/[MITgcm]/manual/s_phys_pkgs/text/gmredi.tex
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revision 1.16 by dfer, Mon Jun 27 02:08:35 2011 UTC revision 1.18 by jmc, Tue Mar 26 15:10:46 2013 UTC
# Line 5  Line 5 
5  \end{rawhtml}  \end{rawhtml}
6    
7  There are two parts to the Redi/GM parameterization of geostrophic  There are two parts to the Redi/GM parameterization of geostrophic
8  eddies. The first, the Redi scheme \citep{re82}, aims to mix tracer properties along isentropes  eddies. The first, the Redi scheme \citep{re82}, aims to mix tracer properties
9  (neutral surfaces) by means of a diffusion operator oriented along the  along isentropes (neutral surfaces) by means of a diffusion operator oriented
10  local isentropic surface. The second part, GM \citep{gen-mcw:90,gen-eta:95}, adiabatically  along the local isentropic surface.
11    The second part, GM \citep{gen-mcw:90,gen-eta:95}, adiabatically
12  re-arranges tracers through an advective flux where the advecting flow  re-arranges tracers through an advective flux where the advecting flow
13  is a function of slope of the isentropic surfaces.  is a function of slope of the isentropic surfaces.
14    
# Line 46  where $\kappa_\rho$ is the along isopycn Line 47  where $\kappa_\rho$ is the along isopycn
47  $\bf{K}_{Redi}$ is a rank 2 tensor that projects the gradient of  $\bf{K}_{Redi}$ is a rank 2 tensor that projects the gradient of
48  $\tau$ onto the isopycnal surface. The unapproximated projection tensor is:  $\tau$ onto the isopycnal surface. The unapproximated projection tensor is:
49  \begin{equation}  \begin{equation}
50  \bf{K}_{Redi} = \left(  \bf{K}_{Redi} = \frac{1}{1 + |S|^2} \left(
51  \begin{array}{ccc}  \begin{array}{ccc}
52  1 + S_x& S_x S_y & S_x \\  1 + S_y^2& -S_x S_y & S_x \\
53  S_x S_y  & 1 + S_y & S_y \\  -S_x S_y  & 1 + S_x^2 & S_y \\
54  S_x & S_y & |S|^2 \\  S_x & S_y & |S|^2 \\
55  \end{array}  \end{array}
56  \right)  \right)
# Line 385  GM\_tap\-er\_scheme = 'dm95'} in {\em da Line 386  GM\_tap\-er\_scheme = 'dm95'} in {\em da
386    
387  \subsubsection*{Tapering: Large, Danabasoglu and Doney, JPO 1997}  \subsubsection*{Tapering: Large, Danabasoglu and Doney, JPO 1997}
388    
389  The tapering used in \cite{ldd:97} is based on the  The tapering used in \cite{lar-eta:97} is based on the
390  DM95 tapering scheme, but also tapers the scheme with an additional  DM95 tapering scheme, but also tapers the scheme with an additional
391  function of height, $f_2(z)$, so that the GM/Redi SGS fluxes are  function of height, $f_2(z)$, so that the GM/Redi SGS fluxes are
392  reduced near the surface:  reduced near the surface:
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