[MITgcm-support] rstar coordinates

[Martin Losch]

Hi Patrick,

a) hydrostatic refers to the hydrostatic approximation under which  
the vertical momentum equation reduces to: dp/dz = -g*rho. If you set  
nonHydrostatic=.true., you'll have vertical accelerations (dw/dt is  
nonzero) and in addition to solving for 2d pressure, you are solving  
a 3d elliptic pressure equation, which makes the integration at least  
twice as expensive. In general, non-hydrostatic dynamics are required  
where strong vertical accelerations are necessary, eg. in simulating  
convective plumes, at horizontal scales <1000m to 100m. See
http://mitgcm.org/r2_web_testing/latest/online_documents/node20.html
http://mitgcm.org/r2_web_testing/latest/online_documents/node39.html
The term hydrodynamic (which is not the same as non-hydrostatic,  
stupid terminology, I agree) is misleading in this context.
b) rigidLid=.false., and implicitFreeSurface=.true.,
c) correct
d) r-star works only with non-linear free surface  
(nonlinFreeSurf=4,select_rstar=2)
http://mitgcm.org/r2_web_testing/latest/online_documents/node40.html
and following chapters for more details
e) no, from model/inc/PARAMS.h:
> C     implicSurfPress :: parameter of the Crank-Nickelson time  
> stepping :
> C                     Implicit part of Surface Pressure Gradient  
> ( 0-1 )
> C     implicDiv2Dflow :: parameter of the Crank-Nickelson time  
> stepping :
> C                     Implicit part of barotropic flow Divergence  
> ( 0-1 )
As far as I can see, setting these two parameters to zero makes the  
free surface explicit, but not sure. See also:
http://mitgcm.org/r2_web_testing/latest/online_documents/node41.html

In principle with linear free surface, the surface elevation can have  
larger amplitudes than the thickness of the surface cell, but that  
does not make sense. So if you observe that it makes sense to switch  
to nonlinear free surface with r-star coordinates. Once the r-star  
coordinates are turned on, the entire vertical grid is scaled with  
the surface elevation (not just the surface layer).

Does this help?

Martin

On 18 Oct 2006, at 13:47, Patrick Rosendahl wrote:

> Hello all,
>
> I hope someone can clearify this.
> a) I want to use hydro"dynamic" code: nonHydrostatic=.TRUE.,
> b) I want to use free surface: rigidLid=.FALSE.,
> c) I want to use the linearized free surface (the only one that  
> works with hydrodynamic): nonlinFreeSurf=0,
> d) I want to use "high waves" (together with a fine resolution) so  
> I use: select_Rstar=2,
> e) I can toggle the handling of the free surface explicit/implicit:  
> implicitFreeSurface=.TRUE.,
>
>
> My questions are
>
> - without R*-coordinates the largest wave is restricted to the  
> discretisation in the uppermost layer ?
> - has R*-switch an effect with nonlinFreeSurf=0 ?
>
>
> The model runs fine, but I dont know how to interpret the eta  
> values. Is the whole column streched (R*-coords), or is it just the  
> uppermost layer width?
>
> Best regards,
> Patrick Rosendahl
>
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