--- manual/s_overview/appendix_atmos.tex	2001/09/26 14:53:10	1.3
+++ manual/s_overview/appendix_atmos.tex	2001/09/27 01:57:17	1.5
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/Attic/appendix_atmos.tex,v 1.3 2001/09/26 14:53:10 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/Attic/appendix_atmos.tex,v 1.5 2001/09/27 01:57:17 cnh Exp $
 % $Name:  $
 
 \section{Appendix ATMOSPHERE}
@@ -10,11 +10,11 @@
 
 The hydrostatic primitive equations (HPEs) in p-coordinates are: 
 \begin{eqnarray}
-\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}}
 _{h}+\mathbf{\nabla }_{p}\phi &=&\vec{\mathbf{\mathcal{F}}}
 \label{eq:atmos-mom} \\
 \frac{\partial \phi }{\partial p}+\alpha &=&0  \label{eq-p-hydro-start} \\
-\mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{%
+\mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{
 \partial p} &=&0  \label{eq:atmos-cont} \\
 p\alpha &=&RT  \label{eq:atmos-eos} \\
 c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q}  
@@ -24,10 +24,10 @@
 surfaces) component of velocity,$\frac{D}{Dt}=\vec{\mathbf{v}}_{h}\cdot 
 \mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$ is the total
 derivative, $f=2\Omega \sin lat$ is the Coriolis parameter, $\phi =gz$ is
-the geopotential, $\alpha =1/\rho $ is the specific volume, $\omega =\frac{Dp%
+the geopotential, $\alpha =1/\rho $ is the specific volume, $\omega =\frac{Dp
 }{Dt}$ is the vertical velocity in the $p-$coordinate. Equation \ref
-{eq-p-firstlaw} 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 $%
+{eq-p-firstlaw} 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 
@@ -36,7 +36,7 @@
 \[
 p\frac{D\alpha }{Dt}+\alpha \frac{Dp}{Dt}=R\frac{DT}{Dt}
 \]
-which, when added to the heat equation \ref{eq-p-firstlaw} and using $%
+which, when added to the heat equation \ref{eq-p-firstlaw} and using $
 c_{p}=c_{v}+R$, gives: 
 \begin{equation}
 c_{p}\frac{DT}{Dt}-\alpha \frac{Dp}{Dt}=\mathcal{Q}
@@ -55,8 +55,8 @@
 the Exner function: 
 \[
 c_{p}T=\Pi \theta \;\;;\;\;\frac{\partial \Pi }{\partial p}=\frac{\kappa \Pi 
-}{p}\;\;;\;\;\alpha =\frac{\kappa \Pi \theta }{p}=\frac{\partial \ \Pi }{%
-\partial p}\theta \;\;;\;\;\frac{D\Pi }{Dt}=\frac{\partial \Pi }{\partial p}%
+}{p}\;\;;\;\;\alpha =\frac{\kappa \Pi \theta }{p}=\frac{\partial \ \Pi }{
+\partial p}\theta \;\;;\;\;\frac{D\Pi }{Dt}=\frac{\partial \Pi }{\partial p}
 \frac{Dp}{Dt}
 \]
 where $b=\frac{\partial \ \Pi }{\partial p}\theta $ is the buoyancy.
@@ -72,7 +72,7 @@
 \end{equation}
 which is in conservative form.
 
-For convenience in the model we prefer to step forward (\ref{theta-equation}%
+For convenience in the model we prefer to step forward (\ref{theta-equation}
 ) rather than (\ref{eq-p-firstlaw}).
 
 \subsubsection{Boundary conditions}
@@ -116,14 +116,14 @@
 
 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}}%
+\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}}}
                   \\
 \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0
                    \\
-\mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{%
+\mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{
 \partial p} &=&0                    \\
 \frac{\partial \Pi }{\partial p}\theta ^{\prime } &=&\alpha ^{\prime }
-                  \
+                  \\
 \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi }  \label{eq:atmos-prime}
 \end{eqnarray}