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--- manual/s_examples/deep_convection/convection.tex 2010/08/27 13:25:31 1.9
+++ manual/s_examples/deep_convection/convection.tex 2010/08/30 23:09:19 1.10
@@ -1,6 +1,6 @@
\section{Surface Driven Convection}
-\label{www:tutorials}
-\label{sect:eg-bconv}
+%\label{www:tutorials}
+\label{sec:eg-bconv}
\begin{rawhtml}
<!-- CMIREDIR:eg-bconv: -->
\end{rawhtml}
@@ -29,10 +29,10 @@
for the surface driven convection experiment. The domain is doubly periodic
with an initially uniform temperature of 20 $^oC$.
}
-\label{FIG:eg-bconv-simulation_config}
+\label{fig:eg-bconv-simulation_config}
\end{figure}
-This experiment, figure \ref{FIG:eg-bconv-simulation_config}, showcasing MITgcm's non-hydrostatic
+This experiment, figure \ref{fig:eg-bconv-simulation_config}, showcasing MITgcm's non-hydrostatic
capability, was designed to explore
the temporal and spatial characteristics of convection plumes as they might exist during a
period of oceanic deep convection. The files for this experiment can be found in the verification
@@ -48,7 +48,7 @@
\end{itemize}
\subsection{Overview}
-\label{www:tutorials}
+%\label{www:tutorials}
The model domain consists of an approximately 3
km square by 1 km deep box of initially
@@ -60,14 +60,14 @@
used in this experiment is linear
\begin{equation}
-\label{EQ:eg-bconv-linear1_eos}
+\label{eq:eg-bconv-linear1_eos}
\rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
\end{equation}
\noindent which is implemented in the model as a density anomaly equation
\begin{equation}
-\label{EQ:eg-bconv-linear1_eos_pert}
+\label{eq:eg-bconv-linear1_eos_pert}
\rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
\end{equation}
@@ -82,7 +82,7 @@
As the fluid in the surface layer is cooled (at a mean rate of 800 Wm$^2$), it becomes
convectively unstable and
overturns, at first close to the grid-scale, but, as the flow matures, on larger scales
-(figures \ref{FIG:eg-bconv-vertsection} and \ref{FIG:eg-bconv-horizsection}), under the influence of
+(figures \ref{fig:eg-bconv-vertsection} and \ref{fig:eg-bconv-horizsection}), under the influence of
rotation ($f_o = 10^{-4}$ s$^{-1}$) .
\begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-vertsection\end{rawhtml}
@@ -94,7 +94,7 @@
\end{center}
\caption{
}
-\label{FIG:eg-bconv-vertsection}
+\label{fig:eg-bconv-vertsection}
\label{fig:surf-convection-vertsection}
\end{figure}
\begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
@@ -108,7 +108,7 @@
\end{center}
\caption{
}
-\label{FIG:eg-bconv-horizsection}
+\label{fig:eg-bconv-horizsection}
\label{fig:surf-convection-horizsection}
\end{figure}
\begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
@@ -118,7 +118,7 @@
in a binary data file generated using the Matlab script {\it input/gendata.m}.
\subsection{Equations solved}
-\label{www:tutorials}
+%\label{www:tutorials}
The model is configured in nonhydrostatic form, that is, all terms in the Navier
Stokes equations are retained and the pressure field is found, subject to appropriate
@@ -128,11 +128,11 @@
pressure equation described in Marshall et. al \cite{marshall:97a} is
employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
dissipation. The thermodynamic forcing appears as a sink in the potential temperature,
-$\theta$, equation (\ref{EQ:eg-bconv-global_forcing_ft}). This produces a set of equations
-solved in this configuration as follows:
+$\theta$, equation (\ref{eq:eg-bconv-theta_equations}).
