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--- manual/s_examples/rotating_tank/tank.tex 2004/06/22 16:56:31 1.2
+++ manual/s_examples/rotating_tank/tank.tex 2004/07/26 16:21:15 1.3
@@ -1,323 +1,205 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.2 2004/06/22 16:56:31 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.3 2004/07/26 16:21:15 afe Exp $
% $Name: $
-\section{Simulating a Rotating Tank in Cylindrical Coordinates}
-\label{www:tutorials}
-\label{sect:eg-tank}
-
\bodytext{bgcolor="#FFFFFFFF"}
%\begin{center}
-%{\Large \bf Simulating a Rotating Tank in Cylindrical Coordinates}
-%
+%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical
+%Coordinates}
%
%\vspace*{4mm}
%
%\vspace*{3mm}
-%{\large June 2004}
+%{\large May 2001}
%\end{center}
-\subsection{Introduction}
-\label{www:tutorials}
-
-This section illustrates an example of MITgcm simulating a laboratory
-experiment on much smaller scales than those common to geophysical
-fluid dynamics.
+This is the first in a series of tutorials describing
+example MITgcm numerical experiments. The example experiments
+include both straightforward examples of idealized geophysical
+fluid simulations and more involved cases encompassing
+large scale modeling and
+automatic differentiation. Both hydrostatic and non-hydrostatic
+experiments are presented, as well as experiments employing
+Cartesian, spherical-polar and cube-sphere coordinate systems.
+These ``case study'' documents include information describing
+the experimental configuration and detailed information on how to
+configure the MITgcm code and input files for each experiment.
-\subsection{Overview}
+\section{A Rotating Tank in Cylindrical Coordinates}
+\label{sect:eg-tank}
\label{www:tutorials}
This example experiment demonstrates using the MITgcm to simulate
-a laboratory experiment with a rotating tank of water with an ice
-bucket in the center. The simulation is configured for a laboratory
-scale on a 3^{\circ} \times 20cm cyclindrical grid with twenty-nine vertical
-levels.
-\\
-
-The model is forced with climatological wind stress data and surface
-flux data from DaSilva \cite{DaSilva94}. Climatological data
-from Levitus \cite{Levitus94} is used to initialize the model hydrography.
-Levitus seasonal climatology data is also used throughout the calculation
-to provide additional air-sea fluxes.
-These fluxes are combined with the DaSilva climatological estimates of
-surface heat flux and fresh water, resulting in a mixed boundary
-condition of the style described in Haney \cite{Haney}.
-Altogether, this yields the following forcing applied
-in the model surface layer.
-
-
-\noindent where ${\cal F}_{u}$, ${\cal F}_{v}$, ${\cal F}_{\theta}$,
-${\cal F}_{s}$ are the forcing terms in the zonal and meridional
-momentum and in the potential temperature and salinity
-equations respectively.
-The term $\Delta z_{s}$ represents the top ocean layer thickness in
-meters.
-It is used in conjunction with a reference density, $\rho_{0}$
-(here set to $999.8\,{\rm kg\,m^{-3}}$), a
-reference salinity, $S_{0}$ (here set to 35~ppt),
-and a specific heat capacity, $C_{p}$ (here set to
-$4000~{\rm J}~^{\circ}{\rm C}^{-1}~{\rm kg}^{-1}$), to convert
-input dataset values into time tendencies of
-potential temperature (with units of $^{\circ}{\rm C}~{\rm s}^{-1}$),
-salinity (with units ${\rm ppt}~s^{-1}$) and
-velocity (with units ${\rm m}~{\rm s}^{-2}$).
-The externally supplied forcing fields used in this
-experiment are $\tau_{x}$, $\tau_{y}$, $\theta^{\ast}$, $S^{\ast}$,
-$\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$)
-have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields
-($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$
-respectively. The salinity forcing fields ($S^{\ast}$ and
-$\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
-respectively.
-\\
-
-
-Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
-relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
-the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
-and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
-in equations \ref{EQ:eg-hs-global_forcing_fu}-\ref{EQ:eg-hs-global_forcing_fs}. The figures
-also indicate the lateral extent and coastline used in the experiment.
-Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
-domain.
