/[MITgcm]/manual/s_overview/text/manual.tex
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revision 1.29 by jmc, Mon Aug 30 23:09:21 2010 UTC revision 1.30 by jmc, Wed May 11 18:45:43 2016 UTC
# Line 34  Line 34 
34    
35  % Section: Overview  % Section: Overview
36    
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37  This document provides the reader with the information necessary to  This document provides the reader with the information necessary to
38  carry out numerical experiments using MITgcm. It gives a comprehensive  carry out numerical experiments using MITgcm. It gives a comprehensive
39  description of the continuous equations on which the model is based, the  description of the continuous equations on which the model is based, the
# Line 139  J. Geophysical Res., 104(C12), 29,529-29 Line 136  J. Geophysical Res., 104(C12), 29,529-29
136  We begin by briefly showing some of the results of the model in action to  We begin by briefly showing some of the results of the model in action to
137  give a feel for the wide range of problems that can be addressed using it.  give a feel for the wide range of problems that can be addressed using it.
138    
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139  \section{Illustrations of the model in action}  \section{Illustrations of the model in action}
140    
141  MITgcm has been designed and used to model a wide range of phenomena,  MITgcm has been designed and used to model a wide range of phenomena,
# Line 376  stratification of the ACC. Line 370  stratification of the ACC.
370  \input{s_overview/text/lab_figure}  \input{s_overview/text/lab_figure}
371  %%CNHend  %%CNHend
372    
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373  \section{Continuous equations in `r' coordinates}  \section{Continuous equations in `r' coordinates}
374  \begin{rawhtml}  \begin{rawhtml}
375  <!-- CMIREDIR:z-p_isomorphism: -->  <!-- CMIREDIR:z-p_isomorphism: -->
# Line 1129  to discretize the model. Line 1120  to discretize the model.
1120  Tangent linear and adjoint counterparts of the forward model are described  Tangent linear and adjoint counterparts of the forward model are described
1121  in Chapter 5.  in Chapter 5.
1122    
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1123  \section{Appendix ATMOSPHERE}  \section{Appendix ATMOSPHERE}
1124    
1125  \subsection{Hydrostatic Primitive Equations for the Atmosphere in pressure  \subsection{Hydrostatic Primitive Equations for the Atmosphere in pressure
# Line 1151  p\alpha &=&RT  \label{eq:atmos-eos} \\ Line 1139  p\alpha &=&RT  \label{eq:atmos-eos} \\
1139  c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q}  \label{eq:atmos-heat}  c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q}  \label{eq:atmos-heat}
1140  \end{eqnarray}  \end{eqnarray}
1141  where $\vec{\mathbf{v}}_{h}=(u,v,0)$ is the `horizontal' (on pressure  where $\vec{\mathbf{v}}_{h}=(u,v,0)$ is the `horizontal' (on pressure
1142  surfaces) component of velocity,$\frac{D}{Dt}=\vec{\mathbf{v}}_{h}\cdot  surfaces) component of velocity, $\frac{D}{Dt}=\frac{\partial}{\partial t}
1143  \mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$ is the total  +\vec{\mathbf{v}}_{h}\cdot \mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$
1144  derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter, $\phi =gz$ is  is the total derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter,
1145  the geopotential, $\alpha =1/\rho $ is the specific volume, $\omega =\frac{Dp  $\phi =gz$ is the geopotential, $\alpha =1/\rho $ is the specific volume,
1146  }{Dt}$ is the vertical velocity in the $p-$coordinate. Equation(\ref  $\omega =\frac{Dp }{Dt}$ is the vertical velocity in the $p-$coordinate.
1147  {eq:atmos-heat}) is the first law of thermodynamics where internal energy $  Equation(\ref {eq:atmos-heat}) is the first law of thermodynamics where internal
1148  e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass and $  energy $e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass
1149  p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing.  and $p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing.
1150    
1151  It is convenient to cast the heat equation in terms of potential temperature  It is convenient to cast the heat equation in terms of potential temperature
1152  $\theta $ so that it looks more like a generic conservation law.  $\theta $ so that it looks more like a generic conservation law.
# Line 1258  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } Line 1246  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime }
1246  \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi }  \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi }
1247  \end{eqnarray}  \end{eqnarray}
1248    
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1249  \section{Appendix OCEAN}  \section{Appendix OCEAN}
1250    
1251  \subsection{Equations of motion for the ocean}  \subsection{Equations of motion for the ocean}
# Line 1475  the perturbation density. Nevertheless, Line 1460  the perturbation density. Nevertheless,
1460  _{nh}=0$ form of these equations that are used throughout the ocean modeling  _{nh}=0$ form of these equations that are used throughout the ocean modeling
1461  community and referred to as the primitive equations (HPE).  community and referred to as the primitive equations (HPE).
1462    
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1463  \section{Appendix:OPERATORS}  \section{Appendix:OPERATORS}
1464    
1465  \subsection{Coordinate systems}  \subsection{Coordinate systems}
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