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1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
 \section{Simulating a Rotating Tank in Cylindrical Coordinates}  
 \label{www:tutorials}  
 \label{sect:eg-tank}  
   
4  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
5    
6  %\begin{center}  %\begin{center}
7  %{\Large \bf Simulating a Rotating Tank in Cylindrical Coordinates}  %{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical
8  %  %Coordinates}
9  %  %
10  %\vspace*{4mm}  %\vspace*{4mm}
11  %  %
12  %\vspace*{3mm}  %\vspace*{3mm}
13  %{\large June 2004}  %{\large May 2001}
14  %\end{center}  %\end{center}
15    
16  \subsection{Introduction}  \section{A Rotating Tank in Cylindrical Coordinates}
17    \label{sect:eg-tank}
18  \label{www:tutorials}  \label{www:tutorials}
19    
20  This section illustrates an example of MITgcm simulating a laboratory  This section illustrates an example of MITgcm simulating a laboratory
21  experiment on much smaller scales than those common to geophysical  experiment on much smaller scales than those commonly considered in  
22    geophysical
23  fluid dynamics.  fluid dynamics.
24    
25  \subsection{Overview}  \subsection{Overview}
26  \label{www:tutorials}  \label{www:tutorials}
27                                                                                    
28                                                                                    
29  This example experiment demonstrates using the MITgcm to simulate  This example configuration demonstrates using the MITgcm to simulate
30  a laboratory experiment with a rotating tank of water with an ice  a laboratory demonstration using a rotating tank of water with an ice
31  bucket in the center. The simulation is configured for a laboratory  bucket in the center. The simulation is configured for a laboratory
32  scale on a 3^{\circ} \times 20cm cyclindrical grid with twenty-nine vertical  scale on a
33  levels.    $3^{\circ}$ $\times$ 20cm
34    cyclindrical grid with twenty-nine vertical
35    levels.
36  \\  \\
37    example illustration from GFD lab here
 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.  
38  \\  \\
39    
40    
 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.  
41    
42    
43    
44  \subsection{Discrete Numerical Configuration}  \subsection{Equations Solved}
45  \label{www:tutorials}  \label{www:tutorials}
46    
47    
48   The model is configured in hydrostatic form.  The domain is discretised with  \subsection{Discrete Numerical Configuration}
 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:  
   
 \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}  
 \\  
 \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}  
 & = &  
 \begin{cases}  
 {\cal F}_v & \text{(surface)} \\  
 0 & \text{(interior)}  
 \end{cases}  
 \\  
 \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.  
 \\  
   
 \subsubsection{Numerical Stability Criteria}  
49  \label{www:tutorials}  \label{www:tutorials}
50    
51  The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.   The domain is discretised with
52  This value is chosen to yield a Munk layer width \cite{adcroft:95},  a uniform cylindrical grid spacing in the horizontal set to
53  \begin{eqnarray}   $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
54  \label{EQ:eg-hs-munk_layer}  that there are 120 grid cells in the azimuthal direction and thirty-one grid cells in the radial. Vertically the
55  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  model is configured with twenty-nine layers of uniform 0.5cm thickness.
 \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 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  
 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}  
 \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.  
56  \\  \\
57    something about heat flux
58    
59  The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients  \subsection{Code Configuration}
 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  
 \cite{adcroft:95}  
   
 \begin{eqnarray}  
 \label{EQ:eg-hs-inertial_stability}  
 S_{i} = f^{2} {\delta t_v}^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 The advective CFL \cite{adcroft:95} for a 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}  
 \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}  
   
 \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}  
60  \label{www:tutorials}  \label{www:tutorials}
61  \label{SEC:eg-hs_examp_exp_config}  \label{SEC:eg-baro-code_config}
62    
63  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
64  directory {\it verification/hs94.128x64x5}.  The experiment files  directory {\it verification/rotatingi\_tank/}.  The experiment files
65  \begin{itemize}  \begin{itemize}
66  \item {\it input/data}  \item {\it input/data}
67  \item {\it input/data.pkg}  \item {\it input/data.pkg}
68  \item {\it input/eedata},  \item {\it input/eedata},
69  \item {\it input/windx.bin},  \item {\it input/bathyPol.bin},
70  \item {\it input/windy.bin},  \item {\it input/thetaPol.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},  
71  \item {\it code/CPP\_EEOPTIONS.h}  \item {\it code/CPP\_EEOPTIONS.h}
72  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
73  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
74  \end{itemize}  \end{itemize}
75  contain the code customizations and parameter settings for these  
76    contain the code customizations and parameter settings for this
77  experiments. Below we describe the customizations  experiments. Below we describe the customizations
78  to these files associated with this experiment.  to these files associated with this experiment.
79    
# Line 330  are Line 86  are
86    
87  \begin{itemize}  \begin{itemize}
88    
89  \item Lines 7-10 and 11-14  \item Line 10, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
90  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$,
91  $\cdots$ \\  which is ususally
92  set reference values for potential  low because of the small scale, presumably.... qqq
93  temperature and salinity at each model level in units of $^{\circ}$C and  
94  ${\rm ppt}$. The entries are ordered from surface to depth.  \item Line 19, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
95  Density is calculated from anomalies at each level evaluated  coriolis term, and represents a tank spinning at 2/s
96  with respect to the reference values set here.\\  \item Line 20, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
97  \fbox{  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
98  \begin{minipage}{5.0in}  
99  {\it S/R INI\_THETA}({\it ini\_theta.F})  \item Lines 27 and 28
100  \end{minipage}  \begin{verbatim}
101  }  rigidLid=.TRUE.,
102    implicitFreeSurface=.FALSE.,
103    \end{verbatim}
104  \item Line 15,  
105  \begin{verbatim} viscAz=1.E-3, \end{verbatim}  qqq these lines do the opposite of the following:
106  this line sets the vertical Laplacian dissipation coefficient to  suppress the rigid lid formulation of the surface
107  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions  pressure inverter and activate the implicit free surface form
108  for this operator are specified later. This variable is copied into  of the pressure inverter.
 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 27,  
 \begin{verbatim}  
 gravity=9.81,  
 \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}  
 }  
   
