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\section[Gyre Advection Example]{Ocean Gyre Advection Schemes} |
\section[Gyre Advection Example]{Ocean Gyre Advection Schemes} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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\label{sect:eg-adv-gyre} |
\label{sec:eg-adv-gyre} |
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\begin{rawhtml} |
\begin{rawhtml} |
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<!-- CMIREDIR:eg-adv-gyre: --> |
<!-- CMIREDIR:eg-adv-gyre: --> |
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\end{rawhtml} |
\end{rawhtml} |
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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, |
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that are described in the tutorial sections \ref{sect:eg-baro} and \ref{sect:eg-fourlayer}. |
that are described in the tutorial sections \ref{sec:eg-baro} and \ref{sec:eg-fourlayer}. |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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}). |
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In other cases tracers are used as a way |
In other cases tracers are used as a way |
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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 |
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\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 |
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In general, the tracer problem we want to solve can be written |
In general, the tracer problem we want to solve can be written |
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\begin{equation} |
\begin{equation} |
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\label{EQ:eg-adv-gyre-generic-tracer} |
\label{eq:eg-adv-gyre-generic-tracer} |
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\frac{\partial C}{partial t} = -U \cdot \nabla C + S |
\frac{\partial C}{partial t} = -U \cdot \nabla C + S |
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\end{equation} |
\end{equation} |
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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 |
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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 |
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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 |
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(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 |
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biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of |
biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of |
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