/[MITgcm]/manual/s_examples/advection_in_gyre/adv_gyre.tex
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revision 1.6 by cnh, Tue Jan 15 21:26:08 2008 UTC revision 1.16 by jmc, Mon Aug 30 23:09:19 2010 UTC
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7  \section[Gyre Advection Example]{Ocean Gyre Advection Schemes}  \section[Gyre Advection Example]{Ocean Gyre Advection Schemes}
8  \label{www:tutorials}  %\label{www:tutorials}
9  \label{sect:eg-adv-gyre}  \label{sec:eg-adv-gyre}
10  \begin{rawhtml}  \begin{rawhtml}
11  <!-- CMIREDIR:eg-adv-gyre: -->  <!-- CMIREDIR:eg-adv-gyre: -->
12  \end{rawhtml}  \end{rawhtml}
13    \begin{center}
14    (in directory: {\it verification/tutorial\_advection\_in\_gyre/})
15    \end{center}
16    
17    Author: Oliver Jahn and Chris Hill
18    
19    
20    
21  This set of examples is based on the barotropic and baroclinic gyre MITgcm configurations,  This set of examples is based on the barotropic and baroclinic gyre MITgcm configurations,
22  that are described in the tutorial sections \label{sect:eg-baro} and \label{sect:eg-fourlayer}.  that are described in the tutorial sections \ref{sec:eg-baro} and \ref{sec:eg-fourlayer}.
23  The examples in this section explain how to introduce a passive tracer into the flow  The examples in this section explain how to introduce a passive tracer into the flow
24  field of the barotropic and baroclinic gyre setups and looks at how the time evolution  field of the barotropic and baroclinic gyre setups and looks at how the time evolution
25  of the passive tracer depends on the advection or transport scheme that is selected  of the passive tracer depends on the advection or transport scheme that is selected
# Line 21  for the tracer. Line 28  for the tracer.
28  Passive tracers are useful in many numerical experiments. In some cases tracers are  Passive tracers are useful in many numerical experiments. In some cases tracers are
29  used to track flow pathways, for example in \cite{Dutay02} a passive tracer is used  used to track flow pathways, for example in \cite{Dutay02} a passive tracer is used
30  to track pathways of CFC-11 in 13 global ocean models, using a numerical  to track pathways of CFC-11 in 13 global ocean models, using a numerical
31  configuration similar to the example described in section \ref{sect:eg-offline-cfc}).  configuration similar to the example described in section \ref{sec:eg-offline-cfc}).
32  In other cases tracers are used as a way  In other cases tracers are used as a way
33  to infer bulk mixing coefficients for a turbulent flow field, for example in  to infer bulk mixing coefficients for a turbulent flow field, for example in
34  \cite{marsh06} a tracer is used to infer eddy mixing coefficients in the  \cite{marsh06} a tracer is used to infer eddy mixing coefficients in the
# Line 44  and behavior. Line 51  and behavior.
51  In general, the tracer problem we want to solve can be written  In general, the tracer problem we want to solve can be written
52    
53  \begin{equation}  \begin{equation}
54  \label{EQ:eg-adv-gyre-generic-tracer}  \label{eq:eg-adv-gyre-generic-tracer}
55  \frac{\partial C}{partial t} = -U \cdot \nabla C + S  \frac{\partial C}{partial t} = -U \cdot \nabla C + S
56  \end{equation}  \end{equation}
57    
58  where $C$ is the tracer concentration in a model cell, $U$ is the model three-dimensional  where $C$ is the tracer concentration in a model cell, $U$ is the model three-dimensional
59  flow field ( $U=(u,v,w)$ ). In (\ref{EQ:eg-adv-gyre-generic-tracer}) $S$ represents source, sink  flow field ( $U=(u,v,w)$ ). In (\ref{eq:eg-adv-gyre-generic-tracer}) $S$ represents source, sink
60  and tendency terms not associated with advective transport. Example of terms in $S$ include  and tendency terms not associated with advective transport. Example of terms in $S$ include
61  (i) air-sea fluxes for a dissolved gas, (ii) biological grazing and growth terms (for a  (i) air-sea fluxes for a dissolved gas, (ii) biological grazing and growth terms (for a
62  biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of  biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of
# Line 61  the $-U \cdot \nabla C$ term that are av Line 68  the $-U \cdot \nabla C$ term that are av
68  \end{enumerate}  \end{enumerate}
69    
70    
71  \subsection{Introducting a tracer into the flow}  \subsection{Introducing a tracer into the flow}
72    
73   The ptracers package (see section \ref{sec:pkg:ptracers} for a more complete discussion   The MITgcm ptracers package (see section \ref{sec:pkg:ptracers} for a more complete discussion
74  of the ptracers package)  of the ptracers package and section \ref{sec:pkg:using} for a general introduction to MITgcm
75  - activating ptracers  packages) provides pre-coded support for a simple passive tracer with an initial
76  - setting initial distribution  distribution at simulation time $t=0$ of $C_0(x,y,z)$. The steps required to use this capability
77    are
78    \begin{enumerate}
79    \item{\bf Activating the ptracers package.} This simply requires adding the line {\tt ptracers} to
80    the {\tt packages.conf} file in the {\it code/} directory for the experiment.
81    \item{\bf Setting an initial tracer distribution.}
82    \end{enumerate}
83    
84    Once the two steps above are complete we can proceed to examine how the tracer we have created is
85    carried by the flow field and what properties of the tracer distribution are preserved under
86    different advection schemes.
87    
 To intro  
88  \subsection{Selecting an advection scheme}  \subsection{Selecting an advection scheme}
89    
90  - flags in data and data.ptracers  - flags in data and data.ptracers
# Line 86  To intro Line 102  To intro
102  \item{Positive definite}  \item{Positive definite}
103  \end{enumerate}  \end{enumerate}
104    
105    \input{s_examples/advection_in_gyre/adv_gyre_figure.tex}
106    
107    \begin{figure}
108    \begin{center}
109     \includegraphics*[width=\textwidth]{s_examples/advection_in_gyre/stats.eps}
110    \end{center}
111    \caption{Maxima, minima and standard deviation (from left) as a function of time (in months)
112    for the gyre circulation experiment from figure~\ref{fig:adv-gyre-all}.}
113    \label{fig:adv-gyre-stats}
114    \end{figure}
115    
116    \subsection{Code and Parameters files for this tutorial}
117    
118    The code and parameters for the experiments can be found in the MITgcm example experiments
119    directory {\it verification/tutorial\_advection\_in\_gyre/}.
120    
   
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