/[MITgcm]/MITgcm/pkg/seaice/seaice_calc_strainrates.F
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revision 1.18 by jmc, Fri Oct 21 17:32:01 2011 UTC revision 1.23 by mlosch, Thu Jun 8 15:10:05 2017 UTC
# Line 7  C $Name$ Line 7  C $Name$
7  #else  #else
8  # define OBCS_UVICE_OLD  # define OBCS_UVICE_OLD
9  #endif  #endif
10    #ifdef ALLOW_AUTODIFF
11    # include "AUTODIFF_OPTIONS.h"
12    #endif
13    
14  CBOP  CBOP
15  C     !ROUTINE: SEAICE_CALC_STRAINRATES  C     !ROUTINE: SEAICE_CALC_STRAINRATES
# Line 33  C     === Global variables === Line 36  C     === Global variables ===
36  #include "EEPARAMS.h"  #include "EEPARAMS.h"
37  #include "PARAMS.h"  #include "PARAMS.h"
38  #include "GRID.h"  #include "GRID.h"
39    #include "SEAICE_SIZE.h"
40  #include "SEAICE_PARAMS.h"  #include "SEAICE_PARAMS.h"
41  #include "SEAICE.h"  #include "SEAICE.h"
42    
# Line 51  C     iStep  :: Sub-time-step number Line 55  C     iStep  :: Sub-time-step number
55  C     myTime :: Simulation time  C     myTime :: Simulation time
56  C     myIter :: Simulation timestep number  C     myIter :: Simulation timestep number
57  C     myThid :: My Thread Id. number  C     myThid :: My Thread Id. number
58        _RL uFld   (1-Olx:sNx+Olx,1-Oly:sNy+Oly,nSx,nSy)        _RL uFld   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
59        _RL vFld   (1-Olx:sNx+Olx,1-Oly:sNy+Oly,nSx,nSy)        _RL vFld   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
60        _RL e11Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)        _RL e11Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
61        _RL e22Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)        _RL e22Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
62        _RL e12Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)        _RL e12Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
# Line 71  C     i,j,bi,bj :: Loop counters Line 75  C     i,j,bi,bj :: Loop counters
75  C     hFacU, hFacV :: determine the no-slip boundary condition  C     hFacU, hFacV :: determine the no-slip boundary condition
76        INTEGER k        INTEGER k
77        _RS hFacU, hFacV, noSlipFac        _RS hFacU, hFacV, noSlipFac
78          _RL third
79          PARAMETER ( third = 0.333333333333333333333333333 _d 0 )
80  C     auxillary variables that help writing code that  C     auxillary variables that help writing code that
81  C     vectorizes even after TAFization  C     vectorizes even after TAFization
82        _RL dudx (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL dudx (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
# Line 83  C     vectorizes even after TAFization Line 89  C     vectorizes even after TAFization
89        k = 1        k = 1
90        noSlipFac = 0. _d 0        noSlipFac = 0. _d 0
91        IF ( SEAICE_no_slip ) noSlipFac = 1. _d 0        IF ( SEAICE_no_slip ) noSlipFac = 1. _d 0
92    C     in order repoduce results before fixing a bug in r1.20 comment out
93    C     the following line
94    CML      IF ( SEAICE_no_slip ) noSlipFac = 2. _d 0
95  C  C
96        DO bj=myByLo(myThid),myByHi(myThid)        DO bj=myByLo(myThid),myByHi(myThid)
97         DO bi=myBxLo(myThid),myBxHi(myThid)         DO bi=myBxLo(myThid),myBxHi(myThid)
98  C     abbreviations on C-points, need to do them in separate loops  C     abbreviations on C-points, need to do them in separate loops
99  C     for vectorization  C     for vectorization
100          DO j=1-Oly,sNy+Oly-1          DO j=1-OLy,sNy+OLy-1
101           DO i=1-Olx,sNx+Olx-1           DO i=1-OLx,sNx+OLx-1
102            dudx(i,j) = _recip_dxF(i,j,bi,bj) *            dudx(i,j) = _recip_dxF(i,j,bi,bj) *
