[MITgcm-support] Variable biharmonic viscosity and energy conservation

[Christopher L. P. Wolfe]

Hi Dimitris,

I should have been more clear. The biharmonic operator is supposed to dissipate energy, but the way it’s implemented in the MITgcm is not guaranteed to dissipate energy. Depending on the alignment of gradients of the biharmonic coefficient and gradients of the vorticity and divergence, the biharmonic operator can actually inject energy into the flow. While there might be physical reasons to inject energy at small scales, this sort of thing is best handled by a physically motivated parameterization where the energy injection can be controlled. Biharmonic viscosity is usually justified by numerical rather than physical considerations and having it inject energy into the flow seems a little dangerous.

Christopher

On Jun 26, 2014, at 6:26 PM, Dimitris Menemenlis <DMenemenlis at gmail.com> wrote:

> ... and isn't the whole point of biharmonic viscosity to dissipate energy?
> (sorry if question is not relevant - I am very ignorant about this topic.)
> 
> On Jun 26, 2014, at 3:18 PM, Dimitris Menemenlis <dmenemenlis at gmail.com> wrote:
> 
>> 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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