| 201 |
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| 202 |
The boundary conditions at top and bottom are given by: |
The boundary conditions at top and bottom are given by: |
| 203 |
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| 204 |
\begin{eqnarray*} |
\begin{eqnarray} |
| 205 |
&&\omega =0~\text{at }r=R_{fixed} \label{eq:fixed-bc-atmos} |
&&\omega =0~\text{at }r=R_{fixed} \label{eq:fixed-bc-atmos} |
| 206 |
\text{ (top of the atmosphere)} \\ |
\text{ (top of the atmosphere)} \\ |
| 207 |
\omega &=&\frac{Dp_{s}}{Dt}\text{; at }r=R_{moving}\text{ (bottom of the |
\omega &=&\frac{Dp_{s}}{Dt}\text{; at }r=R_{moving}\text{ (bottom of the |
| 208 |
atmosphere)} |
atmosphere)} |
| 209 |
\label{eq:moving-bc-atmos} |
\label{eq:moving-bc-atmos} |
| 210 |
\end{eqnarray*} |
\end{eqnarray} |
| 211 |
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| 212 |
Then the (hydrostatic form of) eq(\ref{incompressible}) yields a consistent |
Then the (hydrostatic form of) eq(\ref{incompressible}) yields a consistent |
| 213 |
set of atmospheric equations which, for convenience, are written out in $p$ |
set of atmospheric equations which, for convenience, are written out in $p$ |
| 242 |
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| 243 |
Boundary conditions are: |
Boundary conditions are: |
| 244 |
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| 245 |
\begin{eqnarray*} |
\begin{eqnarray} |
| 246 |
w &=&0~\text{at }r=R_{fixed}\text{ (ocean bottom)} |
w &=&0~\text{at }r=R_{fixed}\text{ (ocean bottom)} |
| 247 |
\label{eq:fixed-bc-ocean}\\ |
\label{eq:fixed-bc-ocean}\\ |
| 248 |
w &=&\frac{D\eta }{Dt}\text{ at }r=R_{moving}=\eta \text{ (ocean surface) |
w &=&\frac{D\eta }{Dt}\text{ at }r=R_{moving}=\eta \text{ (ocean surface) |
| 249 |
\label{eq:moving-bc-ocean}} |
\label{eq:moving-bc-ocean}} |
| 250 |
\end{eqnarray*} |
\end{eqnarray} |
| 251 |
where $\eta $ is the elevation of the free surface. |
where $\eta $ is the elevation of the free surface. |
| 252 |
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| 253 |
Then eq(\ref{incompressible}) yields a consistent set of oceanic equations |
Then eq(\ref{incompressible}) yields a consistent set of oceanic equations |
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