[MITgcm-support] Variable biharmonic viscosity and energy conservation

[Ryan Abernathey]

Is there any way to know how much energy is being dissipated / generated by
the viscosity scheme? Can the model output "epsilon"? This would be useful
in many contexts.


On Fri, Jun 27, 2014 at 12:10 PM, Christopher L. P. Wolfe <
christopher.wolfe at stonybrook.edu> wrote:

> 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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