[MITgcm-support] Vertical diffusion for non-hydrostatic ocean model with a stretched grid

[Burns, Paul]

Hi Jean-Michel,

Many thanks for your quick and clear response.

I agree that I should try option 2), which appears to calculate both the viscosity and diffusivity for the tracers (simply by using a constant Prandtl number)?  Yes, the Smagorinsky model essentially parameterises subgrid mixing by using the resolved shear and grid resolution, and so does not explicitly account for stratification.  I hope that my very fine vertical grid resolves most buoyancy-driven (and mechanical) mixing.

MITgcm does have a TKE 1.5-order closure scheme (i.e., package ggl90), however, it seems only suitable for hydrostatic simulations, when the mixing length in the scheme doesn't need to be limited to the grid resolution.  This at least is my understanding from the paper by Blanke and Delecluse (1993).

My grid is certainly not isotropic, but I have no bottom topography so the grid cells are at least aligned with the horizontal.  I am not sure what errors my grid may introduce when using the Smagorinsky scheme?  I guess I can test the results using the Smagorinsky scheme against simply specifying a profile of viscosity and diffusivity using the relevant Reynolds number (i.e. setting viscArNr).


Cheers,
Paul








Dr Paul Burns MInstP FRMetS

Research Fellow

Geophysical and Astrophysical Fluid Dynamics Group

Department of Mathematics

Harrison Building

University of Exeter

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From: MITgcm-support <mitgcm-support-bounces at mitgcm.org> on behalf of Jean-Michel Campin <jmc at mit.edu>
Sent: 01 February 2023 15:25
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Subject: Re: [MITgcm-support] Vertical diffusion for non-hydrostatic ocean model with a stretched grid

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Hi Paul,

There is some confusion about Smagorinsky in MITgcm since we have 2 implementations:
1) a Smagorinsky like horizontal viscosity that is function of horizontal shear,
  with the choice of harmonic (viscC2smag) or bi-harmonic (viscC4smag) viscosity.
2) a simple 3-D Smagorinsky harmonic viscosity that work best when the grid is
  near isotropic (mostly for Non-Hydrostatic simulation) and does not acount for
  stratification.
  Need ALLOW_SMAG_3D_DIFFUSIVITY to be defined and uses run-time parameter:
   useSmag3D = .TRUE., with smag3D_coeff,
  see experiment: tutorial_deep_convection, with input.smag3d/data

You may want to try this second implementation.
Alternatively, you could always set a vertical profile of (background)
vertical viscosity using Nr values to set vector "viscArNr" in main parameter
input file "data" (note that the fist value corresponds to the very top,
i.e., surface, vertical index k=1, and has no effect).

Cheers,
Jean-Michel

On Wed, Feb 01, 2023 at 12:55:22PM +0000, Burns, Paul wrote:
> Hi,
>
> I was hoping that someone could give me some advice about the best way to define the vertical viscosity (and diffusivity) in MITgcm for a non-hydrostatic model using a stretched vertical grid.  I've used a stretched vertical grid to resolve very small features of interest (~0.2 m) in the upper ocean and to keep the simulation practical.
>
> The viscosity should vary with the grid resolution (e.g., Smagorinsky, 1993), however, the MITgcm documentation says that the Smagorinsky scheme isn't implemented in the vertical. So would a reasonable approach be to compute a vertical profile of viscosities using a vertical Reynolds number and use that to set viscArNr?
>
>
> Many thanks,
> Paul
>
>
>
>
> Dr Paul Burns MInstP FRMetS
>
> Research Fellow
>
> Geophysical and Astrophysical Fluid Dynamics Group
>
> Department of Mathematics
>
> Harrison Building
>
> University of Exeter
>

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