Home Contact Us Site Map  
 
       
    next up previous contents
Next: 6.3.3 Griffies Skew Flux Up: 6.3 Gent/McWiliams/Redi SGS Eddy Previous: 6.3.1 Redi scheme: Isopycnal   Contents

6.3.2 GM parameterization

The GM parameterization aims to parameterise the ``advective'' or ``transport'' effect of geostrophic eddies by means of a ``bolus'' velocity, $ \bf {u}^*$. The divergence of this advective flux is added to the tracer tendency equation (on the rhs):

$\displaystyle - \bf {\nabla} \cdot \tau \bf {u}^*$ (6.4)

The bolus velocity is defined as:

$\displaystyle u^*$ $\displaystyle =$ $\displaystyle - \partial_z F_x$ (6.5)
$\displaystyle v^*$ $\displaystyle =$ $\displaystyle - \partial_z F_y$ (6.6)
$\displaystyle w^*$ $\displaystyle =$ $\displaystyle \partial_x F_x + \partial_y F_y$ (6.7)

where $ F_x$ and $ F_y$ are stream-functions with boundary conditions $ F_x=F_y=0$ on upper and lower boundaries. The virtue of casting the bolus velocity in terms of these stream-functions is that they are automatically non-divergent ( $ \partial_x u^* + \partial_y v^* = - \partial_{xz} F_x - \partial_{yz} F_y = - \partial_z w^*$). $ F_x$ and $ F_y$ are specified in terms of the isoneutral slopes $ S_x$ and $ S_y$:
$\displaystyle F_x$ $\displaystyle =$ $\displaystyle \kappa_{GM} S_x$ (6.8)
$\displaystyle F_y$ $\displaystyle =$ $\displaystyle \kappa_{GM} S_y$ (6.9)

This is the form of the GM parameterization as applied by Donabasaglu, 1997, in MOM versions 1 and 2.

next up previous contents
Next: 6.3.3 Griffies Skew Flux Up: 6.3 Gent/McWiliams/Redi SGS Eddy Previous: 6.3.1 Redi scheme: Isopycnal   Contents
mitgcm-support@dev.mitgcm.org
Copyright © 2002 Massachusetts Institute of Technology