103       &         (uFld(i+1,j,bi,bj)-uFld(i,j,bi,bj))       &         (uFld(i+1,j,bi,bj)-uFld(i,j,bi,bj))
104            uave(i,j) = 0.5 _d 0 * (uFld(i,j,bi,bj)+uFld(i+1,j,bi,bj))            uave(i,j) = 0.5 _d 0 * (uFld(i,j,bi,bj)+uFld(i+1,j,bi,bj))
105           ENDDO           ENDDO
106          ENDDO          ENDDO
107          DO j=1-Oly,sNy+Oly-1          DO j=1-OLy,sNy+OLy-1
108           DO i=1-Olx,sNx+Olx-1           DO i=1-OLx,sNx+OLx-1
109            dvdy(i,j) = _recip_dyF(i,j,bi,bj) *            dvdy(i,j) = _recip_dyF(i,j,bi,bj) *
110       &         (vFld(i,j+1,bi,bj)-vFld(i,j,bi,bj))       &         (vFld(i,j+1,bi,bj)-vFld(i,j,bi,bj))
111            vave(i,j) = 0.5 _d 0 * (vFld(i,j,bi,bj)+vFld(i,j+1,bi,bj))            vave(i,j) = 0.5 _d 0 * (vFld(i,j,bi,bj)+vFld(i,j+1,bi,bj))
112           ENDDO           ENDDO
113          ENDDO          ENDDO
114  C     evaluate strain rates at C-points  C     evaluate strain rates at C-points
115          DO j=1-Oly,sNy+Oly-1          DO j=1-OLy,sNy+OLy-1
116           DO i=1-Olx,sNx+Olx-1           DO i=1-OLx,sNx+OLx-1
117            e11Loc(i,j,bi,bj) = dudx(i,j) + vave(i,j) * k2AtC(i,j,bi,bj)            e11Loc(i,j,bi,bj) = dudx(i,j) + vave(i,j) * k2AtC(i,j,bi,bj)
118            e22Loc(i,j,bi,bj) = dvdy(i,j) + uave(i,j) * k1AtC(i,j,bi,bj)            e22Loc(i,j,bi,bj) = dvdy(i,j) + uave(i,j) * k1AtC(i,j,bi,bj)
119           ENDDO           ENDDO
120          ENDDO          ENDDO
121  #ifndef OBCS_UVICE_OLD  #ifndef OBCS_UVICE_OLD
122  C--     for OBCS: assume no gradient beyong OB  C--     for OBCS: assume no gradient beyong OB
123          DO j=1-Oly,sNy+Oly-1          DO j=1-OLy,sNy+OLy-1
124           DO i=1-Olx,sNx+Olx-1           DO i=1-OLx,sNx+OLx-1
125            e11Loc(i,j,bi,bj) = e11Loc(i,j,bi,bj)*maskInC(i,j,bi,bj)            e11Loc(i,j,bi,bj) = e11Loc(i,j,bi,bj)*maskInC(i,j,bi,bj)
126            e22Loc(i,j,bi,bj) = e22Loc(i,j,bi,bj)*maskInC(i,j,bi,bj)            e22Loc(i,j,bi,bj) = e22Loc(i,j,bi,bj)*maskInC(i,j,bi,bj)
127           ENDDO           ENDDO
# Line 121  C--     for OBCS: assume no gradient bey Line 130  C--     for OBCS: assume no gradient bey
130    
131  C     abbreviations at Z-points, need to do them in separate loops  C     abbreviations at Z-points, need to do them in separate loops
132  C     for vectorization  C     for vectorization
133          DO j=1-Oly+1,sNy+Oly          DO j=1-OLy+1,sNy+OLy
134           DO i=1-Olx+1,sNx+Olx           DO i=1-OLx+1,sNx+OLx
135            dudy(i,j) = ( uFld(i,j,bi,bj) - uFld(i  ,j-1,bi,bj) )            dudy(i,j) = ( uFld(i,j,bi,bj) - uFld(i  ,j-1,bi,bj) )
136       &         * _recip_dyU(i,j,bi,bj)       &         * _recip_dyU(i,j,bi,bj)
137            uave(i,j) = 0.5 _d 0 * (uFld(i,j,bi,bj)+uFld(i  ,j-1,bi,bj))            uave(i,j) = 0.5 _d 0 * (uFld(i,j,bi,bj)+uFld(i  ,j-1,bi,bj))
138           ENDDO           ENDDO
139          ENDDO          ENDDO
140          DO j=1-Oly+1,sNy+Oly          DO j=1-OLy+1,sNy+OLy
141           DO i=1-Olx+1,sNx+Olx           DO i=1-OLx+1,sNx+OLx
142            dvdx(i,j) = ( vFld(i,j,bi,bj) - vFld(i-1,j  ,bi,bj) )            dvdx(i,j) = ( vFld(i,j,bi,bj) - vFld(i-1,j  ,bi,bj) )
143       &         * _recip_dxV(i,j,bi,bj)       &         * _recip_dxV(i,j,bi,bj)
144            vave(i,j) = 0.5 _d 0 * (vFld(i,j,bi,bj)+vFld(i-1,j  ,bi,bj))            vave(i,j) = 0.5 _d 0 * (vFld(i,j,bi,bj)+vFld(i-1,j  ,bi,bj))
145           ENDDO           ENDDO
146          ENDDO          ENDDO
147  C     evaluate strain rates at Z-points  C     evaluate strain rates at Z-points
148          DO j=1-Oly+1,sNy+Oly          DO j=1-OLy+1,sNy+OLy
149           DO i=1-Olx+1,sNx+Olx           DO i=1-OLx+1,sNx+OLx
