[MITgcm-support] non-hydrostatic momentum budget

[Jean-Michel Campin]

Hi Andrea,

There is one thing that I forgot but just came back to my mind yesterday:
you could try to compute the pressure gradient using diagnostic PHI_SURF 
(instead of gravity*ETAN), PHI_NH (as you did) and Um_dPHdx,Vm_dPHdy.

When using: exactConserv=.TRUE., etaN is (re-)computed from the vertically 
integrated continuity eq. and this could introduce differences in the momentum 
budget:
1) if a large solver tolerance is used and the 2-D solver convergence is poor.
2) when filters (Shapiro, Fourier) are used after solve_for_pressure
 (e.g., shap_filt_uvStar=.FALSE.,)
3) in Non-Hydrostatic simulation: In this case, the separation between surface 
  pressure and NH pressure is not made clearly; the sum of two is correct (i.e., 
  PHI_SURF + PHI_NH ) and gravity*ETAN should represent the free-surface contribution
  but there is no reason for PHI_NH to be just the NH pressure (free of
  any surface contribution).

At some point, I tried to separate the 2 contributions (zeroPsNH=True
 in solve_for_pressure.F) but it did not work well, partly because
changing the initial guess for the 3-D solver was slowing down the convergence.
So at the end, zeroPsNH=F is hard-coded.

Cheers,
Jean-Michel

On Fri, Jul 07, 2017 at 10:39:29AM +0200, Andrea Cimatoribus wrote:
> One step ahead:
> 
> as hinted in http://mitgcm.org/sealion/online_documents/node38.html
> I tried summing the nonhydrostatic pressure term:
> 
> Um_NHP = -(PHI_NH(i) - PHI_NH(i-1)) / DXC
> 
> The results definitely improve near the boundary, but I am still missing
> something.
> 
> Best,
> Andrea
> 
> Andrea Cimatoribus
> postdoctoral researcher
> EPFL ENAC IIE ECOL
> https://people.epfl.ch/andrea.cimatoribus
> 
> On 06/07/17 17:30, Andrea Cimatoribus wrote:
> >Dear all,
> >I am trying to compute the budget of momentum in my
> >non-hydrostatic configuration. First of all, thanks to all those
> >who contributed in the past on this topic, it certainly saved me
> >huge amounts of time and head-scratching.
> >
> >I put here the recipe from JMC for reference:
> >[du/dt] = - gravity * ( ETAN(i) - ETAN(i-1) ) / DXC
> >         + Um_dPHdx
> >         + Um_Advec   (+ Um_Cori : but only if using CD-Scheme )
> >         + Um_Diss    (+ Implicit vertical viscosity tendency)
> >         + Um_Ext
> >         + AB_gU
> >
> >The problem:
> >the recipe above works beautifully (relative error <<1e-3) in the
> >hydrostatic case, with only some issues near the boundary, I guess
> >because of my cheap ETA derivatives. However, in the
> >nonhydrostatic case, the above budget gives relative errors around
> >10% in many places (10% of the "truth" diagnosed via
> >TOTUTEND/TOTVTEND).
> >
> >What term am I missing? Could it be that TOTUTEND does not have
> >all the terms in the NH case? I tried looking into mom_vecinv.F,
> >but I could not reach any conclusion. I also tried playing with
> >ADVrE_Um/ADVrE_Vm fluxes (treating it as the implicit vertical
> >viscosity term), but that didn't help either (I thought the
> >vertical advection was missing).
> >
> >Thank you for your insights,
> >Andrea
> >
> >
> >PS: I attach the data file and a figure for the curious ones, it
> >shows the relative error of the diagnosed acceleration (magnitude
> >of vector) with respect to the one directly produced via
> >TOTUTEND/TOTVTEND. There seems to be some correlation (not
> >perfect, though) between the relative error and the advective
> >term.
> >
> >
> >
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> 
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