/[MITgcm]/manual/s_examples/baroclinic_gyre/fourlayer.tex
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revision 1.9 by cnh, Thu Oct 25 18:36:55 2001 UTC revision 1.11 by adcroft, Tue Nov 13 20:13:54 2001 UTC
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2  % $Name$  % $Name$
3    
4  \section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}  \section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}
5  \label{sec:eg-fourlayer}  \label{sect:eg-fourlayer}
6    
7  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
8    
# Line 19  Line 19 
19  This document describes an example experiment using MITgcm  This document describes an example experiment using MITgcm
20  to simulate a baroclinic ocean gyre in spherical  to simulate a baroclinic ocean gyre in spherical
21  polar coordinates. The barotropic  polar coordinates. The barotropic
22  example experiment in section \ref{sec:eg-baro}  example experiment in section \ref{sect:eg-baro}
23  illustrated how to configure the code for a single layer  illustrated how to configure the code for a single layer
24  simulation in a Cartesian grid. In this example a similar physical problem  simulation in a Cartesian grid. In this example a similar physical problem
25  is simulated, but the code is now configured  is simulated, but the code is now configured
# Line 63  $\tau_0$ is set to $0.1N m^{-2}$. Line 63  $\tau_0$ is set to $0.1N m^{-2}$.
63    
64  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:simulation_config}
65  summarizes the configuration simulated.  summarizes the configuration simulated.
66  In contrast to the example in section \ref{sec:eg-baro}, the  In contrast to the example in section \ref{sect:eg-baro}, the
67  current experiment simulates a spherical polar domain. As indicated  current experiment simulates a spherical polar domain. As indicated
68  by the axes in the lower left of the figure the model code works internally  by the axes in the lower left of the figure the model code works internally
69  in a locally orthogonal coordinate $(x,y,z)$. For this experiment description  in a locally orthogonal coordinate $(x,y,z)$. For this experiment description
# Line 119  The vertical spacing, $\Delta z$, is con Line 119  The vertical spacing, $\Delta z$, is con
119    
120  \subsection{Equations solved}  \subsection{Equations solved}
121  For this problem  For this problem
122  the implicit free surface, {\bf HPE} (see section \ref{sec:hydrostatic_and_quasi-hydrostatic_forms}) form of the  the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the
123  equations described in Marshall et. al \cite{Marshall97a} are  equations described in Marshall et. al \cite{marshall:97a} are
124  employed. The flow is three-dimensional with just temperature, $\theta$, as  employed. The flow is three-dimensional with just temperature, $\theta$, as
125  an active tracer.  The equation of state is linear.  an active tracer.  The equation of state is linear.
126  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
# Line 221  y=r\varphi,~\Delta y &= &r\Delta \varphi Line 221  y=r\varphi,~\Delta y &= &r\Delta \varphi
221    
222  The procedure for generating a set of internal grid variables from a  The procedure for generating a set of internal grid variables from a
223  spherical polar grid specification is discussed in section  spherical polar grid specification is discussed in section
224  \ref{sec:spatial_discrete_horizontal_grid}.  \ref{sect:spatial_discrete_horizontal_grid}.
225    
226  \noindent\fbox{ \begin{minipage}{5.5in}  \noindent\fbox{ \begin{minipage}{5.5in}
227  {\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em  {\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em
# Line 242  $\Delta x_v$, $\Delta y_u$: {\bf DXv}, { Line 242  $\Delta x_v$, $\Delta y_u$: {\bf DXv}, {
242    
243    
244    
245  As described in \ref{sec:tracer_equations}, the time evolution of potential  As described in \ref{sect:tracer_equations}, the time evolution of potential
246  temperature,  temperature,
247  $\theta$, (equation \ref{eq:eg_fourl_theta})  $\theta$, (equation \ref{eq:eg_fourl_theta})
248  is evaluated prognostically. The centered second-order scheme with  is evaluated prognostically. The centered second-order scheme with
249  Adams-Bashforth time stepping described in section  Adams-Bashforth time stepping described in section
250  \ref{sec:tracer_equations_abII} is used to step forward the temperature  \ref{sect:tracer_equations_abII} is used to step forward the temperature
251  equation. Prognostic terms in  equation. Prognostic terms in
252  the momentum equations are solved using flux form as  the momentum equations are solved using flux form as
253  described in section \ref{sec:flux-form_momentum_eqautions}.  described in section \ref{sect:flux-form_momentum_eqautions}.
254  The pressure forces that drive the fluid motions, (  The pressure forces that drive the fluid motions, (
255  $\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface  $\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface
256  elevation $\eta$ and the hydrostatic pressure. The hydrostatic part of the  elevation $\eta$ and the hydrostatic pressure. The hydrostatic part of the
# Line 258  pressure is diagnosed explicitly by inte Line 258  pressure is diagnosed explicitly by inte
258  height, $\eta$, is diagnosed using an implicit scheme. The pressure  height, $\eta$, is diagnosed using an implicit scheme. The pressure
259  field solution method is described in sections  field solution method is described in sections
260  \ref{sect:pressure-method-linear-backward} and  \ref{sect:pressure-method-linear-backward} and
261  \ref{sec:finding_the_pressure_field}.  \ref{sect:finding_the_pressure_field}.
262    
263  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
264    
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