--- manual/s_examples/rotating_tank/tank.tex	2004/07/26 16:21:15	1.3
+++ manual/s_examples/rotating_tank/tank.tex	2005/06/14 20:09:04	1.12
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.3 2004/07/26 16:21:15 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.12 2005/06/14 20:09:04 afe Exp $
 % $Name:  $
 
 \bodytext{bgcolor="#FFFFFFFF"}
@@ -13,192 +13,72 @@
 %{\large May 2001}
 %\end{center}
 
-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.
-
 \section{A Rotating Tank in Cylindrical Coordinates}
 \label{sect:eg-tank}
 \label{www:tutorials}
-
-
-This example experiment demonstrates using the MITgcm to simulate
-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 $\beta = 10^{-11}s^{-1}m^{-1}$. 
-\\
+\begin{rawhtml}
+<!-- CMIREDIR:eg-tank: -->
+\end{rawhtml}
+
+This section illustrates an example of MITgcm simulating a laboratory
+experiment on much smaller scales than those commonly considered in  
+geophysical
+fluid dynamics.
+
+\subsection{Overview}
+\label{www:tutorials}
+                                                                          
+This example configuration demonstrates using the MITgcm to simulate a
+laboratory demonstration using a differentially heated rotating
+annulus of water.  The simulation is configured for a laboratory scale
+on a $3^{\circ}$ $\times$ 1cm cyclindrical grid with twenty-nine
+vertical levels of 0.5cm each.  This is a typical laboratory setup for
+illustration principles of GFD, as well as for a laboratory data
+assimilation project.
 \\
- 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 $0.1N m^{-2}$. 
+example illustration from GFD lab here
 \\
-\\
-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-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 + g\frac{\partial \eta}{\partial y} -
-              A_{h}\nabla_{h}^2v
-& = &
-0
-\\
-\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
-&=&
-0
-\end{eqnarray}
-
-\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 $400 m s^{-1}$.
-This value is chosen to yield a Munk layer width \cite{adcroft:95},
-
-\begin{eqnarray}
-\label{EQ:eg-baro-munk_layer}
-M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
-\end{eqnarray}
-
-\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 $\delta t=1200$secs. With this time step the stability 
-parameter to the horizontal Laplacian friction \cite{adcroft:95}
-
-
-
-\begin{eqnarray}
-\label{EQ:eg-baro-laplacian_stability}
-S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
-\end{eqnarray}
-
-\noindent evaluates to 0.012, which is well below the 0.3 upper limit
-for stability. 
-\\
-
-\noindent The numerical stability for inertial oscillations  
-\cite{adcroft:95} 
-
-\begin{eqnarray}
-\label{EQ:eg-baro-inertial_stability}
-S_{i} = f^{2} {\delta t}^2
-\end{eqnarray}
-
-\noindent evaluates to $0.0144$, which is well below the $0.5$ upper 
-limit for stability.
+ The domain is discretised with a uniform cylindrical grid spacing in
+the horizontal set to $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
+that there are 120 grid cells in the azimuthal direction and
+thirty-one grid cells in the radial, representing a tank 62cm in
+diameter.  The bathymetry file sets the depth=0 in the nine lowest
+radial rows to represent the central of the annulus.  Vertically the
+model is configured with twenty-nine layers of uniform 0.5cm
+thickness.
 \\
-
-\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-baro-cfl_stability}
-S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
-\end{eqnarray}
-
-\noindent evaluates to 0.12. This is approaching the stability limit
-of 0.5 and limits $\delta t$ to $1200s$.
+something about heat flux
 
 \subsection{Code Configuration}
 \label{www:tutorials}
 \label{SEC:eg-baro-code_config}
 
