<p><b>mpetersen@lanl.gov</b> 2013-03-20 07:48:20 -0600 (Wed, 20 Mar 2013)</p><p>update ocean section of user's guide<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/documents/users_guide/ocean/core_intro.tex
===================================================================
--- trunk/documents/users_guide/ocean/core_intro.tex        2013-03-20 13:38:30 UTC (rev 2632)
+++ trunk/documents/users_guide/ocean/core_intro.tex        2013-03-20 13:48:20 UTC (rev 2633)
@@ -4,7 +4,7 @@
The governing equations for MPAS-Ocean are\\ \\
{\it momentum equation:}
\begin{equation}
-\label{ocean:momentum continuous 1}
+\label{ocean:momentum}
\frac{\partial {\bf u}}{\partial t}
+ \eta {\bf k} \times {\bf u}
+ w\frac{\partial {\bf u}}{\partial z}
@@ -14,7 +14,7 @@
\end{equation}
{\it thickness equation:}
\begin{equation}
-\label{ocean:thickness continuous 1}
+\label{ocean:thickness}
\frac{\partial h}{\partial t}
+ </font>
<font color="gray">abla\cdot\left(h \overline{ {\bf u} }^z\right)
+ \left. w \right|_{z=s^{top}}
@@ -23,7 +23,7 @@
\end{equation}
{\it tracer equation:}
\begin{equation}
-\label{ocean:tracer continuous 1}
+\label{ocean:tracer}
\frac{\partial}{\partial t} h \overline{\varphi}^z
+ </font>
<font color="gray">abla\cdot\left(h \overline{\varphi {\bf u} }^z\right)
+ \left. \varphi w \right|_{z=s^{top}}
@@ -33,16 +33,16 @@
\end{equation}
{\it hydrostatic condition:}
\begin{equation}
-\label{ocean:pressure continuous 1}
+\label{ocean:pressure}
p(x,y,z) = p^{s}(x,y) + \int_{z}^{z^s} \rho g dz'
\end{equation}
{\it equation of state:}
\begin{equation}
-\label{ocean:eos continuous 1}
+\label{ocean:eos}
\rho = f_{eos}(\Theta,S,p)
\end{equation}
-Equations \ref{ocean:momentum continuous 1} through \ref{ocean:eos continuous 1} are a normal expression of the primitive equations; i.e. the incompressible Boussinesq equations in hydrostatic balance. Variable definitions are in Tables \ref{oceanTable:variables} and \ref{oceanTable:variables_Greek}. The momentum advection and Coriolis terms in (\ref{ocean:momentum continuous 1}) are presented in vorticity-kinetic energy form \citep[eqn 5]{Ringler_ea10jcp}. The thickness and tracer equations describe a single layer in the vertical, where the operator $\overline{\left(\cdot\right)}^z$ is a vertical average over that layer (see derivation in Appedix A.2 of \citet{Ringler_ea13om}). Otherwise, \ref{ocean:momentum continuous 1}--\ref{ocean:eos continuous 1} are the model equations in continuous form. Details of the conversion to fully discretized equations are given in the appendices of \citet{Ringler_ea13om}.
+Equations \ref{ocean:momentum} through \ref{ocean:eos} are a normal expression of the primitive equations; i.e. the incompressible Boussinesq equations in hydrostatic balance. Variable definitions are in Tables \ref{oceanTable:variables} and \ref{oceanTable:variables_Greek}. The momentum advection and Coriolis terms in (\ref{ocean:momentum}) are presented in vorticity-kinetic energy form \citep[eqn 5]{Ringler_ea10jcp}. The thickness and tracer equations describe a single layer in the vertical, where the operator $\overline{\left(\cdot\right)}^z$ is a vertical average over that layer (see derivation in Appedix A.2 of \citet{Ringler_ea13om}). Otherwise, \ref{ocean:momentum}--\ref{ocean:eos} are the model equations in continuous form. Details of the conversion to fully discretized equations are given in the appendices of \citet{Ringler_ea13om}.
