--- manual/s_examples/deep_convection/convection.tex 2001/12/19 14:34:39 1.1 +++ manual/s_examples/deep_convection/convection.tex 2002/02/28 19:32:19 1.2 @@ -1,4 +1,4 @@ -\section{Example: Surface driven convection} +\section{Surface Driven Convection} \label{sect:eg-bconv} \bodytext{bgcolor="#FFFFFFFF"} @@ -22,10 +22,10 @@ for the surface driven convection experiment. The domain is doubly periodic with an initially uniform temperature of 20 $^oC$. } -\label{FIG:simulation_config} +\label{FIG:eg-bconv-simulation_config} \end{figure} -This experiment, figure \ref{FIG:simulation_config}, showcasing MITgcm's non-hydrostatic capability, was designed to explore +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. It is @@ -50,14 +50,14 @@ used in this experiment is linear \begin{equation} -\label{EQ: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:linear1_eos_pert} +\label{EQ:eg-bconv-linear1_eos_pert} \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'} \end{equation} @@ -72,9 +72,10 @@ 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:vertsection} and \ref{FIG: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} \begin{figure} \begin{center} \resizebox{15cm}{10cm}{ @@ -83,9 +84,12 @@ \end{center} \caption{ } -\label{FIG:vertsection} +\label{FIG:eg-bconv-vertsection} +\label{fig:surf-convection-vertsection} \end{figure} +\begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml} +\begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-horizsection\end{rawhtml} \begin{figure} \begin{center} \resizebox{10cm}{10cm}{ @@ -94,8 +98,10 @@ \end{center} \caption{ } -\label{FIG:horizsection} +\label{FIG:eg-bconv-horizsection} +\label{fig:surf-convection-horizsection} \end{figure} +\begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml} Model parameters are specified in file {\it input/data}. The grid dimensions are prescribed in {\it code/SIZE.h}. The forcing (file {\it input/Qsurf.bin}) is specified @@ -111,11 +117,11 @@ 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:global_forcing_ft}). This produces a set of equations +$\theta$, equation (\ref{EQ:eg-bconv-global_forcing_ft}). This produces a set of equations solved in this configuration as follows: \begin{eqnarray} -\label{EQ: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 - @@ -190,7 +196,7 @@ 50 m, the implied maximum timestep for stability, $\delta t_u$ is \begin{eqnarray} -\label{EQ:advectiveCFLcondition} +\label{EQ:eg-bconv-advectiveCFLcondition} %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s \end{eqnarray} @@ -669,7 +675,7 @@ \end{verbatim} Sets the tolerance which the three-dimensional, conjugate gradient solver will use to test for convergence in equation -\ref{EQ:congrad_3d_resid} to $1 \times 10^{-9}$. +\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 @@ -801,7 +807,7 @@ \end{center} \caption{ } -\label{FIG:Qsurf} +\label{FIG:eg-bconv-Qsurf} \end{figure} \subsection{Running the example}