/[MITgcm]/manual/s_examples/baroclinic_gyre/fourlayer.tex

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-revision 1.8 by cnh,
Thu Oct 25 12:06:56 2001 UTC
+revision 1.10 by adcroft,
Tue Nov 13 19:01:42 2001 UTC
 Line 20 
 This document describes an example exper
  to simulate a baroclinic ocean gyre in spherical
  polar coordinates. The barotropic
  example experiment in section \ref{sec:eg-baro}
- ilustrated how to configure the code for a single layer
+ illustrated how to configure the code for a single layer
- simulation in a cartesian grid. In this example a similar physical problem
+ simulation in a Cartesian grid. In this example a similar physical problem
  is simulated, but the code is now configured
  for four layers and in a spherical polar coordinate system.
 Line 29 
 for four layers and in a spherical polar
  This example experiment demonstrates using the MITgcm to simulate
  a baroclinic, wind-forced, ocean gyre circulation. The experiment
- is a numerical rendition of the gyre circulation problem simliar
+ is a numerical rendition of the gyre circulation problem similar
  to the problems described analytically by Stommel in 1966
  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
  \\
 Line 62 
 $\tau_0$ is set to $0.1N m^{-2}$.
  \\
  Figure \ref{FIG:simulation_config}
- summarises the configuration simulated.
+ summarizes the configuration simulated.
  In contrast to the example in section \ref{sec:eg-baro}, the
  current experiment simulates a spherical polar domain. As indicated
  by the axes in the lower left of the figure the model code works internally
- in a locally orthoganal coordinate $(x,y,z)$. For this experiment description
+ in a locally orthogonal coordinate $(x,y,z)$. For this experiment description
- the local orthogonal model coordinate $(x,y,z)$ is synonomous
+ the local orthogonal model coordinate $(x,y,z)$ is synonymous
  with the coordinates $(\lambda,\varphi,r)$ shown in figure
  \ref{fig:spherical-polar-coord}
  \\
 Line 120 
 The vertical spacing, $\Delta z$, is con
  \subsection{Equations solved}
  For this problem
  the implicit free surface, {\bf HPE} (see section \ref{sec:hydrostatic_and_quasi-hydrostatic_forms}) form of the
- equations described in Marshall et. al \cite{Marshall97a} are
+ equations described in Marshall et. al \cite{marshall:97a} are
  employed. The flow is three-dimensional with just temperature, $\theta$, as
  an active tracer.  The equation of state is linear.
- A horizontal laplacian operator $\nabla_{h}^2$ provides viscous
+ A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
  dissipation and provides a diffusive sub-grid scale closure for the
  temperature equation. A wind-stress momentum forcing is added to the momentum
  equation for the zonal flow, $u$. Other terms in the model
- are explicitly switched off for this experiement configuration (see section
+ are explicitly switched off for this experiment configuration (see section
  \ref{SEC:eg_fourl_code_config} ). This yields an active set of equations
  solved in this configuration, written in spherical polar coordinates as
  follows
 Line 210 
 that there are sixty grid cells in the z
  Vertically the
  model is configured with four layers with constant depth,
  $\Delta z$, of $500$~m. The internal, locally orthogonal, model coordinate
- variables $x$ and $y$ are initialised from the values of
+ variables $x$ and $y$ are initialized from the values of
  $\lambda$, $\varphi$, $\Delta \lambda$ and $\Delta \varphi$ in
  radians according to
 Line 262 
 field solution method is described in se
  \subsubsection{Numerical Stability Criteria}
- The laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
+ The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
  This value is chosen to yield a Munk layer width,
  \begin{eqnarray}
 Line 279 
 boundary layer is well resolved.
  \noindent The model is stepped forward with a
  time step $\delta t=1200$secs. With this time step the stability
- parameter to the horizontal laplacian friction
+ parameter to the horizontal Laplacian friction
  \begin{eqnarray}
  \label{EQ:laplacian_stability}
 Line 329 
 limit of 0.5.
  \\
  \noindent The stability parameter for internal gravity waves
- propogating at $2~{\rm m}~{\rm s}^{-1}$
+ propagating at $2~{\rm m}~{\rm s}^{-1}$
  \begin{eqnarray}
  \label{EQ:igw_stability}
 Line 355 
 directory {\it verification/exp2/}.  The
  \item {\it code/SIZE.h}.
  \end{itemize}
  contain the code customisations and parameter settings for this
- experiements. Below we describe the customisations
+ experiments. Below we describe the customisations
  to these files associated with this experiment.
  \subsubsection{File {\it input/data}}
 Line 372 
 this line sets
  the initial and reference values of potential temperature at each model
  level in units of $^{\circ}$C.
  The entries are ordered from surface to depth. For each
- depth level the inital and reference profiles will be uniform in
+ depth level the initial and reference profiles will be uniform in
  $x$ and $y$. The values specified here are read into the
  variable
  {\bf
 Line 418 
 goto code
  \item Line 6,
  \begin{verbatim} viscAz=1.E-2, \end{verbatim}
- this line sets the vertical laplacian dissipation coefficient to
+ this line sets the vertical Laplacian dissipation coefficient to
  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
  for this operator are specified later.
  The variable
 Line 438 
 and is copied into model general vertica
  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}
  viscAr
  \begin{rawhtml} </A>\end{rawhtml}
- }. At each time step, the viscous term contribution to the momentum eqautions
+ }. At each time step, the viscous term contribution to the momentum equations
  is calculated in routine
  {\it S/R CALC\_DIFFUSIVITY}.
 Line 697 
 usingSphericalPolarGrid=.TRUE.,
  \end{verbatim}
  This line requests that the simulation be performed in a
  spherical polar coordinate system. It affects the interpretation of
- grid inoput parameters, for exampl {\bf delX} and {\bf delY} and
+ grid input parameters, for example {\bf delX} and {\bf delY} and
- causes the grid generation routines to initialise an internal grid based
+ causes the grid generation routines to initialize an internal grid based
  on spherical polar geometry.
  The variable
  {\bf
 Line 733 
 phiMin=0.,
  This line sets the southern boundary of the modeled
  domain to $0^{\circ}$ latitude. This value affects both the
  generation of the locally orthogonal grid that the model
- uses internally and affects the initialisation of the coriolis force.
+ uses internally and affects the initialization of the coriolis force.
  Note - it is not required to set
  a longitude boundary, since the absolute longitude does
  not alter the kernel equation discretisation.
 Line 960 
 customisations for this experiment.
  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the
  default for MITgcm).
- Although $\tau_{x}$ is only a function of latituted, $y$,
+ Although $\tau_{x}$ is only a function of latitude, $y$,
  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
 Line 1061 
 Instructions for downloading the code ca
  % pwd
  \end{verbatim}
-  You shold see a response on the screen ending in
+  You should see a response on the screen ending in
  {\it verification/exp2/input }

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