/[MITgcm]/manual/s_examples/advection_in_gyre/adv_gyre.tex
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7  \section[Gyre Advection Example]{Ocean Gyre Advection Schemes}  \section[Gyre Advection Example]{Ocean Gyre Advection Schemes}
 \label{sect:eg-adv-gyre}  
8  \label{www:tutorials}  \label{www:tutorials}
9    \label{sect:eg-adv-gyre}
10  \begin{rawhtml}  \begin{rawhtml}
11  <!-- CMIREDIR:eg-adv-gyre: -->  <!-- CMIREDIR:eg-adv-gyre: -->
12  \end{rawhtml}  \end{rawhtml}
13    
14    Author: Oliver Jahn and Chris Hill
15    
16    
17    
18  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,
19  that are described in the tutorial sections \label{sect:eg-baro} and \label{sect:eg-fourlayer}.  that are described in the tutorial sections \ref{sect:eg-baro} and \ref{sect:eg-fourlayer}.
20  The example in this section explains how to introduce a passive tracer into the flow  The examples in this section explain how to introduce a passive tracer into the flow
21  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
22  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
23  for the tracer.  for the tracer.
24    
25    Passive tracers are useful in many numerical experiments. In some cases tracers are
26    used to track flow pathways, for example in \cite{Dutay02} a passive tracer is used
27    to track pathways of CFC-11 in 13 global ocean models, using a numerical
28    configuration similar to the example described in section \ref{sect:eg-offline-cfc}).
29    In other cases tracers are used as a way
30    to infer bulk mixing coefficients for a turbulent flow field, for example in
31    \cite{marsh06} a tracer is used to infer eddy mixing coefficients in the
32    Antarctic Circumpolar Current region. In biogeochemical and ecological simulations large numbers
33    of tracers are used that carry the concentrations of biological nutrients and concentrations of
34    biological species, for example in ....
35    When using tracers for these and other purposes it is useful to have a feel for the role
36    that the advection scheme employed plays in determining properties of the tracer distribution.
37    In particular, in a discrete numerical model tracer advection only approximates the
38    continuum behavior in space and time and different advection schemes introduce diferent
39    approximations so that the resulting tracer distributions vary. In the following
40    text we illustrate how
41    to use the different advection schemes available in MITgcm here, and discuss which properties
42    are well represented by each one. The advection schemes selections also apply to active
43    tracers (e.g. $T$ and $S$) and the character of the schemes also affect their distributions
44    and behavior.
45    
46    \subsection{Advection and tracer transport}
47    
48    In general, the tracer problem we want to solve can be written
49    
50    \begin{equation}
51    \label{EQ:eg-adv-gyre-generic-tracer}
52    \frac{\partial C}{partial t} = -U \cdot \nabla C + S
53    \end{equation}
54    
55    where $C$ is the tracer concentration in a model cell, $U$ is the model three-dimensional
56    flow field ( $U=(u,v,w)$ ). In (\ref{EQ:eg-adv-gyre-generic-tracer}) $S$ represents source, sink
57    and tendency terms not associated with advective transport. Example of terms in $S$ include
58    (i) air-sea fluxes for a dissolved gas, (ii) biological grazing and growth terms (for a
59    biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of
60    mixing. In this section we are primarily concerned with
61    \begin{enumerate}
62    \item how to introduce the tracer term, $C$, into an integration
63    \item the different discretized forms of
64    the $-U \cdot \nabla C$ term that are available
65    \end{enumerate}
66    
67    
68    \subsection{Introducing a tracer into the flow}
69    
70     The MITgcm ptracers package (see section \ref{sec:pkg:ptracers} for a more complete discussion
71    of the ptracers package and section \ref{sec:pkg:using} for a general introduction to MITgcm
72    packages) provides pre-coded support for a simple passive tracer with an initial
73    distribution at simulation time $t=0$ of $C_0(x,y,z)$. The steps required to use this capability
74    are
75    \begin{enumerate}
76    \item{\bf Activating the ptracers package.} This simply requires adding the line {\tt ptracers} to
77    the {\tt packages.conf} file in the {\it code/} directory for the experiment.
78    \end{enumerate}
79    
80    - activating ptracers
81    - setting initial distribution
82    
83    To intro
84    \subsection{Selecting an advection scheme}
85    
86    - flags in data and data.ptracers
87    
88    - overlap width
89    
90    - CPP GAD\_ALLOW\_SOM\_ADVECT required for SOM case
91    
92    \subsection{Comparison of different advection schemes}
93    
94    \begin{enumerate}
95    \item{Conservation}
96    \item{Dispersion}
97    \item{Diffusion}
98    \item{Positive definite}
99    \end{enumerate}
100    
101    \subsection{Code and Parameters files for this tutorial}
102    
103    The code and parameters for the experiments can be found in the MITgcm example experiments
104    directory {\it verification/tutorial\_advection\_in\_gyre/}.
105    
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