sNx+Olx |
404 |
|
dfy(i,1-Oly)=0. _d 0 |
405 |
|
ENDDO |
406 |
|
DO j=1-Oly+1,sNy+Oly |
407 |
|
DO i=1-Olx,sNx+Olx |
408 |
|
dfy(i,j) = -GGL90diffTKEh*yA(i,j) |
409 |
|
& *_recip_dyC(i,j,bi,bj) |
410 |
|
& *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i,j-1,k,bi,bj)) |
411 |
|
#ifdef ISOTROPIC_COS_SCALING |
412 |
|
& *CosFacV(j,bi,bj) |
413 |
|
#endif /* ISOTROPIC_COS_SCALING */ |
414 |
|
ENDDO |
415 |
|
ENDDO |
416 |
|
C Compute divergence of fluxes |
417 |
|
DO j=1-Oly,sNy+Oly-1 |
418 |
|
DO i=1-Olx,sNx+Olx-1 |
419 |
|
gTKE(i,j,k)=gTKE(i,j,k) |
420 |
|
& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)*recip_rA(i,j,bi,bj) |
421 |
|
& *( (dfx(i+1,j)-dfx(i,j)) |
422 |
|
& +(dfy(i,j+1)-dfy(i,j)) |
423 |
|
& )*deltaTggl90 |
424 |
|
ENDDO |
425 |
|
ENDDO |
426 |
|
C end of k-loop |
427 |
|
ENDDO |
428 |
|
C end if GGL90diffTKEh .eq. 0. |
429 |
|
ENDIF |
430 |
|
#endif /* ALLOW_GGL90_HORIZDIFF */ |
431 |
|
|
432 |
|
C ============================================ |
433 |
|
C Implicit time step to update TKE for k=1,Nr; |
434 |
|
C TKE(Nr+1)=0 by default |
435 |
|
C ============================================ |
436 |
C set up matrix |
C set up matrix |
437 |
C-- Old aLower |
C-- Lower diagonal |
438 |
DO j=jMin,jMax |
DO j=jMin,jMax |
439 |
DO i=iMin,iMax |
DO i=iMin,iMax |
440 |
a(i,j,1) = 0. _d 0 |
a(i,j,1) = 0. _d 0 |
441 |
ENDDO |
ENDDO |
442 |
ENDDO |
ENDDO |
443 |
DO k=2,Nr |
DO k=2,Nr |
444 |
km1=MAX(1,k-1) |
km1=MAX(2,k-1) |
445 |
DO j=jMin,jMax |
DO j=jMin,jMax |
446 |
DO i=iMin,iMax |
DO i=iMin,iMax |
447 |
|
C- We keep recip_hFacC in the diffusive flux calculation, |
448 |
|
C- but no hFacC in TKE volume control |
449 |
|
C- No need for maskC(k-1) with recip_hFacC(k-1) |
450 |
a(i,j,k) = -deltaTggl90 |
a(i,j,k) = -deltaTggl90 |
451 |
& *recip_drF(km1)*recip_hFacI(i,j,k,bi,bj) |
& *recip_drF(k-1)*recip_hFacC(i,j,k-1,bi,bj) |
452 |
& *.5*(KappaE(i,j, k )+KappaE(i,j,km1)) |
& *.5 _d 0*(KappaE(i,j, k )+KappaE(i,j,km1)) |
453 |
& *recip_drC(k) |
& *recip_drC(k)*maskC(i,j,k,bi,bj) |
|
IF (recip_hFacI(i,j,km1,bi,bj).EQ.0.) a(i,j,k)=0. |
|
454 |
ENDDO |
ENDDO |
455 |
ENDDO |
ENDDO |
456 |
ENDDO |
ENDDO |
457 |
|
C-- Upper diagonal |
|
C-- Old aUpper |
|
458 |
DO j=jMin,jMax |
DO j=jMin,jMax |
459 |
DO i=iMin,iMax |
DO i=iMin,iMax |
460 |
c(i,j,1) = 0. _d 0 |
c(i,j,1) = 0. _d 0 |
|
c(i,j,Nr) = 0. _d 0 |
|
461 |
ENDDO |
ENDDO |
462 |
