--- manual/s_overview/text/manual.tex 2004/10/15 14:44:25 1.20 +++ manual/s_overview/text/manual.tex 2004/10/17 04:15:13 1.22 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.20 2004/10/15 14:44:25 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.22 2004/10/17 04:15:13 jmc Exp $ % $Name: $ %tci%\documentclass[12pt]{book} @@ -34,7 +34,7 @@ % Section: Overview -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.20 2004/10/15 14:44:25 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.22 2004/10/17 04:15:13 jmc Exp $ % $Name: $ This document provides the reader with the information necessary to @@ -137,7 +137,7 @@ 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 1.20 2004/10/15 14:44:25 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.22 2004/10/17 04:15:13 jmc Exp $ % $Name: $ \section{Illustrations of the model in action} @@ -372,7 +372,7 @@ \input{part1/lab_figure} %%CNHend -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.20 2004/10/15 14:44:25 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.22 2004/10/17 04:15:13 jmc Exp $ % $Name: $ \section{Continuous equations in `r' coordinates} @@ -611,9 +611,11 @@ atmosphere)} \label{eq:moving-bc-atmos} \end{eqnarray} -Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) -yields a consistent set of atmospheric equations which, for convenience, are written out in $p$ -coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}). +Then the (hydrostatic form of) equations +(\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yields a consistent +set of atmospheric equations which, for convenience, are written out +in $p$ coordinates in Appendix Atmosphere - see +eqs(\ref{eq:atmos-prime}). \subsection{Ocean} @@ -1098,8 +1100,9 @@ \subsection{Vector invariant form} -For some purposes it is advantageous to write momentum advection in eq(\ref -{eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the (so-called) `vector invariant' form: +For some purposes it is advantageous to write momentum advection in +eq(\ref {eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the +(so-called) `vector invariant' form: \begin{equation} \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t} @@ -1120,7 +1123,7 @@ 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 1.20 2004/10/15 14:44:25 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.22 2004/10/17 04:15:13 jmc Exp $ % $Name: $ \section{Appendix ATMOSPHERE} @@ -1210,6 +1213,7 @@ surface ($\phi $ is imposed and $\omega \neq 0$). \subsubsection{Splitting the geo-potential} +\label{sec:hpe-p-geo-potential-split} For the purposes of initialization and reducing round-off errors, the model deals with perturbations from reference (or ``standard'') profiles. For @@ -1239,7 +1243,8 @@ The final form of the HPE's in p coordinates is then: \begin{eqnarray} \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}} -_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \label{eq:atmos-prime} \\ +_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} +\label{eq:atmos-prime} \\ \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\ \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{ \partial p} &=&0 \\ @@ -1247,7 +1252,7 @@ \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } \end{eqnarray} -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.20 2004/10/15 14:44:25 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.22 2004/10/17 04:15:13 jmc Exp $ % $Name: $ \section{Appendix OCEAN} @@ -1285,8 +1290,9 @@ _{\theta ,S}\frac{Dp}{Dt} \label{EOSexpansion} \end{equation} -Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is the -reciprocal of the sound speed ($c_{s}$) squared. Substituting into \ref{eq-zns-cont} gives: +Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is +the reciprocal of the sound speed ($c_{s}$) squared. Substituting into +\ref{eq-zns-cont} gives: \begin{equation} \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{ v}}+\partial _{z}w\approx 0 \label{eq-zns-pressure} @@ -1463,7 +1469,7 @@ _{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 1.20 2004/10/15 14:44:25 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.22 2004/10/17 04:15:13 jmc Exp $ % $Name: $ \section{Appendix:OPERATORS}