s_examples/advection_in_gyre/adv_gyre.tex

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\section[Gyre Advection Example]{Ocean Gyre Advection Schemes}
%%%% \label{www:tutorials}
\label{sect:eg-adv-gyre}
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This set of examples is based on the barotropic and baroclinic gyre MITgcm configurations,
that are described in the tutorial sections \ref{sect:eg-baro} and \ref{sect:eg-fourlayer}. 
The examples in this section explain how to introduce a passive tracer into the flow 
field of the barotropic and baroclinic gyre setups and looks at how the time evolution
of the passive tracer depends on the advection or transport scheme that is selected 
for the tracer. 

Passive tracers are useful in many numerical experiments. In some cases tracers are
used to track flow pathways, for example in \cite{Dutay02} a passive tracer is used
to track pathways of CFC-11 in 13 global ocean models, using a numerical
configuration similar to the example described in section \ref{sect:eg-offline-cfc}).
In other cases tracers are used as a way
to infer bulk mixing coefficients for a turbulent flow field, for example in 
\cite{marsh06} a tracer is used to infer eddy mixing coefficients in the
Antarctic Circumpolar Current region. In biogeochemical and ecological simulations large numbers 
of tracers are used that carry the concentrations of biological nutrients and concentrations of 
biological species, for example in ....
When using tracers for these and other purposes it is useful to have a feel for the role
that the advection scheme employed plays in determining properties of the tracer distribution.
In particular, in a discrete numerical model tracer advection only approximates the 
continuum behavior in space and time and different advection schemes introduce diferent 
approximations so that the resulting tracer distributions vary. In the following 
text we illustrate how
to use the different advection schemes available in MITgcm here, and discuss which properties 
are well represented by each one. The advection schemes selections also apply to active
tracers (e.g. $T$ and $S$) and the character of the schemes also affect their distributions
and behavior.

\subsection{Advection and tracer transport}

In general, the tracer problem we want to solve can be written

\begin{equation}
\label{EQ:eg-adv-gyre-generic-tracer}
\frac{\partial C}{partial t} = -U \cdot \nabla C + S
\end{equation}

where $C$ is the tracer concentration in a model cell, $U$ is the model three-dimensional
flow field ( $U=(u,v,w)$ ). In (\ref{EQ:eg-adv-gyre-generic-tracer}) $S$ represents source, sink 
and tendency terms not associated with advective transport. Example of terms in $S$ include
(i) air-sea fluxes for a dissolved gas, (ii) biological grazing and growth terms (for a 
biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of 
mixing. In this section we are primarily concerned with 
\begin{enumerate}
\item how to introduce the tracer term, $C$, into an integration
\item the different discretized forms of 
the $-U \cdot \nabla C$ term that are available
\end{enumerate}


\subsection{Introducting a tracer into the flow}

 The ptracers package (see section \ref{sec:pkg:ptracers} for a more complete discussion
of the ptracers package) 
- activating ptracers
- setting initial distribution

To intro
\subsection{Selecting an advection scheme}

- flags in data and data.ptracers

- overlap width

- CPP GAD\_ALLOW\_SOM\_ADVECT required for SOM case

\subsection{Comparison of different advection schemes}

\begin{enumerate}
\item{Conservation}
\item{Dispersion}
\item{Diffusion}
\item{Positive definite}
\end{enumerate}


1	cnh	1.7	% $Header: /u/u0/gcmpack/mitgcmdoc/part3/case_studies/advection_in_gyre_circulation/adv_gyre.tex,v 1.6 2008/01/15 21:26:08 cnh Exp $
2	jahn	1.1	% $Name: $
3
4			\bodytext{bgcolor="#FFFFFFFF"}
5
6
7			\section[Gyre Advection Example]{Ocean Gyre Advection Schemes}
8	cnh	1.7	%%%% \label{www:tutorials}
9	jahn	1.1	\label{sect:eg-adv-gyre}
10			\begin{rawhtml}
11			<!-- CMIREDIR:eg-adv-gyre: -->
12			\end{rawhtml}
13
14	cnh	1.2	This set of examples is based on the barotropic and baroclinic gyre MITgcm configurations,
15	cnh	1.7	that are described in the tutorial sections \ref{sect:eg-baro} and \ref{sect:eg-fourlayer}.
16	cnh	1.4	The examples in this section explain how to introduce a passive tracer into the flow
17	cnh	1.2	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
19			for the tracer.
20
21	cnh	1.3	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
23	cnh	1.4	to track pathways of CFC-11 in 13 global ocean models, using a numerical
24			configuration similar to the example described in section \ref{sect:eg-offline-cfc}).
25	cnh	1.3	In other cases tracers are used as a way
26	cnh	1.4	to infer bulk mixing coefficients for a turbulent flow field, for example in
27			\cite{marsh06} a tracer is used to infer eddy mixing coefficients in the
28			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	cnh	1.3	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.
33	cnh	1.4	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	cnh	1.3
42			\subsection{Advection and tracer transport}
43	cnh	1.4
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	cnh	1.5	The ptracers package (see section \ref{sec:pkg:ptracers} for a more complete discussion
67			of the ptracers package)
68	cnh	1.4	- 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	cnh	1.6	- CPP GAD\_ALLOW\_SOM\_ADVECT required for SOM case
79	cnh	1.4
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	cnh	1.3
91
92
93
94	cnh	1.2
95	jahn	1.1
96