-
-
-\subsection{Discrete Numerical Configuration}
-\label{www:tutorials}
-
-
- The model is configured in hydrostatic form. The domain is discretised with
-a uniform grid spacing in latitude and longitude on the sphere
- $\Delta \phi=\Delta \lambda=4^{\circ}$, so
-that there are ninety grid cells in the zonal and forty in the
-meridional direction. The internal model coordinate variables
-$x$ and $y$ are initialized according to
-\begin{eqnarray}
-x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
-y=r\lambda,~\Delta x &= &r\Delta \lambda
-\end{eqnarray}
-
-Arctic polar regions are not
-included in this experiment. Meridionally the model extends from
-$80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
-Vertically the model is configured with twenty layers with the
-following thicknesses
-$\Delta z_{1} = 50\,{\rm m},\,
- \Delta z_{2} = 50\,{\rm m},\,
- \Delta z_{3} = 55\,{\rm m},\,
- \Delta z_{4} = 60\,{\rm m},\,
- \Delta z_{5} = 65\,{\rm m},\,
-$
-$
- \Delta z_{6}~=~70\,{\rm m},\,
- \Delta z_{7}~=~80\,{\rm m},\,
- \Delta z_{8}~=95\,{\rm m},\,
- \Delta z_{9}=120\,{\rm m},\,
- \Delta z_{10}=155\,{\rm m},\,
-$
-$
- \Delta z_{11}=200\,{\rm m},\,
- \Delta z_{12}=260\,{\rm m},\,
- \Delta z_{13}=320\,{\rm m},\,
- \Delta z_{14}=400\,{\rm m},\,
- \Delta z_{15}=480\,{\rm m},\,
-$
-$
- \Delta z_{16}=570\,{\rm m},\,
- \Delta z_{17}=655\,{\rm m},\,
- \Delta z_{18}=725\,{\rm m},\,
- \Delta z_{19}=775\,{\rm m},\,
- \Delta z_{20}=815\,{\rm m}
-$ (here the numeric subscript indicates the model level index number, ${\tt k}$).
-The implicit free surface form of the pressure equation described in Marshall et. al
-\cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
-dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
-
-Wind-stress forcing is added to the momentum equations for both
-the zonal flow, $u$ and the meridional flow $v$, according to equations
-(\ref{EQ:eg-hs-global_forcing_fu}) and (\ref{EQ:eg-hs-global_forcing_fv}).
-Thermodynamic forcing inputs are added to the equations for
-potential temperature, $\theta$, and salinity, $S$, according to equations
-(\ref{EQ:eg-hs-global_forcing_ft}) and (\ref{EQ:eg-hs-global_forcing_fs}).
-This produces a set of equations solved in this configuration as follows:
+a Barotropic, wind-forced, ocean gyre circulation. The experiment
+is a numerical rendition of the gyre circulation problem similar
+to the problems described analytically by Stommel in 1966
+\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
+
+In this experiment the model
+is configured to represent a rectangular enclosed box of fluid,
+$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
+by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
+in the ``north-south'' direction. Topologically the grid is Cartesian and
+the coriolis parameter $f$ is defined according to a mid-latitude beta-plane
+equation
+
+\begin{equation}
+\label{EQ:eg-baro-fcori}
+f(y) = f_{0}+\beta y
+\end{equation}
+
+\noindent where $y$ is the distance along the ``north-south'' axis of the
+simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in
+(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
+\\
+\\
+ The sinusoidal wind-stress variations are defined according to
+
+\begin{equation}
+\label{EQ:eg-baro-taux}
+\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
+\end{equation}
+
+\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and
+$\tau_0$ is set to $0.1N m^{-2}$.
+\\
+\\
+Figure \ref{FIG:eg-baro-simulation_config}
+summarizes the configuration simulated.
+
+%% === eh3 ===
+\begin{figure}
+%% \begin{center}
+%% \resizebox{7.5in}{5.5in}{
+%% \includegraphics*[0.2in,0.7in][10.5in,10.5in]
+%% {part3/case_studies/barotropic_gyre/simulation_config.eps} }
+%% \end{center}
+\centerline{
+ \scalefig{.95}
+ \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
+}
+\caption{Schematic of simulation domain and wind-stress forcing function
+for barotropic gyre numerical experiment. The domain is enclosed bu solid
+walls at $x=$~0,1200km and at $y=$~0,1200km.}
+\label{FIG:eg-baro-simulation_config}
+\end{figure}
+
+\subsection{Equations Solved}
+\label{www:tutorials}
+The model is configured in hydrostatic form. The implicit free surface form of the
+pressure equation described in Marshall et. al \cite{marshall:97a} is
+employed.
