/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
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revision 1.4 by cnh, Thu Oct 25 18:36:54 2001 UTC revision 1.7 by adcroft, Tue Nov 13 20:13:54 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}  \label{sect:eg-baro}
6    
7  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
8    
# Line 82  walls at $x=$~0,1200km and at $y=$~0,120 Line 82  walls at $x=$~0,1200km and at $y=$~0,120
82    
83  \subsection{Equations Solved}  \subsection{Equations Solved}
84  The model is configured in hydrostatic form. The implicit free surface form of the  The model is configured in hydrostatic form. The implicit free surface form of the
85  pressure equation described in Marshall et. al \cite{Marshall97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
86  employed.  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
# Line 125  model is configured with a single layer Line 125  model is configured with a single layer
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 $400 m s^{-1}$.
128  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
129    
130  \begin{eqnarray}  \begin{eqnarray}
131  \label{EQ:munk_layer}  \label{EQ:munk_layer}
# Line 139  layer is well resolved. Line 139  layer is well resolved.
139    
140  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
141  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
142  parameter to the horizontal Laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
143    
144    
145    
# Line 153  for stability. Line 153  for stability.
153  \\  \\
154    
155  \noindent The numerical stability for inertial oscillations    \noindent The numerical stability for inertial oscillations  
156  \cite{Adcroft_thesis}  \cite{adcroft:95}
157    
158  \begin{eqnarray}  \begin{eqnarray}
159  \label{EQ:inertial_stability}  \label{EQ:inertial_stability}
# Line 164  S_{i} = f^{2} {\delta t}^2 Line 164  S_{i} = f^{2} {\delta t}^2
164  limit for stability.  limit for stability.
165  \\  \\
166    
167  \noindent The advective CFL \cite{Adcroft_thesis} for an extreme maximum  \noindent The advective CFL \cite{adcroft:95} for an extreme maximum
168  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
169    
170  \begin{eqnarray}  \begin{eqnarray}
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