150            hFacU = _maskW(i,j,k,bi,bj) - _maskW(i,j-1,k,bi,bj)            hFacU = _maskW(i,j,k,bi,bj) - _maskW(i,j-1,k,bi,bj)
151            hFacV = _maskS(i,j,k,bi,bj) - _maskS(i-1,j,k,bi,bj)            hFacV = _maskS(i,j,k,bi,bj) - _maskS(i-1,j,k,bi,bj)
152            e12Loc(i,j,bi,bj) = 0.5 _d 0 * (            e12Loc(i,j,bi,bj) = 0.5 _d 0 * (
# Line 147  C     evaluate strain rates at Z-points Line 156  C     evaluate strain rates at Z-points
156       &         )       &         )
157       &         *maskC(i  ,j  ,k,bi,bj)*maskC(i-1,j  ,k,bi,bj)       &         *maskC(i  ,j  ,k,bi,bj)*maskC(i-1,j  ,k,bi,bj)
158       &         *maskC(i  ,j-1,k,bi,bj)*maskC(i-1,j-1,k,bi,bj)       &         *maskC(i  ,j-1,k,bi,bj)*maskC(i-1,j-1,k,bi,bj)
159       &         + 2.0 _d 0 * noSlipFac * (       &         + noSlipFac * (
160       &           2.0 _d 0 * uave(i,j) * _recip_dyU(i,j,bi,bj) * hFacU       &           2.0 _d 0 * uave(i,j) * _recip_dyU(i,j,bi,bj) * hFacU
161       &         + 2.0 _d 0 * vave(i,j) * _recip_dxV(i,j,bi,bj) * hFacV       &         + 2.0 _d 0 * vave(i,j) * _recip_dxV(i,j,bi,bj) * hFacV
162       &         )       &         )
# Line 158  c$$$     &         - hFacV * k1AtZ(i,j,b Line 167  c$$$     &         - hFacV * k1AtZ(i,j,b
167  c$$$     &         - hFacU * k2AtZ(i,j,bi,bj) * uave(i,j)  c$$$     &         - hFacU * k2AtZ(i,j,bi,bj) * uave(i,j)
168           ENDDO           ENDDO
169          ENDDO          ENDDO
170            IF ( SEAICE_no_slip .AND. SEAICE_2ndOrderBC ) THEN
171             DO j=1-OLy+2,sNy+OLy-1
172              DO i=1-OLx+2,sNx+OLx-1
173               hFacU = (_maskW(i,j,k,bi,bj) - _maskW(i,j-1,k,bi,bj))*third
174               hFacV = (_maskS(i,j,k,bi,bj) - _maskS(i-1,j,k,bi,bj))*third
175               hFacU = hFacU*( _maskW(i,j-2,k,bi,bj)*_maskW(i,j-1,k,bi,bj)
176         &                   + _maskW(i,j+1,k,bi,bj)*_maskW(i,j,  k,bi,bj) )
177               hFacV = hFacV*( _maskS(i-2,j,k,bi,bj)*_maskS(i-1,j,k,bi,bj)
178         &                   + _maskS(i+1,j,k,bi,bj)*_maskS(i  ,j,k,bi,bj) )
179    C     right hand sided dv/dx = (9*v(i,j)-v(i+1,j))/(4*dxv(i,j)-dxv(i+1,j))
180    C     according to a Taylor expansion to 2nd order. We assume that dxv
181    C     varies very slowly, so that the denominator simplifies to 3*dxv(i,j),
182    C     then dv/dx = (6*v(i,j)+3*v(i,j)-v(i+1,j))/(3*dxv(i,j))
183    C                = 2*v(i,j)/dxv(i,j) + (3*v(i,j)-v(i+1,j))/(3*dxv(i,j))
184    C     the left hand sided dv/dx is analogously
185    C                = - 2*v(i-1,j)/dxv(i,j) - (3*v(i-1,j)-v(i-2,j))/(3*dxv(i,j))
186    C     the first term is the first order part, which is already added.
187    C     For e12 we only need 0.5 of this gradient and vave = is either
188    C     0.5*v(i,j) or 0.5*v(i-1,j) near the boundary so that we need an
189    C     extra factor of 2. This explains the six. du/dy is analogous.
190    C     The masking is ugly, but hopefully effective.
191               e12Loc(i,j,bi,bj) = e12Loc(i,j,bi,bj) + 0.5 _d 0 * (
192         &            _recip_dyU(i,j,bi,bj) * ( 6.0 _d 0 * uave(i,j)
193         &          - uFld(i,j-2,bi,bj)*_maskW(i,j-1,k,bi,bj)
194         &          - uFld(i,j+1,bi,bj)*_maskW(i,j  ,k,bi,bj) ) * hFacU
195         &          + _recip_dxV(i,j,bi,bj) * ( 6.0 _d 0 * vave(i,j)
196         &          - vFld(i-2,j,bi,bj)*_maskS(i-1,j,k,bi,bj)
197         &          - vFld(i+1,j,bi,bj)*_maskS(i  ,j,k,bi,bj) ) * hFacV
198         &          )
199              ENDDO
200             ENDDO
201            ENDIF
202         ENDDO         ENDDO
203        ENDDO        ENDDO
204    
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