[MITgcm-support] anisotropic cosine scaling?

[Martin Losch]

Hi Madeline,

you are problably familiar with the CLF criterion for advection U*dt/dx < 1 (or even 1/2). There is a similar criterion for the viscosity terms that requires Ah*dt/dx^2 < 1/4, or something like that (you can find these relations in some of the tutorial descriptions). Imagine you have a constant Ah, but your grid spacing in varying, e.g. dx = dl*cos(lat), dy = dl (which is the typical case for a, say, "(1/6)deg-model", with dl=(1/6)deg). Then Ah*dt/dx^2 is different from Ah*dt/dy^2. At high resolution the stability of a numerical simulation can be so fragile, that for one direction the Ah may be over the stability criterion, but for the other there is not enough dissipation to control the energy. In this case it may be necessary to scale Ah for one direction so that for both directions Ah*scaling is such that it lies in the narrow "stability band".

For high-resolution experiments its much better (from a numerical stability point of view) to have "isotropic" grids (where dx ~ dy) and have Ah scaled with the local grid cell size (as is done for viscAhGrid, leigth/smag, etc)

Martin

On Nov 11, 2010, at 9:14 PM, Madeline Miller wrote:

> Dear List,
> 
> Can anyone point me in the direction of a reference that explains why it is stabilizing to make the viscous stress tensor asymmetric?
> 
> e.g: http://mitgcm.org/sealion/online_documents/node57.html 
> which translates to the generic_advdiff flag ISOTROPIC_COS_SCALING
> 
> Thanks,
> 
> Madeline
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