--- manual/s_examples/baroclinic_gyre/fourlayer.tex 2001/11/13 20:13:54 1.11 +++ manual/s_examples/baroclinic_gyre/fourlayer.tex 2002/02/28 19:32:19 1.12 @@ -1,7 +1,7 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.11 2001/11/13 20:13:54 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.12 2002/02/28 19:32:19 cnh Exp $ % $Name: $ -\section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates} +\section{Four Layer Baroclinic Ocean Gyre In Spherical Coordinates} \label{sect:eg-fourlayer} \bodytext{bgcolor="#FFFFFFFF"} @@ -43,7 +43,7 @@ according to latitude, $\varphi$ \begin{equation} -\label{EQ:fcori} +\label{EQ:eg-fourlayer-fcori} f(\varphi) = 2 \Omega \sin( \varphi ) \end{equation} @@ -61,7 +61,7 @@ $\tau_0$ is set to $0.1N m^{-2}$. \\ -Figure \ref{FIG:simulation_config} +Figure \ref{FIG:eg-fourlayer-simulation_config} summarizes the configuration simulated. In contrast to the example in section \ref{sect:eg-baro}, the current experiment simulates a spherical polar domain. As indicated @@ -82,14 +82,14 @@ linear \begin{equation} -\label{EQ:linear1_eos} +\label{EQ:eg-fourlayer-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-fourlayer-linear1_eos_pert} \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'} \end{equation} @@ -114,7 +114,7 @@ imposed by setting the potential temperature, $\theta$, in each layer. The vertical spacing, $\Delta z$, is constant and equal to $500$m. } -\label{FIG:simulation_config} +\label{FIG:eg-fourlayer-simulation_config} \end{figure} \subsection{Equations solved} @@ -133,7 +133,7 @@ follows \begin{eqnarray} -\label{EQ:model_equations} +\label{EQ:eg-fourlayer-model_equations} \frac{Du}{Dt} - fv + \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} - A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}} @@ -266,7 +266,7 @@ This value is chosen to yield a Munk layer width, \begin{eqnarray} -\label{EQ:munk_layer} +\label{EQ:eg-fourlayer-munk_layer} M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} \end{eqnarray} @@ -282,7 +282,7 @@ parameter to the horizontal Laplacian friction \begin{eqnarray} -\label{EQ:laplacian_stability} +\label{EQ:eg-fourlayer-laplacian_stability} S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} \end{eqnarray} @@ -294,7 +294,7 @@ $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit \begin{eqnarray} -\label{EQ:laplacian_stability_z} +\label{EQ:eg-fourlayer-laplacian_stability_z} S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2} \end{eqnarray} @@ -307,7 +307,7 @@ \noindent The numerical stability for inertial oscillations \begin{eqnarray} -\label{EQ:inertial_stability} +\label{EQ:eg-fourlayer-inertial_stability} S_{i} = f^{2} {\delta t}^2 \end{eqnarray} @@ -320,7 +320,7 @@ speed of $ | \vec{u} | = 2 ms^{-1}$ \begin{eqnarray} -\label{EQ:cfl_stability} +\label{EQ:eg-fourlayer-cfl_stability} C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} \end{eqnarray} @@ -332,7 +332,7 @@ propagating at $2~{\rm m}~{\rm s}^{-1}$ \begin{eqnarray} -\label{EQ:igw_stability} +\label{EQ:eg-fourlayer-igw_stability} S_{c} = \frac{c_{g} \delta t}{ \Delta x} \end{eqnarray}