--- 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} \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}\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} \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