ENDDO |
ENDDO |
|
CML DO k=1,Nr-1 |
|
463 |
DO k=2,Nr |
DO k=2,Nr |
|
kp1=min(Nr,k+1) |
|
464 |
DO j=jMin,jMax |
DO j=jMin,jMax |
465 |
DO i=iMin,iMax |
DO i=iMin,iMax |
466 |
|
kp1=MAX(1,MIN(klowC(i,j,bi,bj),k+1)) |
467 |
|
C- We keep recip_hFacC in the diffusive flux calculation, |
468 |
|
C- but no hFacC in TKE volume control |
469 |
|
C- No need for maskC(k) with recip_hFacC(k) |
470 |
c(i,j,k) = -deltaTggl90 |
c(i,j,k) = -deltaTggl90 |
471 |
& *recip_drF( k )*recip_hFacI(i,j,k,bi,bj) |
& *recip_drF( k ) * recip_hFacC(i,j,k,bi,bj) |
472 |
& *.5*(KappaE(i,j,k)+KappaE(i,j,kp1)) |
& *.5 _d 0*(KappaE(i,j,k)+KappaE(i,j,kp1)) |
473 |
& *recip_drC(k) |
& *recip_drC(k)*maskC(i,j,k-1,bi,bj) |
|
C IF (recip_hFacI(i,j,kp1,bi,bj).EQ.0.) c(i,j,k)=0. |
|
474 |
ENDDO |
ENDDO |
475 |
ENDDO |
ENDDO |
476 |
ENDDO |
ENDDO |
477 |
|
C-- Center diagonal |
|
C-- Old aCenter |
|
478 |
DO k=1,Nr |
DO k=1,Nr |
479 |
|
km1 = MAX(k-1,1) |
480 |
DO j=jMin,jMax |
DO j=jMin,jMax |
481 |
DO i=iMin,iMax |
DO i=iMin,iMax |
482 |
b(i,j,k) = 1. _d 0 - c(i,j,k) - a(i,j,k) |
b(i,j,k) = 1. _d 0 - c(i,j,k) - a(i,j,k) |
483 |
& + ab15*deltaTggl90*GGL90ceps*SQRT(GGL90TKE(I,J,K,bi,bj)) |
& + ab15*deltaTggl90*GGL90ceps*SQRTTKE(I,J,K) |
484 |
& /GGL90mixingLength(I,J,K) |
& * rMixingLength(I,J,K) |
485 |
|
& * maskC(i,j,k,bi,bj)*maskC(i,j,km1,bi,bj) |
486 |
ENDDO |
ENDDO |
487 |
ENDDO |
ENDDO |
488 |
ENDDO |
ENDDO |
489 |
C end set up matrix |
C end set up matrix |
490 |
|
|
|
C |
|
491 |
C Apply boundary condition |
C Apply boundary condition |
492 |
C |
kp1 = MIN(Nr,kSurf+1) |
493 |
DO J=jMin,jMax |
DO J=jMin,jMax |
494 |
DO I=iMin,iMax |
DO I=iMin,iMax |
495 |
C estimate friction velocity uStar from surface forcing |
C estimate friction velocity uStar from surface forcing |
496 |
uStarSquare = SQRT( |
uStarSquare = SQRT( |
497 |
& ( .5*( surfaceForcingU(I, J, bi,bj) |
& ( .5 _d 0*( surfaceForcingU(I, J, bi,bj) |
498 |
& + surfaceForcingU(I+1,J, bi,bj) ) )**2 |
& + surfaceForcingU(I+1,J, bi,bj) ) )**2 |
499 |
& + ( .5*( surfaceForcingV(I, J, bi,bj) |
& + ( .5 _d 0*( surfaceForcingV(I, J, bi,bj) |
500 |
& + surfaceForcingV(I, J+1,bi,bj) ) )**2 |
& + surfaceForcingV(I, J+1,bi,bj) ) )**2 |
501 |
& ) |
& ) |
502 |
C Dirichlet surface boundary condition for TKE |
C Dirichlet surface boundary condition for TKE |
503 |
gTKE(I,J,kSurf) = MAX(GGL90TKEmin,GGL90m2*uStarSquare) |