+This produces a set of equations solved in this configuration as follows:
\begin{eqnarray}
-\label{EQ:eg-bconv-model_equations}
+\label{eq:eg-bconv-model_equations}
\frac{Du}{Dt} - fv +
\frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
\nabla_{h}\cdot A_{h}\nabla_{h}u -
@@ -177,6 +177,7 @@
{\cal F}_\theta & \text{(surface)} \\
0 & \text{(interior)}
\end{cases}
+\label{eq:eg-bconv-theta_equations}
\end{eqnarray}
\noindent where $u=\frac{Dx}{Dt}$, $v=\frac{Dy}{Dt}$ and
@@ -188,14 +189,14 @@
\\
\subsection{Discrete numerical configuration}
-\label{www:tutorials}
+%\label{www:tutorials}
The domain is discretised with a uniform grid spacing in each direction. There are 64
grid cells in directions $x$ and $y$ and 20 vertical levels thus the domain
comprises a total of just over 80 000 gridpoints.
\subsection{Numerical stability criteria and other considerations}
-\label{www:tutorials}
+%\label{www:tutorials}
For a heat flux of 800 Wm$^2$ and a rotation rate of $10^{-4}$ s$^{-1}$ the
plume-scale can be expected to be a few hundred meters guiding our choice of grid
@@ -209,7 +210,7 @@
50 m, the implied maximum timestep for stability, $\delta t_u$ is
\begin{eqnarray}
-\label{EQ:eg-bconv-advectiveCFLcondition}
+\label{eq:eg-bconv-advectiveCFLcondition}
%\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s
\end{eqnarray}
@@ -221,7 +222,7 @@
correlated over 50 m.
\subsection{Experiment configuration}
-\label{www:tutorials}
+%\label{www:tutorials}
The model configuration for this experiment resides under the directory
{\it verification/convection/}. The experiment files
@@ -238,19 +239,19 @@
experiment. Below we describe these experiment-specific customisations.
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it code/CPP\_OPTIONS.h}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it code/SIZE.h}}
-\label{www:tutorials}
+%\label{www:tutorials}
Three lines are customized in this file. These prescribe the domain grid dimensions.
\begin{itemize}
@@ -278,7 +279,7 @@
\begin{rawhtml}</PRE>\end{rawhtml}
\subsubsection{File {\it input/data}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file, reproduced completely below, specifies the main parameters
for the experiment. The parameters that are significant for this configuration
@@ -693,10 +694,13 @@
\end{verbatim}
Sets the tolerance which the three-dimensional, conjugate
gradient solver will use to test for convergence in equation
-\ref{EQ:eg-bconv-congrad_3d_resid} to $1 \times 10^{-9}$.
-The solver will iterate until the
-tolerance falls below this value or until the maximum number of
-solver iterations is reached. Used in routine
+%- note: Description of Conjugate gradient method (& related params) is missing
+% in the mean time, substitute this eq ref:
+\ref{eq:phi-nh} %\ref{eq:eg-bconv-congrad_3d_resid}
+to $1 \times 10^{-9}$.
+The solver will iterate until the tolerance falls below this value
+or until the maximum number of solver iterations is reached.
+Used in routine
{\it
\begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
S/R CG3D ({\it cg3d.F})
@@ -796,20 +800,20 @@
\subsubsection{File {\it input/data.pkg}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it input/eedata}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it input/Qsurf.bin}}
-\label{www:tutorials}
+%\label{www:tutorials}
The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)
map of heat flux values where
@@ -828,20 +832,20 @@
\end{center}
\caption{
}
-\label{FIG:eg-bconv-Qsurf}
+\label{fig:eg-bconv-Qsurf}
\end{figure}
\subsection{Running the example}
-\label{www:tutorials}
+%\label{www:tutorials}
\subsubsection{Code download}
-\label{www:tutorials}
+%\label{www:tutorials}
In order to run the examples you must first download the code distribution.
-Instructions for downloading the code can be found in \ref{sect:obtainingCode}.
+Instructions for downloading the code can be found in \ref{sec:obtainingCode}.
\subsubsection{Experiment Location}
-\label{www:tutorials}
+%\label{www:tutorials}
This example experiments is located under the release sub-directory
@@ -849,7 +853,7 @@
{\it verification/convection/ }
\subsubsection{Running the Experiment}
-\label{www:tutorials}
+%\label{www:tutorials}
To run the experiment
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