/[MITgcm]/manual/s_algorithm/text/mom_vecinv.tex
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revision 1.3 by adcroft, Tue Nov 13 15:20:12 2001 UTC revision 1.7 by jmc, Mon Aug 30 23:09:18 2010 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Vector invariant momentum equations}  \section{Vector invariant momentum equations}
5    \label{sec:vect-inv_momentum_equations}
6    \begin{rawhtml}
7    <!-- CMIREDIR:vector_invariant_momentum_eqautions: -->
8    \end{rawhtml}
9    
10  The finite volume method lends itself to describing the continuity and  The finite volume method lends itself to describing the continuity and
11  tracer equations in curvilinear coordinate systems. However, in  tracer equations in curvilinear coordinate systems. However, in
# Line 44  G_w & = & G_w^{fu} + G_w^{\zeta_1 v} + G Line 48  G_w & = & G_w^{fu} + G_w^{\zeta_1 v} + G
48  \end{eqnarray}  \end{eqnarray}
49    
50  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
51  {\em S/R CALC\_MOM\_RHS} ({\em pkg/mom\_vecinv/calc\_mom\_rhs.F})  {\em S/R MOM\_VECINV} ({\em pkg/mom\_vecinv/mom\_vecinv.F})
52    
53  $G_u$: {\bf Gu} ({\em DYNVARS.h})  $G_u$: {\bf Gu} ({\em DYNVARS.h})
54    
# Line 71  the vertical and $\Gamma$ is the circula Line 75  the vertical and $\Gamma$ is the circula
75  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
76  {\em S/R MOM\_VI\_CALC\_RELVORT3} ({\em mom\_vi\_calc\_relvort3.F})  {\em S/R MOM\_VI\_CALC\_RELVORT3} ({\em mom\_vi\_calc\_relvort3.F})
77    
78  $\zeta_3$: {\bf vort3} (local to {\em calc\_mom\_rhs.F})  $\zeta_3$: {\bf vort3} (local to {\em mom\_vecinv.F})
79  \end{minipage} }  \end{minipage} }
80    
81    
# Line 86  KE = \frac{1}{2} ( \overline{ u^2 }^i + Line 90  KE = \frac{1}{2} ( \overline{ u^2 }^i +
90  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
91  {\em S/R MOM\_VI\_CALC\_KE} ({\em mom\_vi\_calc\_ke.F})  {\em S/R MOM\_VI\_CALC\_KE} ({\em mom\_vi\_calc\_ke.F})
92    
93  $KE$: {\bf KE} (local to {\em calc\_mom\_rhs.F})  $KE$: {\bf KE} (local to {\em mom\_vecinv.F})
94  \end{minipage} }  \end{minipage} }
95    
96    
# Line 146  available only through commented subrout Line 150  available only through commented subrout
150    
151  {\em S/R MOM\_VI\_V\_CORIOLIS} ({\em mom\_vi\_v\_coriolis.F})  {\em S/R MOM\_VI\_V\_CORIOLIS} ({\em mom\_vi\_v\_coriolis.F})
152    
153  $G_u^{fv}$, $G_u^{\zeta_3 v}$: {\bf uCf} (local to {\em calc\_mom\_rhs.F})  $G_u^{fv}$, $G_u^{\zeta_3 v}$: {\bf uCf} (local to {\em mom\_vecinv.F})
154    
155  $G_v^{fu}$, $G_v^{\zeta_3 u}$: {\bf vCf} (local to {\em calc\_mom\_rhs.F})  $G_v^{fu}$, $G_v^{\zeta_3 u}$: {\bf vCf} (local to {\em mom\_vecinv.F})
156  \end{minipage} }  \end{minipage} }
157    
158    
# Line 175  G_v^{\zeta_1 w} & = & Line 179  G_v^{\zeta_1 w} & = &
179    
180  {\em S/R MOM\_VI\_V\_VERTSHEAR} ({\em mom\_vi\_v\_vertshear.F})  {\em S/R MOM\_VI\_V\_VERTSHEAR} ({\em mom\_vi\_v\_vertshear.F})