-The model configuration for this experiment resides under the 
-directory {\it verification/exp0/}.  The experiment files 
+The model configuration for this experiment resides under the
+directory {\it verification/rotatingi\_tank/}.  The experiment files
 \begin{itemize}
 \item {\it input/data}
 \item {\it input/data.pkg}
 \item {\it input/eedata},
-\item {\it input/windx.sin\_y},
-\item {\it input/topog.box},
+\item {\it input/bathyPol.bin},
+\item {\it input/thetaPol.bin},
 \item {\it code/CPP\_EEOPTIONS.h}
 \item {\it code/CPP\_OPTIONS.h},
-\item {\it code/SIZE.h}. 
+\item {\it code/SIZE.h}.
 \end{itemize}
+
 contain the code customizations and parameter settings for this 
 experiments. Below we describe the customizations
 to these files associated with this experiment.
@@ -212,107 +92,142 @@
 
 \begin{itemize}
 
-\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 9-10, \begin{verbatim} 
+viscAh=5.0E-6, 
+viscAz=5.0E-6,
+\end{verbatim} 
+
+
+These lines set the Laplacian friction coefficient in the horizontal
+and vertical, respectively.  Note that they are several orders of
+magnitude smaller than the other examples due to the small scale of
+this example.
+
+\item Lines 13-16, \begin{verbatim} 
+ diffKhT=2.5E-6,
+ diffKzT=2.5E-6,
+ diffKhS=1.0E-6,
+ diffKzS=1.0E-6,
+
+\end{verbatim} 
+
+
+These lines set horizontal and vertical diffusion coefficients for
+temperature and salinity.  Similarly to the friction coefficients, the
+values are a couple of orders of magnitude less than most
+ configurations.
+
 
-\item Lines 15 and 16
+\item Line 17, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the 
+coriolis term, and represents a tank spinning at about 2.4 rpm.
+
+\item Lines 23 and 24
 \begin{verbatim}
-rigidLid=.FALSE.,
-implicitFreeSurface=.TRUE.,
+rigidLid=.TRUE.,
+implicitFreeSurface=.FALSE.,
 \end{verbatim}
-these lines suppress the rigid lid formulation of the surface
-pressure inverter and activate the implicit free surface form
+
+These lines activate  the rigid lid formulation of the surface
+pressure inverter and suppress the implicit free surface form
 of the pressure inverter.
 
-\item Line 27,
+\item Line 40,
 \begin{verbatim}
-startTime=0,
+nIter=0,
 \end{verbatim}
-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.
+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.
+Instead, the file thetaPol.bin will be loaded to initialized the
+temperature fields as indicated below, and other variables will be
+initialized to their defaults.
 
-\item Line 29,
-\begin{verbatim}
-endTime=12000,
-\end{verbatim}
-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,
+\item Line 43,
 \begin{verbatim}
-deltaTmom=1200,
+deltaT=0.1,
 \end{verbatim}
-This line sets the momentum equation timestep to $1200s$.
+This line sets the integration timestep to $0.1s$.  This is an
+unsually small value among the examples due to the small physical
+scale of the experiment.  Using the ensemble Kalman filter to produce
+input fields can necessitate even shorter timesteps.
 
-\item Line 39,
+\item Line 56,
 \begin{verbatim}
-usingCartesianGrid=.TRUE.,
+usingCylindricalGrid=.TRUE.,
 \end{verbatim}
 This line requests that the simulation be performed in a 
-Cartesian coordinate system.
+cylindrical coordinate system.
 
-\item Line 41,
+\item Line 57,
 \begin{verbatim}
-delX=60*20E3,
+dXspacing=3,
 \end{verbatim}
-This line sets the horizontal grid spacing between each x-coordinate line
+This line sets the azimuthal 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).
+should be comprised of $120$ grid lines each separated by $3^{\circ}$.
+                                                                               
 
-\item Line 42,
+\item Line 58,
 \begin{verbatim}
-delY=60*20E3,
+dYspacing=0.01,
 \end{verbatim}
-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,
+This line sets the radial cylindrical grid spacing between each
+$a$-coordinate line in the discrete grid to $1cm$.
+
+\item Line 59,
 \begin{verbatim}
-delZ=5000,
+delZ=29*0.005,
 \end{verbatim}
-This line sets the vertical grid spacing between each z-coordinate line
-in the discrete grid to $5000m$ ($5$~km).
 
