| 409 |
\input{part1/vertcoord_figure.tex} |
\input{part1/vertcoord_figure.tex} |
| 410 |
%%CNHend |
%%CNHend |
| 411 |
|
|
| 412 |
\begin{equation*} |
\begin{equation} |
| 413 |
\frac{D\vec{\mathbf{v}_{h}}}{Dt}+\left( 2\vec{\Omega}\times \vec{\mathbf{v}} |
\frac{D\vec{\mathbf{v}_{h}}}{Dt}+\left( 2\vec{\Omega}\times \vec{\mathbf{v}} |
| 414 |
\right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}} |
\right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}} |
| 415 |
\text{ horizontal mtm} \label{eq:horizontal_mtm} |
\text{ horizontal mtm} \label{eq:horizontal_mtm} |
| 416 |
\end{equation*} |
\end{equation} |
| 417 |
|
|
| 418 |
\begin{equation} |
\begin{equation} |
| 419 |
\frac{D\dot{r}}{Dt}+\widehat{k}\cdot \left( 2\vec{\Omega}\times \vec{\mathbf{ |
\frac{D\dot{r}}{Dt}+\widehat{k}\cdot \left( 2\vec{\Omega}\times \vec{\mathbf{ |
| 666 |
\phi (x,y,r)=\phi _{s}(x,y)+\phi _{hyd}(x,y,r)+\phi _{nh}(x,y,r) |
\phi (x,y,r)=\phi _{s}(x,y)+\phi _{hyd}(x,y,r)+\phi _{nh}(x,y,r) |
| 667 |
\label{eq:phi-split} |
\label{eq:phi-split} |
| 668 |
\end{equation} |
\end{equation} |
| 669 |
and write eq(\ref{eq:incompressible}) in the form: |
%and write eq(\ref{eq:incompressible}) in the form: |
| 670 |
|
% ^- this eq is missing (jmc) ; replaced with: |
| 671 |
|
and write eq( \ref{eq:horizontal_mtm}) in the form: |
| 672 |
|
|
| 673 |
\begin{equation} |
\begin{equation} |
| 674 |
\frac{\partial \vec{\mathbf{v}_{h}}}{\partial t}+\mathbf{\nabla }_{h}\phi |
\frac{\partial \vec{\mathbf{v}_{h}}}{\partial t}+\mathbf{\nabla }_{h}\phi |
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