+A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
+dissipation. The wind-stress momentum input is added to the momentum equation
+for the ``zonal flow'', $u$. Other terms in the model
+are explicitly switched off for this experiment configuration (see section
+\ref{SEC:code_config} ), yielding an active set of equations solved in this
+configuration as follows
\begin{eqnarray}
-\label{EQ:eg-hs-model_equations}
-\frac{Du}{Dt} - fv +
- \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
- \nabla_{h}\cdot A_{h}\nabla_{h}u -
- \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}
- & = &
-\begin{cases}
-{\cal F}_u & \text{(surface)} \\
-0 & \text{(interior)}
-\end{cases}
+\label{EQ:eg-baro-model_equations}
+\frac{Du}{Dt} - fv +
+ g\frac{\partial \eta}{\partial x} -
+ A_{h}\nabla_{h}^2u
+& = &
+\frac{\tau_{x}}{\rho_{0}\Delta z}
\\
-\frac{Dv}{Dt} + fu +
- \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
- \nabla_{h}\cdot A_{h}\nabla_{h}v -
- \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}
+\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
+ A_{h}\nabla_{h}^2v
& = &
-\begin{cases}
-{\cal F}_v & \text{(surface)} \\
-0 & \text{(interior)}
-\end{cases}
+0
\\
\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
&=&
0
-\\
-\frac{D\theta}{Dt} -
- \nabla_{h}\cdot K_{h}\nabla_{h}\theta
- - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}
-& = &
-\begin{cases}
-{\cal F}_\theta & \text{(surface)} \\
-0 & \text{(interior)}
-\end{cases}
-\\
-\frac{D s}{Dt} -
- \nabla_{h}\cdot K_{h}\nabla_{h}s
- - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}
-& = &
-\begin{cases}
-{\cal F}_s & \text{(surface)} \\
-0 & \text{(interior)}
-\end{cases}
-\\
-g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
\end{eqnarray}
-\noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
-$v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
-are the zonal and meridional components of the
-flow vector, $\vec{u}$, on the sphere. As described in
-MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
-evolution of potential temperature, $\theta$, equation is solved prognostically.
-The total pressure, $p$, is diagnosed by summing pressure due to surface
-elevation $\eta$ and the hydrostatic pressure.
+\noindent where $u$ and $v$ and the $x$ and $y$ components of the
+flow vector $\vec{u}$.
\\
+
+\subsection{Discrete Numerical Configuration}
+\label{www:tutorials}
+
+ The domain is discretised with
+a uniform grid spacing in the horizontal set to
+ $\Delta x=\Delta y=20$~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.
+
\subsubsection{Numerical Stability Criteria}
\label{www:tutorials}
-The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
+The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
This value is chosen to yield a Munk layer width \cite{adcroft:95},
+
\begin{eqnarray}
-\label{EQ:eg-hs-munk_layer}
+\label{EQ:eg-baro-munk_layer}
M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
\end{eqnarray}
-\noindent of $\approx 600$km. This is greater than the model
-resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional
-boundary layer is adequately resolved.
+\noindent of $\approx 100$km. This is greater than the model
+resolution $\Delta x$, ensuring that the frictional boundary
+layer is well resolved.
\\
\noindent The model is stepped forward with a
-time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
-$\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
+time step $\delta t=1200$secs. With this time step the stability
parameter to the horizontal Laplacian friction \cite{adcroft:95}
-\begin{eqnarray}
-\label{EQ:eg-hs-laplacian_stability}
-S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
-\end{eqnarray}
-\noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the
-0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at
-$\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.
-\\
-\noindent The vertical dissipation coefficient, $A_{z}$, is set to
-$1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
+
\begin{eqnarray}
-\label{EQ:eg-hs-laplacian_stability_z}
-S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
+\label{EQ:eg-baro-laplacian_stability}
+S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
\end{eqnarray}
-\noindent evaluates to $0.015$ for the smallest model
-level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
-the upper stability limit.
+\noindent evaluates to 0.012, which is well below the 0.3 upper limit
+for stability.
\\
-The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
-for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
-and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
-related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
-Here the stability parameter
-\begin{eqnarray}
-\label{EQ:eg-hs-laplacian_stability_xtheta}
-S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
-\end{eqnarray}
-evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
-stability parameter related to $K_{z}$
-\begin{eqnarray}
-\label{EQ:eg-hs-laplacian_stability_ztheta}
-S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
-\end{eqnarray}
-evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
-of $S_{l} \approx 0.5$.
