| 194 |
|
|
| 195 |
For the non-hydrostatic equations, dropping the thin-atmosphere |
For the non-hydrostatic equations, dropping the thin-atmosphere |
| 196 |
approximation re-introduces metric terms involving $w$ and are |
approximation re-introduces metric terms involving $w$ and are |
| 197 |
required to conserve anglular momentum: |
required to conserve angular momentum: |
| 198 |
\begin{eqnarray} |
\begin{eqnarray} |
| 199 |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
| 200 |
- \overline{ \frac{ \overline{u}^i \overline{w}^k }{a} {\cal A}_c \Delta r_f h_c }^i \\ |
- \overline{ \frac{ \overline{u}^i \overline{w}^k }{a} {\cal A}_c \Delta r_f h_c }^i \\ |
| 258 |
``lat-lon'' grid for Laplacian viscosity. |
``lat-lon'' grid for Laplacian viscosity. |
| 259 |
\marginpar{Need to tidy up method for controlling this in code} |
\marginpar{Need to tidy up method for controlling this in code} |
| 260 |
|
|
| 261 |
It should be noted that dispite the ad-hoc nature of the scaling, some |
It should be noted that despite the ad-hoc nature of the scaling, some |
| 262 |
scaling must be done since on a lat-lon grid the converging meridians |
scaling must be done since on a lat-lon grid the converging meridians |
| 263 |
make it very unlikely that a stable viscosity parameter exists across |
make it very unlikely that a stable viscosity parameter exists across |
| 264 |
the entire model domain. |
the entire model domain. |
| 308 |
|
|
| 309 |
In fact, the above discretization is not quite complete because it |
In fact, the above discretization is not quite complete because it |
| 310 |
assumes that the bathymetry at velocity points is deeper than at |
assumes that the bathymetry at velocity points is deeper than at |
| 311 |
neighbouring vorticity points, e.g. $1-h_w < 1-h_\zeta$ |
neighboring vorticity points, e.g. $1-h_w < 1-h_\zeta$ |
| 312 |
|
|
| 313 |
\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
| 314 |
{\em S/R MOM\_U\_SIDEDRAG} ({\em mom\_u\_sidedrag.F}) |
{\em S/R MOM\_U\_SIDEDRAG} ({\em mom\_u\_sidedrag.F}) |
| 325 |
to the variable grid lengths introduced by the finite volume |
to the variable grid lengths introduced by the finite volume |
| 326 |
formulation. This reduces the formal accuracy of these terms to just |
formulation. This reduces the formal accuracy of these terms to just |
| 327 |
first order but only next to boundaries; exactly where other terms |
first order but only next to boundaries; exactly where other terms |
| 328 |
appear such as linar and quadratic bottom drag. |
appear such as linear and quadratic bottom drag. |
| 329 |
\begin{eqnarray} |
\begin{eqnarray} |
| 330 |
G_u^{v-diss} & = & |
G_u^{v-diss} & = & |
| 331 |
\frac{1}{\Delta r_f h_w} \delta_k \tau_{13} \\ |
\frac{1}{\Delta r_f h_w} \delta_k \tau_{13} \\ |
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