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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 common to geophysical
22  fluid dynamics.  fluid dynamics.
23    
24  \subsection{Overview}  \subsection{Overview}
25  \label{www:tutorials}  \label{www:tutorials}
26                                                                                    
27                                                                                    
28  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
29  a laboratory experiment with a rotating tank of water with an ice  a laboratory experiment with a rotating tank of water with an ice
30  bucket in the center. The simulation is configured for a laboratory  bucket in the center. The simulation is configured for a laboratory
31  scale on a 3^{\circ} \times 20cm cyclindrical grid with twenty-nine vertical  scale on a
32  levels.    $3^{\circ}$ $\times$ 20cm
33  \\  cyclindrical grid with twenty-nine vertical
34    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.  
35  \\  \\
36    
37    
 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.  
38    
39    
40    
41  \subsection{Discrete Numerical Configuration}  \subsection{Equations Solved}
42  \label{www:tutorials}  \label{www:tutorials}
43    
44    
45   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}  
46  \label{www:tutorials}  \label{www:tutorials}
47    
48  The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.   The domain is discretised with
49  This value is chosen to yield a Munk layer width \cite{adcroft:95},  a uniform grid spacing in the horizontal set to
50  \begin{eqnarray}   $\Delta x=\Delta y=20$~km, so
51  \label{EQ:eg-hs-munk_layer}  that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
52  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
 \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.  
 \\  
53    
 \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 $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.  
 \\  
54    
55  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \subsection{Code Configuration}
 $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. 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.  
 \\  
   
 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  
 \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}  
56  \label{www:tutorials}  \label{www:tutorials}
57  \label{SEC:eg-hs_examp_exp_config}  \label{SEC:eg-baro-code_config}
58    
59  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
60  directory {\it verification/hs94.128x64x5}.  The experiment files  directory {\it verification/rotatingi\_tank/}.  The experiment files
61  \begin{itemize}  \begin{itemize}
62  \item {\it input/data}  \item {\it input/data}
63  \item {\it input/data.pkg}  \item {\it input/data.pkg}
64  \item {\it input/eedata},  \item {\it input/eedata},
65  \item {\it input/windx.bin},  \item {\it input/bathyPol.bin},
66  \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},  
67  \item {\it code/CPP\_EEOPTIONS.h}  \item {\it code/CPP\_EEOPTIONS.h}
68  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
69  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
70  \end{itemize}  \end{itemize}
71  contain the code customizations and parameter settings for these  
72    contain the code customizations and parameter settings for this
73  experiments. Below we describe the customizations  experiments. Below we describe the customizations
74  to these files associated with this experiment.  to these files associated with this experiment.
75    
# Line 330  are Line 82  are
82    
83  \begin{itemize}  \begin{itemize}
84    
85  \item Lines 7-10 and 11-14  \item Line X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
86  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally
87  $\cdots$ \\  low because of the small scale, presumably.... qqq
 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}  
 }  
88    
89  \item Line 16,  \item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
90  \begin{verbatim}  coriolis term, and represents a tank spinning at qqq
91  viscAh=5.E5,  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
92  \end{verbatim}  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
 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 $x$.  
93    
94  \item Lines 9,  \item Lines 15 and 16
95  \begin{verbatim}  \begin{verbatim}
96  no_slip_bottom=.TRUE.  rigidLid=.TRUE.,
97    implicitFreeSurface=.FALSE.,
98  \end{verbatim}  \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.  
99    
100  \item Line 19,  these lines do the opposite of the following:
101  \begin{verbatim}  suppress the rigid lid formulation of the surface
102  diffKhT=1.E3,  pressure inverter and activate the implicit free surface form
103  \end{verbatim}  of the pressure inverter.
 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.  
