/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
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revision 1.1 by adcroft, Wed Aug 8 16:15:49 2001 UTC revision 1.3 by cnh, Mon Oct 22 11:55:47 2001 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Example: Barotropic Ocean Gyre In Cartesian Coordinates}  \section{Example: Barotropic Ocean Gyre In Cartesian Coordinates}
5    \label{sec:eg-baro}
6    
7  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
8    
# Line 15  Line 16 
16  %{\large May 2001}  %{\large May 2001}
17  %\end{center}  %\end{center}
18    
19  \subsection{Introduction}  This is the first in a series of sections describing
   
 This document is the first in a series of documents describing  
20  example MITgcm numerical experiments. The example experiments  example MITgcm numerical experiments. The example experiments
21  include both straightforward examples of idealised geophysical  include both straightforward examples of idealised geophysical
22  fluid simulations and more involved cases encompassing  fluid simulations and more involved cases encompassing
23  large scale modeling and  large scale modeling and
24  automatic differentiation. Both hydrostatic and non-hydrostatic  automatic differentiation. Both hydrostatic and non-hydrostatic
25  experiements are presented, as well as experiments employing  experiments are presented, as well as experiments employing
26  cartesian, spherical-polar and cube-sphere coordinate systems.  cartesian, spherical-polar and cube-sphere coordinate systems.
27  These ``case study'' documents include information describing  These ``case study'' documents include information describing
28  the experimental configuration and detailed information on how to  the experimental configuration and detailed information on how to
# Line 70  Figure \ref{FIG:simulation_config} Line 69  Figure \ref{FIG:simulation_config}
69  summarises the configuration simulated.  summarises the configuration simulated.
70    
71  \begin{figure}  \begin{figure}
72  \centerline{  \begin{center}
73   \resizebox{7.5in}{5.5in}{   \resizebox{7.5in}{5.5in}{
74     \includegraphics*[0.2in,0.7in][10.5in,10.5in]     \includegraphics*[0.2in,0.7in][10.5in,10.5in]
75      {part3/case_studies/barotropic_gyre/simulation_config.eps} }      {part3/case_studies/barotropic_gyre/simulation_config.eps} }
76  }  \end{center}
77  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
78  for barotropic gyre numerical experiment. The domain is enclosed bu solid  for barotropic gyre numerical experiment. The domain is enclosed bu solid
79  walls at $x=$~0,1200km and at $y=$~0,1200km.}  walls at $x=$~0,1200km and at $y=$~0,1200km.}
80  \label{FIG:simulation_config}  \label{FIG:simulation_config}
81  \end{figure}  \end{figure}
82    
83  \subsection{Discrete Numerical Configuration}  \subsection{Equations Solved}
84    The model is configured in hydrostatic form. The implicit free surface form of the
85   The model is configured in hydrostatic form.  The domain is discretised with  pressure equation described in Marshall et. al \cite{Marshall97a} is
86  a uniform grid spacing in the horizontal set to  employed.
  $\Delta x=\Delta y=20$~km, so  
 that there are sixty grid cells in the $x$ and $y$ directions. Vertically the  
 model is configured with a single layer with depth, $\Delta z$, of $5000$~m.  
 The implicit free surface form of the  
 pressure equation described in Marshall et. al \cite{Marshall97a} is  
 employed.  
87  A horizontal laplacian operator $\nabla_{h}^2$ provides viscous  A horizontal laplacian operator $\nabla_{h}^2$ provides viscous
88  dissipation. The wind-stress momentum input is added to the momentum equation  dissipation. The wind-stress momentum input is added to the momentum equation
89  for the ``zonal flow'', $u$. Other terms in the model  for the ``zonal flow'', $u$. Other terms in the model
90  are explicitly switched off for this experiement configuration (see section  are explicitly switched off for this experiement configuration (see section
91  \ref{SEC:code_config} ), yielding an active set of equations solved in this  \ref{SEC:code_config} ), yielding an active set of equations solved in this
92  configuration as follows  configuration as follows
93    
94  \begin{eqnarray}  \begin{eqnarray}
95  \label{EQ:model_equations}  \label{EQ:model_equations}
96  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
97                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
98                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
99  & = &  & = &
100  \frac{\tau_{x}}{\rho_{0}\Delta z}  \frac{\tau_{x}}{\rho_{0}\Delta z}
101  \\  \\
102  \frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -  \frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
103                A_{h}\nabla_{h}^2v                A_{h}\nabla_{h}^2v
104  & = &  & = &
105  0  0
106  \\  \\
# Line 117  configuration as follows Line 110  configuration as follows
110  \end{eqnarray}  \end{eqnarray}
111    
112  \noindent where $u$ and $v$ and the $x$ and $y$ components of the  \noindent where $u$ and $v$ and the $x$ and $y$ components of the
113  flow vector $\vec{u}$.  flow vector $\vec{u}$.
114  \\  \\
115    
116    
117    \subsection{Discrete Numerical Configuration}
118    
119     The domain is discretised with
120    a uniform grid spacing in the horizontal set to
121     $\Delta x=\Delta y=20$~km, so
122    that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
123    model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
124    
125  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
126    
127  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
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