HydrostaticFreeSurfaceModel and TKEBudgetTerms

[rafacmartins]

Hi all, that's more a question than an issue.

So, I run a few simulations using the HydrostaticFreeSurfaceModel configuration and wanted to calculate some diagnostics for it's output so I found this package (awesome btw).
I don't know if that's some silly question but I want to calculate some terms using the TKEBudgetTerms, for example the BuoyancyProductionTerm or the AdvectionTerm and it returns me an error when I use the HydrostaticFreeSurfaceModel config and I don't see why.
Like, for the AdvectionTerm ADV = uᵢ∂ⱼ(uᵢuⱼ), why the HydrostaticFreeSurfaceModel not work? For the BP term I think that's related to the fact that the w in this configuration it's just a product of the divergence/convergence of u and v, but even though I thought that it may work.

I don't know if that's something I'm missing and it's pretty obvious or not.
Any help is appreciated!

Cheers.

[glwagner]

I think to be correct, the "turbulent" kinetic energy has to be defined differently; within the hydrostatic approximation the vertical velocity is asymptotically smaller than the horizontal velocities, so the fluctuating kinetic energy will be (u^2 + v^2) / 2 I think. Note, this is usually called "eddy kinetic energy", because we are now referring tot he energy contained in quasi-2D submesoscale/mesoscale turbulence, rather than a 3D TKE from a large eddy simulation for example.

[tomchor]

Yeah I agree with @glwagner. "TKE" for the hydrostatic model is a bit different. The reason why it's failing is because I haven't taken the time to figure out what the best approach is, so it's not yet programmed. Would you be interested in opening a PR so that we can work on this together and hopefully get that working for you (and other users)?

[glwagner]

Another issue with the hydrostatic model is that part of the buoyancy production will typically be parameterized with a vertical diffusivity, right? For example, closures like CATKEVerticalDiffusivity and TKEDissipationVerticalDiffusivity use an explicit TKE budget equation to evolve the tracer e that represents TKE. To build a user interface for diagnostics with the hydrostatic model, one should take care to distinguish between terms that appear in a parameterized budget equation, versus explicitly resolved terms that must be diagnosed. The total buoyancy production should properly include both, but one might want one or the other for some purpose.

It could make sense to throw an error if one is attempting to use nonhydrostatic-specific diagnostics for a hydrostatic model.

[rafacmartins]

I think to be correct, the "turbulent" kinetic energy has to be defined differently; within the hydrostatic approximation the vertical velocity is asymptotically smaller than the horizontal velocities, so the fluctuating kinetic energy will be (u^2 + v^2) / 2 I think. Note, this is usually called "eddy kinetic energy", because we are now referring tot he energy contained in quasi-2D submesoscale/mesoscale turbulence, rather than a 3D TKE from a large eddy simulation for example.

I'm not sure if I understood it right...
I agree with the fact that vertical velocity tend to be asymptotically smaller than the horizontal velocities in a hydrostatic model, but in my case (maybe I should've mentioned this before) where I'm doing analysis of the development of submesoscale instabilities the w is not so small. So I'm not sure if I should consider only the zonal and meridional components of the velocity to calculate the TKE budget.

Yeah I agree with @glwagner. "TKE" for the hydrostatic model is a bit different. The reason why it's failing is because I haven't taken the time to figure out what the best approach is, so it's not yet programmed. Would you be interested in opening a PR so that we can work on this together and hopefully get that working for you (and other users)?

Yes, I would be very interested in work together on this! I can open a PR on this.

Another issue with the hydrostatic model is that part of the buoyancy production will typically be parameterized with a vertical diffusivity, right? For example, closures like CATKEVerticalDiffusivity and TKEDissipationVerticalDiffusivity use an explicit TKE budget equation to evolve the tracer e that represents TKE. To build a user interface for diagnostics with the hydrostatic model, one should take care to distinguish between terms that appear in a parameterized budget equation, versus explicitly resolved terms that must be diagnosed. The total buoyancy production should properly include both, but one might want one or the other for some purpose.

It could make sense to throw an error if one is attempting to use nonhydrostatic-specific diagnostics for a hydrostatic model.

Yes, that's something we need to consider, which exactly closure was used for the simulation. In my case, so far I've been using VerticalScalarDiffusivity and HorizontalScalarDiffusivity.

[tomchor]

Yeah I agree with @glwagner. "TKE" for the hydrostatic model is a bit different. The reason why it's failing is because I haven't taken the time to figure out what the best approach is, so it's not yet programmed. Would you be interested in opening a PR so that we can work on this together and hopefully get that working for you (and other users)?

Yes, I would be very interested in work together on this! I can open a PR on this.

Nice! Looking forward to working on that with you. Let me know if you need help or are otherwise unclear on the steps for opening a PR.

[glwagner]

but in my case (maybe I should've mentioned this before) where I'm doing analysis of the development of submesoscale instabilities the w is not so small.

w has to be asymptotically small for the hydrostatic approximation to be valid. If w is not small then you may want to consider using the NonhydrostaticModel!

[rafacmartins]

Nice! Looking forward to working on that with you. Let me know if you need help or are otherwise unclear on the steps for opening a PR.

I would appreciate! It would be my first time doing something like this, so I would be grateful if you could guide me on what I should do to opening a PR.

[rafacmartins]

w has to be asymptotically small for the hydrostatic approximation to be valid. If w is not small then you may want to consider using the NonhydrostaticModel!

Well, this is true! I think that maybe in my simulation I'm always dealing with the non-dimensional value of w (w/W_0) so that's why I may have think that the values are somehow bigger enough to be consider into the calculation of the TKE for example, but looking at the values of w itself, they're still considered asymptotically small.

[tomchor]

Nice! Looking forward to working on that with you. Let me know if you need help or are otherwise unclear on the steps for opening a PR.

I would appreciate! It would be my first time doing something like this, so I would be grateful if you could guide me on what I should do to opening a PR.

No worries! You can look at the Oceananigans' contributor's guide for guidance on Oceanostics as well. Basically the first step is to fork Oceanostics.

After that you make the changes that are appropriate on your own fork. In this case I'd recommend starting with the simplest way to deal with the problem, which is to define a kinetic energy quantity for hydrostatic models that takes only the horizontal components. This banks on the assumption that $w$ is vanishingly small in hydrostatic dynamics and should be asymptotically true. Curious if @glwagner has a different idea though

Then you open a PR and get comments on the code :)

[glwagner]

w has to be asymptotically small for the hydrostatic approximation to be valid. If w is not small then you may want to consider using the NonhydrostaticModel!

Well, this is true! I think that maybe in my simulation I'm always dealing with the non-dimensional value of w (w/W_0) so that's why I may have think that the values are somehow bigger enough to be consider into the calculation of the TKE for example, but looking at the values of w itself, they're still considered asymptotically small.

Ok, but the problem is that there is not room for interpretation on this matter. You cannot form an evolution equation for 3D kinetic energy from the hydrostatic model equations, because there is no term dt w. You can compute a 3D kinetic energy, but it is not the kinetic energy that corresponds to your model equations. The variance of vertical velocity obeys a different constraint than it does in the nonhydrostatic system.

That said, we can still use the buoyancy flux term in the KE budget if we use it consistently along side the pressure transport term (eg this is the budget we get if we add w (dz p = b) to KE balance).

[glwagner]

More generally all of the diagnostics here should correspond identically to terms that can be derived from a principle / rational argument.