This would be a major new feature for Oceananigans!

The implementation would probably resemble what we've done for "CATKE", which has a prognostic TKE variable:

https://github.com/CliMA/Oceananigans.jl/tree/main/src/TurbulenceClosures/turbulence_closure_implementations/CATKEVerticalDiffusivities

I would vote to implement Burchard and Umlauf's "generic length scale" equation. In this formulation there's a TKE variable (like CATKE), and also a "length scale" variable, which can either be epsilon, omega, or Mellor-Yamada's "q^2 l". So we get all of those models with one implementation:

https://www.ingentaconnect.com/content/jmr/jmr/2003/00000061/00000002/art00004

The implementation might also want to take into account / support a few other formulations like

• Harcourt 2015
• Kantha Clayon 2004

I think @simone-silvestri could be interested in this kind of thing. It's a major undertaking! I think we should refactor TurbulenceClosures to make implementing new models (like this one) easier, either before or at the same time.

By the way, the CATKEVerticalDiffusivity() might achieve what you want (but cheaper and more accurately, maybe?), since it bears a lot of structural resemblance to traditional k-epsilon closures. It's really in development now (I'm working on calibrating the parameters as we speak), but it might be ready for usage pretty soon...

Hi @iurt! Very nice that you are thinking to implement a new parametrization!

To start I would try to implement the additional prognostic equations, decoupled from the main solution.
You can use the existing infrastructure for tracer evolution and modify the k or epsilon (or omega or whatever quantity you choose to evolve) "specific" dissipation terms in the TurbulenceClosures module.

Once that is done and validated we can couple them to the momentum equations through the definition of a new "eddy viscosity" which uses values from the newly defined tracers