/[MITgcm]/manual/s_overview/text/manual.tex
ViewVC logotype

Diff of /manual/s_overview/text/manual.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.20 by jmc, Fri Oct 15 14:44:25 2004 UTC revision 1.21 by edhill, Sat Oct 16 03:40:12 2004 UTC
# Line 611  The boundary conditions at top and botto Line 611  The boundary conditions at top and botto
611  atmosphere)}  \label{eq:moving-bc-atmos}  atmosphere)}  \label{eq:moving-bc-atmos}
612  \end{eqnarray}  \end{eqnarray}
613    
614  Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt})  Then the (hydrostatic form of) equations
615  yields a consistent set of atmospheric equations which, for convenience, are written out in $p$  (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yields a consistent
616  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).  set of atmospheric equations which, for convenience, are written out
617    in $p$ coordinates in Appendix Atmosphere - see
618    eqs(\ref{eq:atmos-prime}).
619    
620  \subsection{Ocean}  \subsection{Ocean}
621    
# Line 1098  salinity ... ). Line 1100  salinity ... ).
1100    
1101  \subsection{Vector invariant form}  \subsection{Vector invariant form}
1102    
1103  For some purposes it is advantageous to write momentum advection in eq(\ref  For some purposes it is advantageous to write momentum advection in
1104  {eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the (so-called) `vector invariant' form:  eq(\ref {eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the
1105    (so-called) `vector invariant' form:
1106    
1107  \begin{equation}  \begin{equation}
1108  \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t}  \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t}
# Line 1239  _{o}(p_{o})=g~Z_{topo}$, defined: Line 1242  _{o}(p_{o})=g~Z_{topo}$, defined:
1242  The final form of the HPE's in p coordinates is then:  The final form of the HPE's in p coordinates is then:
1243  \begin{eqnarray}  \begin{eqnarray}
1244  \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}  \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}
1245  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \label{eq:atmos-prime} \\  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}}
1246    \label{eq:atmos-prime} \\
1247  \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\  \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\
1248  \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{  \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{
1249  \partial p} &=&0 \\  \partial p} &=&0 \\
# Line 1285  _{\theta ,p}\frac{DS}{Dt}+\left. \frac{\ Line 1289  _{\theta ,p}\frac{DS}{Dt}+\left. \frac{\
1289  _{\theta ,S}\frac{Dp}{Dt}  \label{EOSexpansion}  _{\theta ,S}\frac{Dp}{Dt}  \label{EOSexpansion}
1290  \end{equation}  \end{equation}
1291    
1292  Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is the  Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is
1293  reciprocal of the sound speed ($c_{s}$) squared. Substituting into \ref{eq-zns-cont} gives:  the reciprocal of the sound speed ($c_{s}$) squared. Substituting into
1294    \ref{eq-zns-cont} gives:
1295  \begin{equation}  \begin{equation}
1296  \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{  \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{
1297  v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}  v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}
Legend:
Removed from v.1.20  
changed lines
  Added in v.1.21
  ViewVC Help
Powered by ViewVC 1.1.22