| 5 |
\end{rawhtml} |
\end{rawhtml} |
| 6 |
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|
| 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 |
|
|
| 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) |
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