-\item Line 46,
+This line sets the vertical grid spacing between each of 29
+z-coordinate lines in the discrete grid to $0.005m$ ($5$~mm).
+
+\item Line 64,
 \begin{verbatim}
-bathyFile='topog.box'
+bathyFile='bathyPol.bin',
 \end{verbatim}
 This line specifies the name of the file from which the domain
-bathymetry is read. This file is a two-dimensional ($x,y$) map of
+``bathymetry'' (tank depth) is read. This file is a two-dimensional 
+($a,\phi$) map of
 depths. This file is assumed to contain 64-bit binary numbers 
-giving the depth of the model at each grid cell, ordered with the x 
+giving the depth of the model at each grid cell, ordered with the $\phi$ 
 coordinate varying fastest. The points are ordered from low coordinate
-to high coordinate for both axes. The units and orientation of the
+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 $-5000m$ indicates open ocean. The matlab program
-{\it input/gendata.m} shows an example of how to generate a
-bathymetry file.
+experiment, a depth of $0m$ indicates an area outside of the tank
+and a depth
+f $-0.145m$ indicates the tank itself. 
 
+\item Line 65,
+\begin{verbatim}
+hydrogThetaFile='thetaPol.bin',
+\end{verbatim}
+This line specifies the name of the file from which the initial values 
+of temperature
+are read. This file is a three-dimensional
+($x,y,z$) map and is enumerated and formatted in the same manner as the 
+bathymetry file. 
 
-\item Line 49,
+\item Lines 66 and 57
 \begin{verbatim}
-zonalWindFile='windx.sin_y'
+ tCylIn  = 0
+ tCylOut  = 20
 \end{verbatim}
-This line specifies the name of the file from which the x-direction
-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.  
+These line specify the temperatures in degrees Celsius of the interior
+and exterior walls of the tank -- typically taken to be icewater on
+the inside and room temperature on the inside.
+
 
 \end{itemize}
 
-\noindent other lines in the file {\it input/data} are standard values
+\noindent Other lines in the file {\it input/data} are standard values
 that are described in the MITgcm Getting Started and MITgcm Parameters
 notes.
 
 \begin{small}
-\input{part3/case_studies/barotropic_gyre/input/data}
+\input{part3/case_studies/rotating_tank/input/data}
 \end{small}
 
 \subsubsection{File {\it input/data.pkg}}
@@ -327,28 +242,23 @@
 This file uses standard default values and does not contain
 customizations for this experiment.
 
-\subsubsection{File {\it input/windx.sin\_y}}
+\subsubsection{File {\it input/thetaPol.bin}}
 \label{www:tutorials}
 
-The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) 
-map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
-Although $\tau_{x}$ is only a function of $y$n in this experiment
-this file must still define a complete two-dimensional map in order
-to be compatible with the standard code for loading forcing fields 
-in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
-code for creating the {\it input/windx.sin\_y} file.
+The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$) 
+map of initial values of $\theta$ in degrees Celsius.  This particular 
+experiment is set to random values x around 20C to provide initial 
+perturbations.
 
-\subsubsection{File {\it input/topog.box}}
+\subsubsection{File {\it input/bathyPol.bin}}
 \label{www:tutorials}
 
 
-The {\it input/topog.box} file specifies a two-dimensional ($x,y$) 
+The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$) 
 map of depth values. For this experiment values are either
-$0m$ 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
+$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
+the tank. 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
-code for creating the {\it input/topog.box} file.
 
 \subsubsection{File {\it code/SIZE.h}}
 \label{www:tutorials}
@@ -358,19 +268,19 @@
 \begin{itemize}
 
 \item Line 39, 
-\begin{verbatim} sNx=60, \end{verbatim} this line sets
+\begin{verbatim} sNx=120, \end{verbatim} this line sets
 the lateral domain extent in grid points for the
 axis aligned with the x-coordinate.
 
 \item Line 40, 
-\begin{verbatim} sNy=60, \end{verbatim} this line sets
+\begin{verbatim} sNy=31, \end{verbatim} this line sets
 the lateral domain extent in grid points for the
 axis aligned with the y-coordinate.
 
 \end{itemize}
 
 \begin{small}
-\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
+\input{part3/case_studies/rotating_tank/code/SIZE.h}
 \end{small}
 
 \subsubsection{File {\it code/CPP\_OPTIONS.h}}