-\\
-
-\noindent The numerical stability for inertial oscillations
+\noindent The numerical stability for inertial oscillations
\cite{adcroft:95}
\begin{eqnarray}
-\label{EQ:eg-hs-inertial_stability}
-S_{i} = f^{2} {\delta t_v}^2
+\label{EQ:eg-baro-inertial_stability}
+S_{i} = f^{2} {\delta t}^2
\end{eqnarray}
-\noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to
-the $S_{i} < 1$ upper limit for stability.
+\noindent evaluates to $0.0144$, which is well below the $0.5$ upper
+limit for stability.
\\
-\noindent The advective CFL \cite{adcroft:95} for a extreme maximum
-horizontal flow
-speed of $ | \vec{u} | = 2 ms^{-1}$
+\noindent The advective CFL \cite{adcroft:95} for an extreme maximum
+horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
\begin{eqnarray}
-\label{EQ:eg-hs-cfl_stability}
-S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
+\label{EQ:eg-baro-cfl_stability}
+S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
\end{eqnarray}
-\noindent evaluates to $6 \times 10^{-2}$. This is well below the stability
-limit of 0.5.
-\\
-
-\noindent The stability parameter for internal gravity waves propagating
-with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
-\cite{adcroft:95}
+\noindent evaluates to 0.12. This is approaching the stability limit
+of 0.5 and limits $\delta t$ to $1200s$.
-\begin{eqnarray}
-\label{EQ:eg-hs-gfl_stability}
-S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
-\end{eqnarray}
-
-\noindent evaluates to $3 \times 10^{-1}$. This is close to the linear
-stability limit of 0.5.
-
-\subsection{Experiment Configuration}
+\subsection{Code Configuration}
\label{www:tutorials}
-\label{SEC:eg-hs_examp_exp_config}
+\label{SEC:eg-baro-code_config}
The model configuration for this experiment resides under the
-directory {\it verification/hs94.128x64x5}. The experiment files
+directory {\it verification/exp0/}. The experiment files
\begin{itemize}
\item {\it input/data}
\item {\it input/data.pkg}
\item {\it input/eedata},
-\item {\it input/windx.bin},
-\item {\it input/windy.bin},
-\item {\it input/salt.bin},
-\item {\it input/theta.bin},
-\item {\it input/SSS.bin},
-\item {\it input/SST.bin},
-\item {\it input/topog.bin},
+\item {\it input/windx.sin\_y},
+\item {\it input/topog.box},
\item {\it code/CPP\_EEOPTIONS.h}
\item {\it code/CPP\_OPTIONS.h},
\item {\it code/SIZE.h}.
\end{itemize}
-contain the code customizations and parameter settings for these
+contain the code customizations and parameter settings for this
experiments. Below we describe the customizations
to these files associated with this experiment.
@@ -330,250 +212,74 @@
\begin{itemize}
-\item Lines 7-10 and 11-14
-\begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim}
-$\cdots$ \\
-set reference values for potential
-temperature and salinity at each model level in units of $^{\circ}$C and
-${\rm ppt}$. The entries are ordered from surface to depth.
-Density is calculated from anomalies at each level evaluated
-with respect to the reference values set here.\\
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R INI\_THETA}({\it ini\_theta.F})
-\end{minipage}
-}
-
-
-\item Line 15,
-\begin{verbatim} viscAz=1.E-3, \end{verbatim}
-this line sets the vertical Laplacian dissipation coefficient to
-$1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
-for this operator are specified later. This variable is copied into
-model general vertical coordinate variable {\bf viscAr}.
-
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
-\end{minipage}
-}
-
-\item Line 16,
-\begin{verbatim}
-viscAh=5.E5,
-\end{verbatim}
-this line sets the horizontal Laplacian frictional dissipation coefficient to
-$5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
-for this operator are specified later.
-
-\item Lines 17,
-\begin{verbatim}
-no_slip_sides=.FALSE.
-\end{verbatim}
-this line selects a free-slip lateral boundary condition for
-the horizontal Laplacian friction operator
-e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
-$\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
-
-\item Lines 9,
-\begin{verbatim}
-no_slip_bottom=.TRUE.
-\end{verbatim}
-this line selects a no-slip boundary condition for bottom
-boundary condition in the vertical Laplacian friction operator
-e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
-
-\item Line 19,
-\begin{verbatim}
-diffKhT=1.E3,
-\end{verbatim}
-this line sets the horizontal diffusion coefficient for temperature
-to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
-operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
-all boundaries.
-
-\item Line 20,
-\begin{verbatim}
-diffKzT=3.E-5,
-\end{verbatim}
-this line sets the vertical diffusion coefficient for temperature
-to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
-condition on this operator is $\frac{\partial}{\partial z}=0$ at both
-the upper and lower boundaries.