104    
105  \item Line 27,  \item Line 27,
106  \begin{verbatim}  \begin{verbatim}
107  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}  
 }  
   
   
 \item Line 28-29,  
 \begin{verbatim}  
 rigidLid=.FALSE.,  
 implicitFreeSurface=.TRUE.,  
108  \end{verbatim}  \end{verbatim}
109  Selects the barotropic pressure equation to be the implicit free surface  this line indicates that the experiment should start from $t=0$
110  formulation.  and implicitly suppresses searching for checkpoint files associated
111    with restarting an numerical integration from a previously saved state.
112    
113  \item Line 30,  \item Line 30,
114  \begin{verbatim}  \begin{verbatim}
115  eosType='POLY3',  deltaT=0.1,
116  \end{verbatim}  \end{verbatim}
117  Selects the third order polynomial form of the equation of state.\\  This line sets the integration timestep to $0.1s$.  This is an unsually
118  \fbox{  small value among the examples due to the small physical scale of the
119  \begin{minipage}{5.0in}  experiment.
 {\it S/R FIND\_RHO}~({\it find\_rho.F})\\  
 {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})  
 \end{minipage}  
 }  
120    
121  \item Line 31,  \item Line 39,
122  \begin{verbatim}  \begin{verbatim}
123  readBinaryPrec=32,  usingCylindricalGrid=.TRUE.,
124  \end{verbatim}  \end{verbatim}
125  Sets format for reading binary input datasets holding model fields to  This line requests that the simulation be performed in a
126  use 32-bit representation for floating-point numbers.\\  cylindrical coordinate system.
 \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}  
 }  
127    
128  \item Line 36,  \item Line qqq,
129  \begin{verbatim}  \begin{verbatim}
130  cg2dMaxIters=1000,  dXspacing=3,
131  \end{verbatim}  \end{verbatim}
132  Sets maximum number of iterations the two-dimensional, conjugate  This line sets the azimuthal grid spacing between each x-coordinate line
133  gradient solver will use, {\bf irrespective of convergence  in the discrete grid. The syntax indicates that the discrete grid
134  criteria being met}.\\  should be comprise of $120$ grid lines each separated by $3^{\circ}$.
135  \fbox{                                                                                  
 \begin{minipage}{5.0in}  
 {\it S/R CG2D}~({\it cg2d.F})  
 \end{minipage}  
 }  
136    
 \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}  
 }  
137    
138  \item Line 42,  \item Line qqq,
139  \begin{verbatim}  \begin{verbatim}
140  startTime=0,  dYspacing=0.01,
141  \end{verbatim}  \end{verbatim}
142  Sets the starting time for the model internal time counter.  This line sets the radial grid spacing between each $\rho$-coordinate line
143  When set to non-zero this option implicitly requests a  in the discrete grid to $1cm$.
 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.  
144    
145  \item Line 43,  \item Line 43,
146  \begin{verbatim}  \begin{verbatim}
147  endTime=2808000.,  delZ=29*0.005,
 \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,  
148  \end{verbatim}  \end{verbatim}
149  A commented out setting for endTime for a 2000 year simulation.  This line sets the vertical grid spacing between each z-coordinate line
150    in the discrete grid to $5000m$ ($5$~km).
 \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}  
 }  
151    
152  \item Line 46,  \item Line 46,
153  \begin{verbatim}  \begin{verbatim}
154  tauCD=321428.,  bathyFile='bathyPol.bin',
 \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'  
155  \end{verbatim}  \end{verbatim}
156  This line specifies the name of the file from which the domain  This line specifies the name of the file from which the domain
157  bathymetry is read. This file is a two-dimensional ($x,y$) map of  ``bathymetry'' (tank depth) is read. This file is a two-dimensional
158    ($x,y$) map of
159  depths. This file is assumed to contain 64-bit binary numbers  depths. This file is assumed to contain 64-bit binary numbers
160  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 $x$
161  coordinate varying fastest. The points are ordered from low coordinate  coordinate varying fastest. The points are ordered from low coordinate
162  to high coordinate for both axes. The units and orientation of the  to high coordinate for both axes.  The units and orientation of the
163  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
164  experiment, a depth of $0m$ indicates a solid wall and a depth  experiment, a depth of $0m$ indicates an area outside of the tank
165  of $-2000m$ indicates open ocean. The matlab program  and a depth
166  {\it input/gendata.m} shows an example of how to generate a  f $-0.145m$ indicates the tank itself.
 bathymetry file.  
