| 43 |
everywhere else. This term is therefore referred to as the surface |
everywhere else. This term is therefore referred to as the surface |
| 44 |
correction term. Global conservation is not possible using the |
correction term. Global conservation is not possible using the |
| 45 |
flux-form (as here) and a linearized free-surface |
flux-form (as here) and a linearized free-surface |
| 46 |
(\cite{Griffies00,Campin02}). |
(\cite{griffies:00,campin:02}). |
| 47 |
|
|
| 48 |
The continuity equation can be recovered by setting |
The continuity equation can be recovered by setting |
| 49 |
$G_{diff}=G_{forc}=0$ and $\tau=1$. |
$G_{diff}=G_{forc}=0$ and $\tau=1$. |
| 200 |
|
|
| 201 |
For non-divergent flow, this discretization can be shown to conserve |
For non-divergent flow, this discretization can be shown to conserve |
| 202 |
the tracer both locally and globally and to globally conserve tracer |
the tracer both locally and globally and to globally conserve tracer |
| 203 |
variance, $\tau^2$. The proof is given in \cite{Adcroft95,Adcroft97}. |
variance, $\tau^2$. The proof is given in \cite{adcroft:95,adcroft:97}. |
| 204 |
|
|
| 205 |
\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
| 206 |
{\em S/R GAD\_C2\_ADV\_X} ({\em gad\_c2\_adv\_x.F}) |
{\em S/R GAD\_C2\_ADV\_X} ({\em gad\_c2\_adv\_x.F}) |
| 387 |
r = \frac{ \tau_{i+1} - \tau_{i} }{ \tau_{i} - \tau_{i-1} } & \forall & u < 0 |
r = \frac{ \tau_{i+1} - \tau_{i} }{ \tau_{i} - \tau_{i-1} } & \forall & u < 0 |
| 388 |
\end{eqnarray} |
\end{eqnarray} |
| 389 |
as it's argument. There are many choices of limiter function but we |
as it's argument. There are many choices of limiter function but we |
| 390 |
only provide the Superbee limiter \cite{Roe85}: |
only provide the Superbee limiter \cite{roe:85}: |
| 391 |
\begin{equation} |
\begin{equation} |
| 392 |
\psi(r) = \max[0,\min[1,2r],\min[2,r]] |
\psi(r) = \max[0,\min[1,2r],\min[2,r]] |
| 393 |
\end{equation} |
\end{equation} |
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