[MITgcm-support] application of Gauss (or Stokes) theorem to vorticity eon on C-grid

[Martin Losch]

Hi Paola,

I never tried this, but I think it is important to know how the Coriolis terms are evaluted in the simulation. For this you need to check the relevant parameters in your STDOUT.0000 (do you use the mom-fluxform or the vector invariant form? parameters like: selectCoriScheme, useJamartWetPoints, useEnergyConservingCoriolis, selectVortScheme, SadournyCoriolis), and then it will be a bit tedious to find out, what the model actually does for the specific parameter set, but as far as I recall, this sets how the boundary conditions are computed, which in turn will give the “correct” (as the model evaluates them) form of the div(fu,fv) terms along the boundary. Does that make sense?

Martin

> On 5. Sep 2023, at 08:03, Paola Cessi <pcessi at ucsd.edu> wrote:
> 
> Dear colleagues,
> 
> I am trying to calculate the circulation balance over a semi-enclosed area, by taking the vorticity balance and integrating over said area. One of the terms in the vorticity balance is div (fu, fv), which, when integrated over the area, should give the integral over the boundary of (fu,fv) \cdot n, where n is the normal to the boundary. Over the closed portion of the boundary, i.e. on the solid walls, (fu,fv) \cdot n should be zero. However, because the vorticity points are not on the velocity boundary faces, these terms do not vanish. The residual left from this contribution dominates the balance, so it is not a small error.
> 
> I have tried different versions of the vorticity definitions, i.e. the volume flux form as in  (equation 13) of Adcroft et al https://journals.ametsoc.org/view/journals/mwre/132/12/mwr2823.1.xml, or the simple derivatives and neither of them work. 
> 
> Does anyone have any words of wisdom or references that could be helpful?
> 
> Many thanks,
> Paola Cessi
> 
> --------------------------------------------------------------------------------------------
> Paola Cessi                                                         Tel: +1 858 534 0622 
> Scripps Institution of Oceanography                  Fax: +1 858 534 8045
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> La Jolla, CA 92093-0213          Web: http://pordlabs.ucsd.edu/pcessi
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