   
 \item Line 28-29,  
 \begin{verbatim}  
 rigidLid=.FALSE.,  
 implicitFreeSurface=.TRUE.,  
 \end{verbatim}  
 Selects the barotropic pressure equation to be the implicit free surface  
 formulation.  
   
 \item Line 30,  
 \begin{verbatim}  
 eosType='POLY3',  
 \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}  
 }  
   
 \item Line 31,  
 \begin{verbatim}  
 readBinaryPrec=32,  
 \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}  
 }  
   
 \item Line 36,  
 \begin{verbatim}  
 cg2dMaxIters=1000,  
 \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}  
 }  
109    
110  \item Line 37,  \item Line 44,
111  \begin{verbatim}  \begin{verbatim}
112  cg2dTargetResidual=1.E-13,  nIter=0,
113  \end{verbatim}  \end{verbatim}
114  Sets the tolerance which the two-dimensional, conjugate  this line indicates that the experiment should start from $t=0$
115  gradient solver will use to test for convergence in equation  and implicitly suppresses searching for checkpoint files associated
116  \ref{EQ:eg-hs-congrad_2d_resid} to $1 \times 10^{-13}$.  with restarting an numerical integration from a previously saved state.
 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}  
 }  
117    
118  \item Line 42,  \item Line 47,
119  \begin{verbatim}  \begin{verbatim}
120  startTime=0,  deltaT=0.1,
121  \end{verbatim}  \end{verbatim}
122  Sets the starting time for the model internal time counter.  This line sets the integration timestep to $0.1s$.  This is an unsually
123  When set to non-zero this option implicitly requests a  small value among the examples due to the small physical scale of the
124  checkpoint file be read for initial state.  experiment.
 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.  
125    
126  \item Line 43,  \item Line 58,
127  \begin{verbatim}  \begin{verbatim}
128  endTime=2808000.,  usingCylindricalGrid=.TRUE.,
129  \end{verbatim}  \end{verbatim}
130  Sets the time (in seconds) at which this simulation will terminate.  This line requests that the simulation be performed in a
131  At the end of a simulation a checkpoint file is automatically  cylindrical coordinate system.
 written so that a numerical experiment can consist of multiple  
 stages.  
132    
133  \item Line 44,  \item Line 60,
134  \begin{verbatim}  \begin{verbatim}
135  #endTime=62208000000,  dXspacing=3,
136  \end{verbatim}  \end{verbatim}
137  A commented out setting for endTime for a 2000 year simulation.  This line sets the azimuthal grid spacing between each $x$-coordinate line
138    in the discrete grid. The syntax indicates that the discrete grid
139    should be comprise of $120$ grid lines each separated by $3^{\circ}$.
140                                                                                    
141    
 \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}  
 }  
142    
143  \item Line 46,  \item Line 61,
144  \begin{verbatim}  \begin{verbatim}
145  tauCD=321428.,  dYspacing=0.01,
146  \end{verbatim}  \end{verbatim}
147  Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.  This line sets the radial cylindrical grid spacing between each $a$-coordinate line
148  See section \ref{SEC:cd_scheme}.  in the discrete grid to $1cm$.
   