-
-\item Line 21,
-\begin{verbatim}
-diffKhS=1.E3,
-\end{verbatim}
-this line sets the horizontal diffusion coefficient for salinity
-to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
-operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
-all boundaries.
-
-\item Line 22,
-\begin{verbatim}
-diffKzS=3.E-5,
-\end{verbatim}
-this line sets the vertical diffusion coefficient for salinity
-to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
-condition on this operator is $\frac{\partial}{\partial z}=0$ at both
-the upper and lower boundaries.
-
-\item Lines 23-26
-\begin{verbatim}
-beta=1.E-11,
-\end{verbatim}
-\vspace{-5mm}$\cdots$\\
-These settings do not apply for this experiment.
+\item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets
+the Laplacian friction coefficient to $400 m^2s^{-1}$
+\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
+$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
+
+\item Lines 15 and 16
+\begin{verbatim}
+rigidLid=.FALSE.,
+implicitFreeSurface=.TRUE.,
+\end{verbatim}
+these lines suppress the rigid lid formulation of the surface
+pressure inverter and activate the implicit free surface form
+of the pressure inverter.
\item Line 27,
\begin{verbatim}
-gravity=9.81,
+startTime=0,
\end{verbatim}
-Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
-{\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\
-{\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\
-{\it S/R INI\_PARMS}~({\it ini\_parms.F})\\
-{\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})
-\end{minipage}
-}
+this line indicates that the experiment should start from $t=0$
+and implicitly suppresses searching for checkpoint files associated
+with restarting an numerical integration from a previously saved state.
-
-\item Line 28-29,
+\item Line 29,
\begin{verbatim}
-rigidLid=.FALSE.,
-implicitFreeSurface=.TRUE.,
+endTime=12000,
\end{verbatim}
-Selects the barotropic pressure equation to be the implicit free surface
-formulation.
+this line indicates that the experiment should start finish at $t=12000s$.
+A restart file will be written at this time that will enable the
+simulation to be continued from this point.
\item Line 30,
\begin{verbatim}
-eosType='POLY3',
+deltaTmom=1200,
\end{verbatim}
-Selects the third order polynomial form of the equation of state.\\
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R FIND\_RHO}~({\it find\_rho.F})\\
-{\it S/R FIND\_ALPHA}~({\it find\_alpha.F})
-\end{minipage}
-}
+This line sets the momentum equation timestep to $1200s$.
-\item Line 31,
+\item Line 39,
\begin{verbatim}
-readBinaryPrec=32,
+usingCartesianGrid=.TRUE.,
\end{verbatim}
-Sets format for reading binary input datasets holding model fields to
-use 32-bit representation for floating-point numbers.\\
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\
-{\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})
-\end{minipage}
-}
+This line requests that the simulation be performed in a
+Cartesian coordinate system.
-\item Line 36,
+\item Line 41,
\begin{verbatim}
-cg2dMaxIters=1000,
+delX=60*20E3,
\end{verbatim}
-Sets maximum number of iterations the two-dimensional, conjugate
-gradient solver will use, {\bf irrespective of convergence
-criteria being met}.\\
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R CG2D}~({\it cg2d.F})
-\end{minipage}
-}
-
-\item Line 37,
-\begin{verbatim}
-cg2dTargetResidual=1.E-13,
-\end{verbatim}
-Sets the tolerance which the two-dimensional, conjugate
-gradient solver will use to test for convergence in equation
-\ref{EQ:eg-hs-congrad_2d_resid} to $1 \times 10^{-13}$.
-Solver will iterate until
-tolerance falls below this value or until the maximum number of
-solver iterations is reached.\\
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R CG2D}~({\it cg2d.F})
-\end{minipage}
-}
+This line sets the horizontal grid spacing between each x-coordinate line
+in the discrete grid. The syntax indicates that the discrete grid
+should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$
+($20$~km).
\item Line 42,
\begin{verbatim}
-startTime=0,
+delY=60*20E3,
\end{verbatim}
-Sets the starting time for the model internal time counter.
-When set to non-zero this option implicitly requests a
-checkpoint file be read for initial state.
-By default the checkpoint file is named according to
-the integer number of time steps in the {\bf startTime} value.
-The internal time counter works in seconds.
+This line sets the horizontal grid spacing between each y-coordinate line
+in the discrete grid to $20 \times 10^{3}m$ ($20$~km).