\begin{table}[ht]
\caption{Latin variables used in prognostic equation set. Column 3 shows the native horizontal grid location. All variables are located at the center of the layer in the vertical unless noted.}
Modified: trunk/documents/users_guide/ocean/section_descriptions/Rayleigh_damping.tex
===================================================================
--- trunk/documents/users_guide/ocean/section_descriptions/Rayleigh_damping.tex        2013-03-20 13:38:30 UTC (rev 2632)
+++ trunk/documents/users_guide/ocean/section_descriptions/Rayleigh_damping.tex        2013-03-20 13:48:20 UTC (rev 2633)
@@ -1,4 +1,4 @@
-A linear damping toward a state of rest is available with this namelist option. It is implemented with a term on the RHS of the momentum equation (\ref{ocean:momentum continuous 1}) of the form
+A linear damping toward a state of rest is available with this namelist option. It is implemented with a term on the RHS of the momentum equation (\ref{ocean:momentum}) of the form
\begin{equation}
{\cal F}^u = -c_R {\bf u}.
\end{equation}
Modified: trunk/documents/users_guide/ocean/section_descriptions/bottom_drag.tex
===================================================================
--- trunk/documents/users_guide/ocean/section_descriptions/bottom_drag.tex        2013-03-20 13:38:30 UTC (rev 2632)
+++ trunk/documents/users_guide/ocean/section_descriptions/bottom_drag.tex        2013-03-20 13:48:20 UTC (rev 2633)
@@ -1,4 +1,4 @@
-The bottom drag is applied as a bottom boundary condition within the implicit solve of vertical mixing in the momentum equation (\ref{ocean:momentum continuous 1}), as
+The bottom drag is applied as a bottom boundary condition within the implicit solve of vertical mixing in the momentum equation (\ref{ocean:momentum}), as
\begin{equation}
\lim_{z\rightarrow z_{bot}} </font>
<font color="gray">u_v \frac{\partial u}{\partial z} = c_{drag} \left|u\right| u,
\end{equation}
Modified: trunk/documents/users_guide/ocean/section_descriptions/forcing.tex
===================================================================
--- trunk/documents/users_guide/ocean/section_descriptions/forcing.tex        2013-03-20 13:38:30 UTC (rev 2632)
+++ trunk/documents/users_guide/ocean/section_descriptions/forcing.tex        2013-03-20 13:48:20 UTC (rev 2633)
@@ -1,10 +1,10 @@
-Forcing may be applied to the RHS of the momentum equation (\ref{ocean:momentum continuous 1}) through the term
+Forcing may be applied to the RHS of the momentum equation (\ref{ocean:momentum}) through the term
\begin{equation}
{\cal F}^u = \frac{1}{\rho_0 h}\tau
\end{equation}
where $\tau$ is typically the wind stress in $N/m^2$ applied to the top layer. More generally, momentum forcing may be applied to any layer in the ocean. The momentum forcing may be given by the input variables \verb|u_src| or \verb|windStressMonthly|, depending on the configuration settings below. When running within the CESM, the wind stress is provided by the coupler (see Chapter \ref{chap:cesm_ocean_coupling}).
-Temperature and salinity restoring are applied to the tracer equation (\ref{ocean:tracer continuous 1}) through the term
+Temperature and salinity restoring are applied to the tracer equation (\ref{ocean:tracer}) through the term
\begin{equation}
{\cal F}^\varphi = -h\frac{\varphi-\varphi_{r}}{\tau_{r}}
\end{equation}
Modified: trunk/documents/users_guide/ocean/section_descriptions/hmix.tex
===================================================================
--- trunk/documents/users_guide/ocean/section_descriptions/hmix.tex        2013-03-20 13:38:30 UTC (rev 2632)
+++ trunk/documents/users_guide/ocean/section_descriptions/hmix.tex        2013-03-20 13:48:20 UTC (rev 2633)
@@ -7,7 +7,7 @@
Each horizontal mixing scheme has its own namelist, and may be turned
on with the \verb|_use_| logical configuration flags. Multiple
schemes may be run simultaneously. The horizontal mixing terms in the
-governing equations (\ref{ocean:momentum continuous 1},
-\ref{ocean:tracer continuous 1}) are ${\bf D}^u_h$ for momentum and
+governing equations (\ref{ocean:momentum},
+\ref{ocean:tracer}) are ${\bf D}^u_h$ for momentum and
$D^\varphi_h$ for tracers. No horizontal mixing is applied to the
thickness equation.
</font>
</pre>