 \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}  
 }  
149    
150  \item Line 47,  \item Line 62,
151  \begin{verbatim}  \begin{verbatim}
152  deltaTtracer=108000.,  delZ=29*0.005,
153  \end{verbatim}  \end{verbatim}
154  Sets the default timestep, $\delta t_{\theta}$, for tracer equations to  This line sets the vertical grid spacing between each z-coordinate line
155  $30~{\rm hours}$.  in the discrete grid to $5000m$ ($5$~km).
 See section \ref{SEC:tracer_time_stepping}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})  
 \end{minipage}  
 }  
156    
157  \item Line 47,  \item Line 68,
158  \begin{verbatim}  \begin{verbatim}
159  bathyFile='topog.box'  bathyFile='bathyPol.bin',
160  \end{verbatim}  \end{verbatim}
161  This line specifies the name of the file from which the domain  This line specifies the name of the file from which the domain
162  bathymetry is read. This file is a two-dimensional ($x,y$) map of  ``bathymetry'' (tank depth) is read. This file is a two-dimensional
163    ($a,\phi$) map of
164  depths. This file is assumed to contain 64-bit binary numbers  depths. This file is assumed to contain 64-bit binary numbers
165  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 $\phi$
166  coordinate varying fastest. The points are ordered from low coordinate  coordinate varying fastest. The points are ordered from low coordinate
167  to high coordinate for both axes. The units and orientation of the  to high coordinate for both axes.  The units and orientation of the
168  depths in this file are the same as used in the MITgcm code. In this  depths in this file are the same as used in the MITgcm code. In this
169  experiment, a depth of $0m$ indicates a solid wall and a depth  experiment, a depth of $0m$ indicates an area outside of the tank
170  of $-2000m$ indicates open ocean. The matlab program  and a depth
171  {\it input/gendata.m} shows an example of how to generate a  f $-0.145m$ indicates the tank itself.
 bathymetry file.  
172    
173    \item Line 67,
174    \begin{verbatim}
175    hydrogThetaFile='thetaPol.bin',
176    \end{verbatim}
177    This line specifies the name of the file from which the initial values
178    of temperature
179    are read. This file is a three-dimensional
180    ($x,y,z$) map and is enumerated and formatted in the same manner as the
181    bathymetry file.
182    
183  \item Line 50,  \item Line qqq
184  \begin{verbatim}  \begin{verbatim}
185  zonalWindFile='windx.sin_y'   tCyl  = 0
186  \end{verbatim}  \end{verbatim}
187  This line specifies the name of the file from which the x-direction  This line specifies the temperature in degrees Celsius of the interior
188  surface wind stress is read. This file is also a two-dimensional  wall of the tank -- usually a bucket of ice water.
189  ($x,y$) 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.    
190    
191  \end{itemize}  \end{itemize}
192    
# Line 608  that are described in the MITgcm Getting Line 195  that are described in the MITgcm Getting
195  notes.  notes.
196    
197  \begin{small}  \begin{small}
198  \input{part3/case_studies/climatalogical_ogcm/input/data}  \input{part3/case_studies/rotating_tank/input/data}
199  \end{small}  \end{small}
200    
201  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
202  \label{www:tutorials}  \label{www:tutorials}
203    
204  This file uses standard default values and does not contain  This file uses standard default values and does not contain
205  customisations for this experiment.  customizations for this experiment.
206    
207  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
208  \label{www:tutorials}  \label{www:tutorials}
209    
210  This file uses standard default values and does not contain  This file uses standard default values and does not contain
211  customisations for this experiment.  customizations for this experiment.
212    
213  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/thetaPol.bin}}
214  \label{www:tutorials}  \label{www:tutorials}
215    
216  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
217  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of initial values of $\theta$ in degrees Celsius.  This particular
218  Although $\tau_{x}$ is only a function of $y$n in this experiment  experiment is set to random values x around 20C to provide initial
219  this file must still define a complete two-dimensional map in order  perturbations.
 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.  
220    
221  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/bathyPol.bin}}
222  \label{www:tutorials}  \label{www:tutorials}
223    
224    
225  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
226  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
227  $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep  $0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
228  ocean. The file contains a raw binary stream of data that is enumerated  the tank. The file contains a raw binary stream of data that is enumerated
229  in the same way as standard MITgcm two-dimensional, horizontal arrays.  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.  
230    
231  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
232  \label{www:tutorials}  \label{www:tutorials}
# Line 654  Two lines are customized in this file fo Line 236  Two lines are customized in this file fo
236  \begin{itemize}  \begin{itemize}
237    
238  \item Line 39,  \item Line 39,
239  \begin{verbatim} sNx=60, \end{verbatim} this line sets  \begin{verbatim} sNx=120, \end{verbatim} this line sets
240  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
241  axis aligned with the x-coordinate.  axis aligned with the x-coordinate.
242    
243  \item Line 40,  \item Line 40,
244  \begin{verbatim} sNy=60, \end{verbatim} this line sets  \begin{verbatim} sNy=31, \end{verbatim} this line sets
245  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
246  axis aligned with the y-coordinate.  axis aligned with the y-coordinate.
247    
 \item Line 49,  
 \begin{verbatim} Nr=4,   \end{verbatim} this line sets  
 the vertical domain extent in grid points.  
   
248  \end{itemize}  \end{itemize}
249    
250  \begin{small}  \begin{small}
251  \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}  \input{part3/case_studies/rotating_tank/code/SIZE.h}
252  \end{small}  \end{small}
253    
254  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
255  \label{www:tutorials}  \label{www:tutorials}
256    
257  This file uses standard default values and does not contain  This file uses standard default values and does not contain
258  customisations for this experiment.  customizations for this experiment.
259    
260    
261  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
262  \label{www:tutorials}  \label{www:tutorials}
263    
264  This file uses standard default values and does not contain  This file uses standard default values and does not contain
265  customisations for this experiment.  customizations for this experiment.
266    
 \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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