--- manual/s_examples/rotating_tank/tank.tex 2004/06/22 16:56:31 1.2 +++ manual/s_examples/rotating_tank/tank.tex 2004/07/27 13:40:09 1.9 @@ -1,323 +1,75 @@ -% $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 1.9 2004/07/27 13:40:09 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} +\section{A Rotating Tank in Cylindrical Coordinates} +\label{sect:eg-tank} \label{www:tutorials} -This section illustrates an example of MITgcm simulating a laboratory -experiment on much smaller scales than those common to geophysical +This section illustrates an example of MITgcm simulating a laboratory +experiment on much smaller scales than those common to geophysical fluid dynamics. \subsection{Overview} \label{www:tutorials} - - + + This example experiment demonstrates using the MITgcm to simulate -a laboratory experiment with a rotating tank of water with an ice +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. +scale on a +$3^{\circ}$ $\times$ 20cm +cyclindrical grid with twenty-nine vertical +levels. \\ -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} +\subsection{Equations Solved} \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: - -\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} +\subsection{Discrete Numerical Configuration} \label{www:tutorials} -The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$. -This value is chosen to yield a Munk layer width \cite{adcroft:95}, -\begin{eqnarray} -\label{EQ:eg-hs-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. -\\ + 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. -\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. -\\ - -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} +\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 +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.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/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 these + +contain the code customizations and parameter settings for this experiments. Below we describe the customizations to these files associated with this experiment. @@ -330,276 +82,106 @@ \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 X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets +the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally +low because of the small scale, presumably.... qqq -\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 Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the +coriolis term, and represents a tank spinning at qqq +\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, +\item Lines 15 and 16 \begin{verbatim} -no_slip_bottom=.TRUE. +rigidLid=.TRUE., +implicitFreeSurface=.FALSE., \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. +these lines do the opposite of the following: +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, -\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., +startTime=0, \end{verbatim} -Selects the barotropic pressure equation to be the implicit free surface -formulation. +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 30, \begin{verbatim} -eosType='POLY3', +deltaT=0.1, \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 integration timestep to $0.1s$. This is an unsually +small value among the examples due to the small physical scale of the +experiment. -\item Line 31, +\item Line 39, \begin{verbatim} -readBinaryPrec=32, +usingCylindricalGrid=.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 +cylindrical coordinate system. -\item Line 36, +\item Line qqq, \begin{verbatim} -cg2dMaxIters=1000, +dXspacing=3, \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} -} +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 $120$ grid lines each separated by $3^{\circ}$. + -\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} -} -\item Line 42, +\item Line qqq, \begin{verbatim} -startTime=0, +dYspacing=0.01, \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 radial grid spacing between each $\rho$-coordinate line +in the discrete grid to $1cm$. \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=29*0.005, \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' +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 +($x,y$) 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 $x$ 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 $-2000m$ 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 49, +\begin{verbatim} +hydrogThetaFile='thetaPol.bin', +\end{verbatim} +This line specifies the name of the file from which the initial values +of $\theta$ +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 50, +\item Line qqq \begin{verbatim} -zonalWindFile='windx.sin_y' + tCyl = 0 \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. +This line specifies the temperature in degrees Celsius of the interior +wall of the tank -- usually a bucket of ice water. + \end{itemize} @@ -608,43 +190,36 @@ notes. \begin{small} -\input{part3/case_studies/climatalogical_ogcm/input/data} +\input{part3/case_studies/rotating_tank/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}} +\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. -\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 $-2000\,{\rm m}$, 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} @@ -654,49 +229,31 @@ \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. -\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/rotating_tank/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.