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%Put here the title of your abstract
\title{Facets of the GHER 3D turbulent closure model.  Application to the
Adriatic Sea, the Bering Sea, the North Sea, the Mediterranean Sea and the 
Black Sea}

%Put here the list of authors and their affiliation
\author{J.-M. Beckers, E.J.M. Delhez, M. Gr\'egoire, G. Martin and J.C.J. Nihoul}
\affiliation{GHER, University of Liege, Belgium}

%If you have authors from different institutions, please adapt one of
%these examples
%
%Example 1
%---------
%\author{Robin Muensch$^1$, Richard Dewey$^2$ and John Gunn$^1$}
%\affiliation{$^1$Earth and Space Research, USA \\
%$^2$University of Victoria, Canada}
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%Example 2
%---------
%\author{Hans Burchard}
%\affiliation{Space Application Institute, Joint Research Center, Italy}
%\author{Ole Peterson}
%\affiliation{Danish Hydraulic Institute, Denmark}

%Do not forget to include this line
\maketitle

%Type in the core of your abstract
  
The GHER model system is based on three modules : the hydrodynamic module,
the ecosystem module and the data module.  These interact and complement each
other to produce a mathematical visualization of the hydrodynamic and ecological
conditions in a wide range of time scales and length scales.

	At the center of the system is the primitive equations hydrodynamic
 model.  From initial conditions and forcing functions provided by the data
 module (inverse modeling), it gives a 3D view of the horizontal and vertical
 structure of the flow.  The model is fully non-linear and fully 3D (with
 the $\sigma$-coordinate).  The output of the hydrodynamic module are then
 fed in the ecosystem module where they ensure a perfect representation of 
the hydrodynamic constraints.

	Many hydrodynamic and biological processes depend strongly on the 
stability of the water column.  A refined turbulent closure scheme is 
therefore included in the hydrodynamic module.  The vertical eddy viscosity 
and diffusivity are computed from the evolution equation for the turbulent 
kinetic energy $k$ and from a parametric algebraic expression of the mixing 
length $\ell$.
  It is argued that more reliable results can be obtained by leaving 
out the equation for turbulent energy dissipation rate $\epsilon$ and the
 associated
 complications and uncertainties and by using the physically more 
understandable empirical equation for $\ell$.
  The influence of the stratification 
on the turbulent fluxes is measured and parameterized by the Richardson flux
 number.

	The GHER model system has been applied to a wide variety of regions 
among which one can list the Adriatic Sea, the Bering Sea, the North Sea, 
the Mediterranean Sea or the Black Sea.  All those regions differ by their 
dominant hydrodynamic processes.  Therefore, particular adaptations of the 
general formulation are required.  In the case of deep water formation, the 
formulation of the influence of the stratification on the vertical turbulent 
fluxes must be extended to describe unstable conditions.  When studying the 
general circulation, the production of turbulence by mesoscale processes $\Pi$ 
must be added to the equations.  According to the level of accuracy required 
and the strength of the mesoscale signal, this can be done by a simple
 parameterization or by the explicit computation of $\Pi$ as the ensemble
 average
 of the corresponding expressions on a wide range of mesoscale events described
 by a separate hydrodynamic model operating at this latter time scale.

%If you want to include acknowledgments, please use this environment :
%\begin{acknowledgments} The authors are grateful to ...
%\end{acknowledgments}

%If you include some references, please use the environment {thebibliography}
%and introduce the reference in the text with the \cite command.
%
% Example
% -------
%
%    ... \cite{Lev}...
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%\begin{thebibliography}{}
%\bibitem[{\em Levine et al.,} 1985]{Lev} Levine, M.D., Paulson, C.A.  and
%Morison J.H., 1985.  Internal waves in the Artic Ocean :  A comparison with
%lower-latitude observations.  {\it J.  Phys.  Oceanog.}, 15, 800-809.
%
%\bibitem[{\em Gregg,} 1989]{Gregg} 
%Gregg, M.C., 1989.  Scaling turbulent diffusion in the thermocline
%{\it J.  Geophys. Res.}, 94, 9686-9698.
%
%\end{thebibliography}


%You can also include your full address at the end of the abstract.  Please 
%insert a blank line between successive addresses
\begin{addresses}
GeoHydrodynamics and Environment Research Lab., University of Liege, Sart Tilman
B5, B-4000 Liege.
\end{addresses}


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