181    
182  $G_u^{\zeta_2 w}$: {\bf uCf} (local to {\em calc\_mom\_rhs.F})  $G_u^{\zeta_2 w}$: {\bf uCf} (local to {\em mom\_vecinv.F})
183    
184  $G_v^{\zeta_1 w}$: {\bf vCf} (local to {\em calc\_mom\_rhs.F})  $G_v^{\zeta_1 w}$: {\bf vCf} (local to {\em mom\_vecinv.F})
185  \end{minipage} }  \end{minipage} }
186    
187    
# Line 198  G_v^{\partial_y B} & = & Line 202  G_v^{\partial_y B} & = &
202    
203  {\em S/R MOM\_VI\_V\_GRAD\_KE} ({\em mom\_vi\_v\_grad\_ke.F})  {\em S/R MOM\_VI\_V\_GRAD\_KE} ({\em mom\_vi\_v\_grad\_ke.F})
204    
205  $G_u^{\partial_x KE}$: {\bf uCf} (local to {\em calc\_mom\_rhs.F})  $G_u^{\partial_x KE}$: {\bf uCf} (local to {\em mom\_vecinv.F})
206    
207  $G_v^{\partial_y KE}$: {\bf vCf} (local to {\em calc\_mom\_rhs.F})  $G_v^{\partial_y KE}$: {\bf vCf} (local to {\em mom\_vecinv.F})
208  \end{minipage} }  \end{minipage} }
209    
210    
211    
212  \subsection{Horizontal dissipation}  \subsection{Horizontal divergence}
213    
214  The horizontal divergence, a complimentary quantity to relative  The horizontal divergence, a complimentary quantity to relative
215  vorticity, is used in parameterizing the Reynolds stresses and is  vorticity, is used in parameterizing the Reynolds stresses and is
# Line 219  D = \frac{1}{{\cal A}_c h_c} ( Line 223  D = \frac{1}{{\cal A}_c h_c} (
223  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
224  {\em S/R MOM\_VI\_CALC\_HDIV} ({\em mom\_vi\_calc\_hdiv.F})  {\em S/R MOM\_VI\_CALC\_HDIV} ({\em mom\_vi\_calc\_hdiv.F})
225    
226  $D$: {\bf hDiv} (local to {\em calc\_mom\_rhs.F})  $D$: {\bf hDiv} (local to {\em mom\_vecinv.F})
227  \end{minipage} }  \end{minipage} }
228    
229    
# Line 250  D^* & = & \frac{1}{{\cal A}_c h_c} ( Line 254  D^* & = & \frac{1}{{\cal A}_c h_c} (
254  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
255  {\em S/R MOM\_VI\_HDISSIP} ({\em mom\_vi\_hdissip.F})  {\em S/R MOM\_VI\_HDISSIP} ({\em mom\_vi\_hdissip.F})
256    
257  $G_u^{h-dissip}$: {\bf uDiss} (local to {\em calc\_mom\_rhs.F})  $G_u^{h-dissip}$: {\bf uDiss} (local to {\em mom\_vecinv.F})
258    
259  $G_v^{h-dissip}$: {\bf vDiss} (local to {\em calc\_mom\_rhs.F})  $G_v^{h-dissip}$: {\bf vDiss} (local to {\em mom\_vecinv.F})
260  \end{minipage} }  \end{minipage} }
261    
262    
# Line 278  In the interior the vertical stresses ar Line 282  In the interior the vertical stresses ar
282    
283  {\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F})  {\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F})
284    
285  $\tau_{13}$: {\bf urf} (local to {\em calc\_mom\_rhs.F})  $\tau_{13}$: {\bf urf} (local to {\em mom\_vecinv.F})
286    
287  $\tau_{23}$: {\bf vrf} (local to {\em calc\_mom\_rhs.F})  $\tau_{23}$: {\bf vrf} (local to {\em mom\_vecinv.F})
288  \end{minipage} }  \end{minipage} }
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