Documenting experience with the Kolmogorov-to-grid scale ratio required for numerical stability about dedales HOT 9 OPEN

Definitely one of the many interesting things about 3D turbulence is how quickly the small scales show up as compared to the 2D one! I am still working on getting a good intuition for exactly why the numerics breaks (or doesn't) for a given situation

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It looks like the zero_max function in AMD is implementing a hard max rather than a soft max. This may be part of the problem -- computing the hard max on a certain grid may result in oscillations leading to negative values at different points.

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@kburns this wouldn't affect ConstantSmagorinsky though, correct?

Can we use a spectral filter on the eddy viscosity/diffusivity itself, rather than the solution?

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Well I'm not sure which closure @wenegrat was referring to, but it doesn't look like we currently have any regularization on the constant smagorinsky eddy viscosity, right?

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Right @kburns there is no regularization on Smagorinsky; it is "guaranteed" > 0. So perhaps negative viscosity is only possible with regularization?

Still puzzled how LES is ordinarily done with spectral methods.

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I think it's only guaranteed to be positive on the dealiased (scales=3/2) grid points, where it is calculated, but the spectral interpolant may end up being negative at other points, perhaps including the output grid (scales=1) if there are sharp features in the field.

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It's a little subtle -- during the simulation, the subgrid viscosity will be calculated on the grid, where it should be non-negative, and immediately multiplied by the other terms to produce the subgrid stress. However, if you designate that you want to save the subgrid viscosity as an output, there may be a round-trip transform to coefficient space and back to grid space before it is saved to disk. Even without dealiasing, this may slightly change the grid values since the Fourier Nyquist mode is dropped during these transforms, so the FFT is not quite exactly 1-to-1 (as an aside, this is a bit of a pain, but when you think about applying operators in coefficient space, it doesn't make much sense to keep and work with the Nyquist mode). So this may result in slightly negative values, on the order of the Nyquist mode amplitude. This may seem bad, but it's also the order-of-magnitude of the truncated terms, so its probably a decent estimate of how negative the truncated spectral interpolant may be between the grid points, anyways.

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