--- manual/s_overview/text/manual.tex 2010/08/30 23:09:21 1.29 +++ manual/s_overview/text/manual.tex 2016/05/11 18:45:43 1.30 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.29 2010/08/30 23:09:21 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.30 2016/05/11 18:45:43 jmc Exp $ % $Name: $ %tci%\documentclass[12pt]{book} @@ -34,9 +34,6 @@ % Section: Overview -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.29 2010/08/30 23:09:21 jmc Exp $ -% $Name: $ - This document provides the reader with the information necessary to carry out numerical experiments using MITgcm. It gives a comprehensive description of the continuous equations on which the model is based, the @@ -139,9 +136,6 @@ We begin by briefly showing some of the results of the model in action to give a feel for the wide range of problems that can be addressed using it. -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.29 2010/08/30 23:09:21 jmc Exp $ -% $Name: $ - \section{Illustrations of the model in action} MITgcm has been designed and used to model a wide range of phenomena, @@ -376,9 +370,6 @@ \input{s_overview/text/lab_figure} %%CNHend -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.29 2010/08/30 23:09:21 jmc Exp $ -% $Name: $ - \section{Continuous equations in `r' coordinates} \begin{rawhtml} @@ -1129,9 +1120,6 @@ Tangent linear and adjoint counterparts of the forward model are described in Chapter 5. -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.29 2010/08/30 23:09:21 jmc Exp $ -% $Name: $ - \section{Appendix ATMOSPHERE} \subsection{Hydrostatic Primitive Equations for the Atmosphere in pressure @@ -1151,14 +1139,14 @@ c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q} \label{eq:atmos-heat} \end{eqnarray} where $\vec{\mathbf{v}}_{h}=(u,v,0)$ is the `horizontal' (on pressure -surfaces) component of velocity,$\frac{D}{Dt}=\vec{\mathbf{v}}_{h}\cdot -\mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$ is the total -derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter, $\phi =gz$ is -the geopotential, $\alpha =1/\rho $ is the specific volume, $\omega =\frac{Dp -}{Dt}$ is the vertical velocity in the $p-$coordinate. Equation(\ref -{eq:atmos-heat}) is the first law of thermodynamics where internal energy $ -e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass and $ -p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing. +surfaces) component of velocity, $\frac{D}{Dt}=\frac{\partial}{\partial t} ++\vec{\mathbf{v}}_{h}\cdot \mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$ +is the total derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter, +$\phi =gz$ is the geopotential, $\alpha =1/\rho $ is the specific volume, +$\omega =\frac{Dp }{Dt}$ is the vertical velocity in the $p-$coordinate. +Equation(\ref {eq:atmos-heat}) is the first law of thermodynamics where internal +energy $e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass +and $p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing. It is convenient to cast the heat equation in terms of potential temperature $\theta $ so that it looks more like a generic conservation law. @@ -1258,9 +1246,6 @@ \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } \end{eqnarray} -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.29 2010/08/30 23:09:21 jmc Exp $ -% $Name: $ - \section{Appendix OCEAN} \subsection{Equations of motion for the ocean} @@ -1475,9 +1460,6 @@ _{nh}=0$ form of these equations that are used throughout the ocean modeling community and referred to as the primitive equations (HPE). -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.29 2010/08/30 23:09:21 jmc Exp $ -% $Name: $ - \section{Appendix:OPERATORS} \subsection{Coordinate systems}