\item Line 43,
\begin{verbatim}
-endTime=2808000.,
-\end{verbatim}
-Sets the time (in seconds) at which this simulation will terminate.
-At the end of a simulation a checkpoint file is automatically
-written so that a numerical experiment can consist of multiple
-stages.
-
-\item Line 44,
-\begin{verbatim}
-#endTime=62208000000,
+delZ=5000,
\end{verbatim}
-A commented out setting for endTime for a 2000 year simulation.
-
-\item Line 45,
-\begin{verbatim}
-deltaTmom=2400.0,
-\end{verbatim}
-Sets the timestep $\delta t_{v}$ used in the momentum equations to
-$20~{\rm mins}$.
-See section \ref{SEC:mom_time_stepping}.
-
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R TIMESTEP}({\it timestep.F})
-\end{minipage}
-}
+This line sets the vertical grid spacing between each z-coordinate line
+in the discrete grid to $5000m$ ($5$~km).
\item Line 46,
\begin{verbatim}
-tauCD=321428.,
-\end{verbatim}
-Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.
-See section \ref{SEC:cd_scheme}.
-
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R INI\_PARMS}({\it ini\_parms.F})\\
-{\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})
-\end{minipage}
-}
-
-\item Line 47,
-\begin{verbatim}
-deltaTtracer=108000.,
-\end{verbatim}
-Sets the default timestep, $\delta t_{\theta}$, for tracer equations to
-$30~{\rm hours}$.
-See section \ref{SEC:tracer_time_stepping}.
-
-\fbox{
-\begin{minipage}{5.0in}
-{\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})
-\end{minipage}
-}
-
-\item Line 47,
-\begin{verbatim}
bathyFile='topog.box'
\end{verbatim}
This line specifies the name of the file from which the domain
@@ -584,12 +290,12 @@
to high coordinate for both axes. The units and orientation of the
depths in this file are the same as used in the MITgcm code. In this
experiment, a depth of $0m$ indicates a solid wall and a depth
-of $-2000m$ indicates open ocean. The matlab program
+of $-5000m$ indicates open ocean. The matlab program
{\it input/gendata.m} shows an example of how to generate a
bathymetry file.
-\item Line 50,
+\item Line 49,
\begin{verbatim}
zonalWindFile='windx.sin_y'
\end{verbatim}
@@ -597,9 +303,7 @@
surface wind stress is read. This file is also a two-dimensional
($x,y$) map and is enumerated and formatted in the same manner as the
bathymetry file. The matlab program {\it input/gendata.m} includes example
-code to generate a valid
-{\bf zonalWindFile}
-file.
+code to generate a valid {\bf zonalWindFile} file.
\end{itemize}
@@ -608,20 +312,20 @@
notes.
\begin{small}
-\input{part3/case_studies/climatalogical_ogcm/input/data}
+\input{part3/case_studies/barotropic_gyre/input/data}
\end{small}
\subsubsection{File {\it input/data.pkg}}
\label{www:tutorials}
This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
\subsubsection{File {\it input/eedata}}
\label{www:tutorials}
This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
\subsubsection{File {\it input/windx.sin\_y}}
\label{www:tutorials}
@@ -640,7 +344,7 @@
The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
map of depth values. For this experiment values are either
-$0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep
+$0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep
ocean. The file contains a raw binary stream of data that is enumerated
in the same way as standard MITgcm two-dimensional, horizontal arrays.
The included matlab program {\it input/gendata.m} gives a complete
@@ -663,40 +367,22 @@
the lateral domain extent in grid points for the
axis aligned with the y-coordinate.
-\item Line 49,
-\begin{verbatim} Nr=4, \end{verbatim} this line sets
-the vertical domain extent in grid points.
-
\end{itemize}
\begin{small}
-\input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}
+\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
\end{small}
\subsubsection{File {\it code/CPP\_OPTIONS.h}}
\label{www:tutorials}
This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
\label{www:tutorials}
This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
-\subsubsection{Other Files }
-\label{www:tutorials}
-
-Other files relevant to this experiment are
-\begin{itemize}
-\item {\it model/src/ini\_cori.F}. This file initializes the model
-coriolis variables {\bf fCorU}.
-\item {\it model/src/ini\_spherical\_polar\_grid.F}
-\item {\it model/src/ini\_parms.F},
-\item {\it input/windx.sin\_y},
-\end{itemize}
-contain the code customisations and parameter settings for this
-experiments. Below we describe the customisations
-to these files associated with this experiment.
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