gTKE(I,J,kSurf) = MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare) |
504 |
& *maskC(I,J,kSurf,bi,bj) |
& *maskC(I,J,kSurf,bi,bj) |
505 |
|
gTKE(i,j,kp1) = gTKE(i,j,kp1) |
506 |
|
& - a(i,j,kp1)*gTKE(i,j,kSurf) |
507 |
|
a(i,j,kp1) = 0. _d 0 |
508 |
C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom |
C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom |
509 |
kBottom = MIN(MAX(kLowC(I,J,bi,bj),1),Nr) |
kBottom = MAX(kLowC(I,J,bi,bj),1) |
510 |
gTKE(I,J,kBottom) = gTKE(I,J,kBottom) |
gTKE(I,J,kBottom) = gTKE(I,J,kBottom) |
511 |
& - GGL90TKEbottom*c(I,J,kBottom) |
& - GGL90TKEbottom*c(I,J,kBottom) |
512 |
|
c(I,J,kBottom) = 0. _d 0 |
513 |
ENDDO |
ENDDO |
514 |
ENDDO |
ENDDO |
515 |
C |
|
516 |
C solve tri-diagonal system, and store solution on gTKE (previously rhs) |
C solve tri-diagonal system, and store solution on gTKE (previously rhs) |
517 |
C |
CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
518 |
CALL GGL90_SOLVE( bi, bj, iMin, iMax, jMin, jMax, |
I a, b, c, |
519 |
I a, b, c, |
U gTKE, |
520 |
U gTKE, |
O errCode, |
521 |
I myThid ) |
I bi, bj, myThid ) |
522 |
C |
c CALL GGL90_SOLVE( bi, bj, iMin, iMax, jMin, jMax, |
523 |
|
c I a, b, c, |
524 |
|
c U gTKE, |
525 |
|
c I myThid ) |
526 |
|
|
527 |
C now update TKE |
C now update TKE |
|
C |
|
528 |
DO K=1,Nr |
DO K=1,Nr |
529 |
DO J=jMin,jMax |
DO J=jMin,jMax |
530 |
DO I=iMin,iMax |
DO I=iMin,iMax |
531 |
C impose minimum TKE to avoid numerical undershoots below zero |
C impose minimum TKE to avoid numerical undershoots below zero |
532 |
GGL90TKE(I,J,K,bi,bj) = MAX( gTKE(I,J,K), GGL90TKEmin ) |
GGL90TKE(I,J,K,bi,bj) = MAX( gTKE(I,J,K), GGL90TKEmin ) |
533 |
& * maskC(I,J,K,bi,bj) |
& * maskC(I,J,K,bi,bj) |
|
C |
|
|
C end of time step |
|
|
C |
|
534 |
ENDDO |
ENDDO |
535 |
ENDDO |
ENDDO |
536 |
ENDDO |
ENDDO |
537 |
C |
|
538 |
C compute viscosity coefficients |
C end of time step |
539 |
C |
C =============================== |
540 |
DO K=2,Nr |
|
541 |
|
#ifdef ALLOW_GGL90_SMOOTH |
542 |
|
DO K=1,Nr |
543 |
DO J=jMin,jMax |
DO J=jMin,jMax |
544 |
DO I=iMin,iMax |
DO I=iMin,iMax |
545 |
C Eq. (11), (18) and (21) |
tmpdiffKrS= |
546 |
KappaM = GGL90ck*GGL90mixingLength(I,J,K)* |
& ( |
547 |
& SQRT( GGL90TKE(I,J,K,bi,bj) ) |
& p4 * GGL90viscAr(i ,j ,k,bi,bj) * mskCor(i ,j ,bi,bj) |
548 |
KappaH = KappaM/TKEPrandtlNumber(I,J,K) |
