[MITgcm-support] Variable biharmonic viscosity and energy conservation

[Dimitris Menemenlis]

Not an expert in this stuff, but there are good arguments why a model that does not
fully resolves all scales of motion should "not" be energy conserving.  For example,
see the neptune papers by Greg Holloway.

On Jun 26, 2014, at 3:11 PM, Christopher L. P. Wolfe <christopher.wolfe at stonybrook.edu> wrote:

> Griffies and Hallberg (2000) note that biharmonic viscosity with a variable coefficient doesn’t conserve energy unless the coefficient is “split” into its square roots and appears in front of both gradient parts of the biharmonic operator; that is, operators of the form
> 
> Gu = div(sqrt(A4) grad( div( sqrt(A4) grad u)))
> 
> conserve energy (and angular momentum), whereas operators of the form
> 
> Gu = div(A4 grad( div( grad u)))
> 
> do not. According to both the manual and what I’ve found in the code, the MITgcm implements the second, non-conservative method rather than the first. Does anyone (perhaps Jean-Michel?) know if biharmonic viscosity is still implemented this way for a reason, or is it just due to inertia? At the first glance, it doesn’t seem like a very difficult change to make, though perhaps I am mistaken.

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