# [MITgcm-support] isotropic_cos_scaling and gmredi

Martin Losch Martin.Losch at awi.de
Sun Jan 14 04:25:01 EST 2007

Hi Jean-Michel,

thanks for the clarification. I agree with your explanation for
coarse resolution models  (although there is a little doubt left in
the back of my head, but I'll ignore it for now), which is what I
need right now.

For eddy-resolving/permitting runs, the story may be different: You
resolve the eddy, and thus don't need GM, but with a lot of small
eddies there's going to be a lot of local diapycnal mixing on the
small scale, if the mixing tensor is oriented horizontally, and we
may use some sort of rotated tensor for that case, too. I don't know
if anybody has ever looked into that issue.

Martin

On 13 Jan 2007, at 19:25, Jean-Michel Campin wrote:

> Hi Martin,
>
> My impression regarding cosFac & Redi (isopycnal) diffusivity:
> The diffusivity is set according to "physical" argument
> (the effect of non-resolved eddies, not dependent of the
> grid spacing, at least at coarse resolution),
> and not numerical (i.e., make the model stable at this
> resolution), and therefore, we don't need and don't want cosFac.
> And regarding GM transport, I think it would not be right to put
> cosFac in it. Just thinking of a kind of "front-relax" experiment,
> with uniform slope, don't think you want to flaten the isopycnal
> much more slowly where the (coarse) grid model is finer (with a
> curious stream function).
> I am not saying that in a kind of "eddy permitting" model, those
> arguments still apply, but at coarse resolution, this seems
> relatively clear to me.
> Hope this will help.
>
> Cheers,
> Jean-Michel
>
> On Sat, Jan 13, 2007 at 11:17:36AM +0100, Martin Losch wrote:
>> Hi,
>>
>> I run a global model on an "isotropic" grid, that is, my dlat is
>> scaled with cos(latitude), that is, dlat = dlat(0)*cos(latitude), so
>> that my grid cells are nearly quadratic (dlon = dlon(0)*cos(latitude)
>> because of converging longitude circles). With the CPP-flag
>> ISOTROPIC_COS_SCALING one can achieve that the viscosity and
>> diffusivity are scaled so that, e.g. d^2\theta/dy^2 is discretized as
>> (roughly): d^2\theta* cos(latitude)^n / ( dlat(0)^2*cos(latitude)^2 )
>> where "n" is set in data (parameter cosPower), that is, the
>> diffusivity decreases with grid spacing.
>>
>> Now, for the viscosity this is depreciated and one should rather use
>> the dimensionless parameters viscAhgrid, which scale automatically
>> with the grid spacing, or even the variable viscosity (Leigth,
>> Smagorinsky), so I have ISOTROPIC_COS_SCALING defined only
>>
>> However, I don't want to use horizontal diffusion, but the GMREDI
>> package, so that tracers are mixed along isopycnals. I made a few
>> suprising observations, had a look at the code and could not find any
>> provisions for the ISOTROPIC_COS_SCALING in the gmredi package. This
>> is the first time that I have a closer look at the gmredi code so I
>> may have missed something, but I assume that the equivalent routines
>> I am wondering why we don't have the
>> cosFacU
>> in gmredi_xtransport.F and
>> #ifdef ISOPYCNAL_COS_SCALING
>> cosFacV
>> #endif
>> in gmredi_ytransport.F in analogy to gad_diff_x/y.F
>> Is this simply not necessary? because the redi-tensor entries already
>> contain this factor, and I just didn't see it?
>>
>> Puzzled,
>>
>> Martin
>>
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