& +p8 *( GGL90viscAr(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) |
549 |
C Set a minium (= background) value |
& + GGL90viscAr(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) |
550 |
KappaM = MAX(KappaM,viscAr) |
& + GGL90viscAr(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) |
551 |
KappaH = MAX(KappaH,diffKrT) |
& + GGL90viscAr(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) |
552 |
C Set a maximum and mask land point |
& +p16*( GGL90viscAr(i+1,j+1,k,bi,bj) * mskCor(i+1,j+1,bi,bj) |
553 |
GGL90viscAr(I,J,K,bi,bj) = MIN(KappaM,GGL90viscMax) |
& + GGL90viscAr(i+1,j-1,k,bi,bj) * mskCor(i+1,j-1,bi,bj) |
554 |
& * maskC(I,J,K,bi,bj) |
& + GGL90viscAr(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) |
555 |
GGL90diffKr(I,J,K,bi,bj) = MIN(KappaH,GGL90diffMax) |
& + GGL90viscAr(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj)) |
556 |
& * maskC(I,J,K,bi,bj) |
& ) |
557 |
|
& /(p4 |
558 |
|
& +p8 *( maskC(i-1,j ,k,bi,bj) * mskCor(i-1,j ,bi,bj) |
559 |
|
& + maskC(i ,j-1,k,bi,bj) * mskCor(i ,j-1,bi,bj) |
560 |
|
& + maskC(i+1,j ,k,bi,bj) * mskCor(i+1,j ,bi,bj) |
561 |
|
& + maskC(i ,j+1,k,bi,bj) * mskCor(i ,j+1,bi,bj)) |
562 |
|
& +p16*( maskC(i+1,j+1,k,bi,bj) * mskCor(i+1,j+1,bi,bj) |
563 |
|
& + maskC(i+1,j-1,k,bi,bj) * mskCor(i+1,j-1,bi,bj) |
564 |
|
& + maskC(i-1,j+1,k,bi,bj) * mskCor(i-1,j+1,bi,bj) |
565 |
|
& + maskC(i-1,j-1,k,bi,bj) * mskCor(i-1,j-1,bi,bj)) |
566 |
|
& )*maskC(i,j,k,bi,bj)*mskCor(i,j,bi,bj) |
567 |
|
& /TKEPrandtlNumber(i,j,k) |
568 |
|
GGL90diffKrS(I,J,K,bi,bj)= MAX( tmpdiffKrS , diffKrNrT(k) ) |
569 |
ENDDO |
ENDDO |
570 |
ENDDO |
ENDDO |
571 |
C end third k-loop |
ENDDO |
572 |
ENDDO |
#endif |
573 |
|
|
574 |
|
#ifdef ALLOW_DIAGNOSTICS |
575 |
|
IF ( useDiagnostics ) THEN |
576 |
|
CALL DIAGNOSTICS_FILL( GGL90TKE ,'GGL90TKE', |
577 |
|
& 0,Nr, 1, bi, bj, myThid ) |
578 |
|
CALL DIAGNOSTICS_FILL( GGL90viscAr,'GGL90Ar ', |
579 |
|
& 0,Nr, 1, bi, bj, myThid ) |
580 |
|
CALL DIAGNOSTICS_FILL( GGL90diffKr,'GGL90Kr ', |
581 |
|
& 0,Nr, 1, bi, bj, myThid ) |
582 |
|
CALL DIAGNOSTICS_FILL( TKEPrandtlNumber ,'GGL90Prl', |
583 |
|
& 0,Nr, 2, bi, bj, myThid ) |
584 |
|
CALL DIAGNOSTICS_FILL( GGL90mixingLength,'GGL90Lmx', |
585 |
|
& 0,Nr, 2, bi, bj, myThid ) |
586 |
|
ENDIF |
587 |
|
#endif |
588 |
|
|
589 |
#endif /* ALLOW_GGL90 */ |
#endif /* ALLOW_GGL90 */ |
590 |
|
|
591 |
RETURN |
RETURN |
592 |
END |
END |
|
|
|