/[MITgcm]/manual/s_examples/tracer_adjsens/co2sens.tex
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revision 1.2 by cnh, Thu Oct 25 18:36:54 2001 UTC revision 1.5 by adcroft, Tue Nov 13 19:01:42 2001 UTC
# Line 118  $ Line 118  $
118   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
119  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
120  The implicit free surface form of the pressure equation described in Marshall et. al  The implicit free surface form of the pressure equation described in Marshall et. al
121  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
122  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
123  \\  \\
124    
# Line 167  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d Line 167  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
167  \noindent where $u$ and $v$ are the $x$ and $y$ components of the  \noindent where $u$ and $v$ are the $x$ and $y$ components of the
168  flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and  flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and
169  interior model levels respectively. As described in  interior model levels respectively. As described in
170  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
171  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
172  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
173  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
# Line 176  elevation $\eta$ and the hydrostatic pre Line 176  elevation $\eta$ and the hydrostatic pre
176  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
177    
178  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
179  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},
180    
181  \begin{eqnarray}  \begin{eqnarray}
182  \label{EQ:munk_layer}  \label{EQ:munk_layer}
# Line 190  boundary layer is well resolved. Line 190  boundary layer is well resolved.
190    
191  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
192  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
193  parameter to the horizontal Laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
194    
195  \begin{eqnarray}  \begin{eqnarray}
196  \label{EQ:laplacian_stability}  \label{EQ:laplacian_stability}
# Line 216  and vertical ($K_{z}$) diffusion coeffic Line 216  and vertical ($K_{z}$) diffusion coeffic
216  \\  \\
217    
218  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
219  \cite{Adcroft_thesis}  \cite{adcroft:95}
220    
221  \begin{eqnarray}  \begin{eqnarray}
222  \label{EQ:inertial_stability}  \label{EQ:inertial_stability}
# Line 227  S_{i} = f^{2} {\delta t}^2 Line 227  S_{i} = f^{2} {\delta t}^2
227  limit for stability.  limit for stability.
228  \\  \\
229    
230  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
231  horizontal flow  horizontal flow
232  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
233    
# Line 241  limit of 0.5. Line 241  limit of 0.5.
241  \\  \\
242    
243  \noindent The stability parameter for internal gravity waves  \noindent The stability parameter for internal gravity waves
244  \cite{Adcroft_thesis}  \cite{adcroft:95}
245    
246  \begin{eqnarray}  \begin{eqnarray}
247  \label{EQ:cfl_stability}  \label{EQ:cfl_stability}
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