167    
168    \item Line 49,
169    \begin{verbatim}
170    hydrogThetaFile='thetaPol.bin',
171    \end{verbatim}
172    This line specifies the name of the file from which the initial values
173    of $\theta$
174    are read. This file is a three-dimensional
175    ($x,y,z$) map and is enumerated and formatted in the same manner as the
176    bathymetry file.
177    
178  \item Line 50,  \item Line qqq
179  \begin{verbatim}  \begin{verbatim}
180  zonalWindFile='windx.sin_y'   tCyl  = 0
181  \end{verbatim}  \end{verbatim}
182  This line specifies the name of the file from which the x-direction  This line specifies the temperature in degrees Celsius of the interior
183  surface wind stress is read. This file is also a two-dimensional  wall of the tank -- usually a bucket of ice water.
184  ($x,y$) 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.    
185    
186  \end{itemize}  \end{itemize}
187    
# Line 608  that are described in the MITgcm Getting Line 190  that are described in the MITgcm Getting
190  notes.  notes.
191    
192  \begin{small}  \begin{small}
193  \input{part3/case_studies/climatalogical_ogcm/input/data}  \input{part3/case_studies/rotating_tank/input/data}
194  \end{small}  \end{small}
195    
196  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
197  \label{www:tutorials}  \label{www:tutorials}
198    
199  This file uses standard default values and does not contain  This file uses standard default values and does not contain
200  customisations for this experiment.  customizations for this experiment.
201    
202  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
203  \label{www:tutorials}  \label{www:tutorials}
204    
205  This file uses standard default values and does not contain  This file uses standard default values and does not contain
206  customisations for this experiment.  customizations for this experiment.
207    
208  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/thetaPol.bin}}
209  \label{www:tutorials}  \label{www:tutorials}
210    
211  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
212  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of initial values of $\theta$ in degrees Celsius.
 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.  
213    
214  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/bathyPol.bin}}
215  \label{www:tutorials}  \label{www:tutorials}
216    
217    
218  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
219  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
220  $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep  $0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
221  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
222  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.  
223    
224  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
225  \label{www:tutorials}  \label{www:tutorials}
# Line 654  Two lines are customized in this file fo Line 229  Two lines are customized in this file fo
229  \begin{itemize}  \begin{itemize}
230    
231  \item Line 39,  \item Line 39,
232  \begin{verbatim} sNx=60, \end{verbatim} this line sets  \begin{verbatim} sNx=120, \end{verbatim} this line sets
233  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
234  axis aligned with the x-coordinate.  axis aligned with the x-coordinate.
235    
236  \item Line 40,  \item Line 40,
237  \begin{verbatim} sNy=60, \end{verbatim} this line sets  \begin{verbatim} sNy=31, \end{verbatim} this line sets
238  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
239  axis aligned with the y-coordinate.  axis aligned with the y-coordinate.
240    
 \item Line 49,  
 \begin{verbatim} Nr=4,   \end{verbatim} this line sets  
 the vertical domain extent in grid points.  
   
241  \end{itemize}  \end{itemize}
242    
243  \begin{small}  \begin{small}
244  \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}  \input{part3/case_studies/rotating_tank/code/SIZE.h}
245  \end{small}  \end{small}
246    
247  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
248  \label{www:tutorials}  \label{www:tutorials}
249    
250  This file uses standard default values and does not contain  This file uses standard default values and does not contain
251  customisations for this experiment.  customizations for this experiment.
252    
253    
254  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.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    
 \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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