[MITgcm-support] Mellor-Yamada in MITgcm

[Martin Losch]

Hi Olivier,

in general, this package is not really maintained. I implemented this almost 20y ago to do some mixing scheme comparisons, but this never went anywhere.

Question 1:
I followed M. Satoh, Atmospheric Circulation Dynamics and General Circulation models, Springer, 2004 and give equation numbers in the code. According to this “l” = MYhbl (in m) and “q" = tkel = sqrt(turbulent kinetic energy) (in m/s), and that would give mixing coefficients in m^2/s. I don’t know if variable tke is really turbulent kinetic energy (even if the name implies it) because it (i.e. tkesquare) is computed from GM and GH, which both have units of 1/s^2 (buoyancy and shear squared).
I cannot remember the details of this and obviously I did not know what I was doing back then, so if you find that this is not correct, it would be best to open an issue on github or even a PR with a suggestion for a fix.

Question 2:
the variable MYdiffKr is defined at the same places as KappaRx, i.e. at W-points,
MYviscAr is defined also at W-Points, and then it’s averaged horizontally to U and V points (but still at the W-interface) to be at the same place as KappaRU/V. The diagnostics are just MYdiffKr/MYviscAr at W-points. (all of this is copied from pkg/kpp), the “diagnostice code” should reflect that (the “L”), but I agree that this is not intuitive, it’s just some code, see https://mitgcm.readthedocs.io/en/latest/outp_pkgs/outp_pkgs.html , table 9.1

Martin

> On 22. Feb 2024, at 21:38, Olivier Marchal <omarchal at whoi.edu> wrote:
> 
> Hello All,
> 
> I would appreciate input on the following two questions which arose when looking at how Mellor-Yamada is implemented in MITgcm:
> 
> 1. The following statements appear one lines 161-162 of my82_calc.F:
> 
> MYviscAr(I,J,K,bi,bj) = MYhbl(I,J,bi,bj)*tkel*SM(I,J,K)
> MYdiffKr (I,J,K,bi,bj) = MYbhl(I,J,bi,bj)*tkel*SH(I,J,K)
> 
> where tkel is calculated one line 159 from
> 
> tkel =  MYhbl(I,J,bi,bj)*tke(I,J,K)
> 
> and tke is calculated on line 113 from
> 
> tke(I,J,K) = sqrt(tkesquare) 
> 
> The coded equations for MYviscAr and MYdiffKr can easily be related to equations (32a)-(32b) of Mellor and Yamada (1982). However, assuming MYhbl is in [m], tke = sqrt(tkesquare) is in [m/s] so that tkel is in [m^2/s], and SM and SH are dimensionless, then MYviscAr and MYdiffKr would be in [m^3/s] and so would not have units of viscosities and diffusivities. Shouldn't tkel on line 161-162 be replaced by tke(I,J,K)?
> 
> 2. At which depths of the C grid do the values in the diagnostic files KPPviscAz.* and KPPdiffKz(T,S).* correspond to? To the depths of the U,V-carrier points, or to the depths of the W-carrier points? Viscosities/diffusivities are often defined at W-carrier points since vertical turbulent flux divergences are often discretized using central-difference schemes, but it is unclear to me whether these are the values in the diagnostic files.
> 
> Any input about (1)-(2) would be deeply appreciated.
> 
> Thank you!
> 
> Olivier.
> 
> 
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