/[MITgcm]/manual/s_examples/advection_in_gyre/adv_gyre.tex
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revision 1.3 by cnh, Tue Jan 15 17:34:49 2008 UTC revision 1.4 by cnh, Tue Jan 15 21:10:12 2008 UTC
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14  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,
15  that are described in the tutorial sections \label{sect:eg-baro} and \label{sect:eg-fourlayer}.  that are described in the tutorial sections \label{sect:eg-baro} and \label{sect:eg-fourlayer}.
16  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
17  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
18  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
19  for the tracer.  for the tracer.
20    
21  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
22  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
23  to track pathways of CFC-11 in 13 global ocean models (similar to the example  to track pathways of CFC-11 in 13 global ocean models, using a numerical
24  described in section \ref{sect:eg-offline-cfc}).  configuration similar to the example described in section \ref{sect:eg-offline-cfc}).
25  In other cases tracers are used as a way  In other cases tracers are used as a way
26  to infer bulk mixing coefficients for a turbulent flow field, for example in ...... In  to infer bulk mixing coefficients for a turbulent flow field, for example in
27  biogeochemical and ecological simulations large numbers of tracers are used that carry the  \cite{marsh06} a tracer is used to infer eddy mixing coefficients in the
28  concentrations of biological nutrients and concentrations of biological species.  Antarctic Circumpolar Current region. In biogeochemical and ecological simulations large numbers
29    of tracers are used that carry the concentrations of biological nutrients and concentrations of
30    biological species, for example in ....
31  When using tracers for these and other purposes it is useful to have a feel for the role  When using tracers for these and other purposes it is useful to have a feel for the role
32  that the advection scheme employed plays in determining properties of the tracer distribution.  that the advection scheme employed plays in determining properties of the tracer distribution.
33    In particular, in a discrete numerical model tracer advection only approximates the
34    continuum behavior in space and time and different advection schemes introduce diferent
35    approximations so that the resulting tracer distributions vary. In the following
36    text we illustrate how
37    to use the different advection schemes available in MITgcm here, and discuss which properties
38    are well represented by each one. The advection schemes selections also apply to active
39    tracers (e.g. $T$ and $S$) and the character of the schemes also affect their distributions
40    and behavior.
41    
42  \subsection{Advection and tracer transport}  \subsection{Advection and tracer transport}
43    
44    In general, the tracer problem we want to solve can be written
45    
46    \begin{equation}
47    \label{EQ:eg-adv-gyre-generic-tracer}
48    \frac{\partial C}{partial t} = -U \cdot \nabla C + S
49    \end{equation}
50    
51    where $C$ is the tracer concentration in a model cell, $U$ is the model three-dimensional
52    flow field ( $U=(u,v,w)$ ). In (\ref{EQ:eg-adv-gyre-generic-tracer}) $S$ represents source, sink
53    and tendency terms not associated with advective transport. Example of terms in $S$ include
54    (i) air-sea fluxes for a dissolved gas, (ii) biological grazing and growth terms (for a
55    biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of
56    mixing. In this section we are primarily concerned with
57    \begin{enumerate}
58    \item how to introduce the tracer term, $C$, into an integration
59    \item the different discretized forms of
60    the $-U \cdot \nabla C$ term that are available
61    \end{enumerate}
62    
63    
64    \subsection{Introducting a tracer into the flow}
65    
66     The ptracers package (see section \ref{sec:} for a more complete discussion
67    of the ptracers package )
68    - activating ptracers
69    - setting initial distribution
70    
71    To intro
72    \subsection{Selecting an advection scheme}
73    
74    - flags in data and data.ptracers
75    
76    - overlap width
77    
78    - CPP GAD_ALLOW_SOM_ADVECT required for SOM case
79    
80    \subsection{Comparison of different advection schemes}
81    
82    \begin{enumerate}
83    \item{Conservation}
84    \item{Dispersion}
85    \item{Diffusion}
86    \item{Positive definite}
87    \end{enumerate}
88    
89    
90    
91    
92    
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