hyper/hypo viscosity in Oceanangians (for a 2D model)

[peitianyi23-sudo]

Hi Oceanangians users!

Previously I studied 2D turbulence using spectral method. Now I wanna try out Oceanangians to use double no-slip BCs and irregular meshs.
I have a question about how to include hyper/hypo viscosity, or a simple linear ekman drag -\alpha \bm{u}, into the simulation. Is there something I can change in the "Turbulence Closures" or i should include this term in the RHS like a forcing? I provide a general NS equation with hyper/hypo viscosity below.

[glwagner]

Linear drag can be implemented with a simple Forcing. Here's the docs for that:

https://clima.github.io/OceananigansDocumentation/stable/models/forcing_functions/

Hypoviscosity cannot be easily implemented in a finite volume model --- to do so, you have to solve a Poisson problem every time-step:

$$ \nabla^2 F_u = u / \mu $$

where $F_u$ is the forcing term that would appear in the momentum equation. In principle it is possible to use the Poisson solvers for this, but it will be a bit of a journey.

[peitianyi23-sudo]

Thanks for the reply！If I am getting this right, I should be able to implement hyperviscosity by adding a forcing on the RHS:
$$
F_{\nu,m}=-\nu_{2m}\nabla^{2m}\bm{u}.
$$
I will try it out then.

[glwagner]

Hyperviscosity is supported internally. Check out ScalarBiharmonicDiffusivity. The internal implementation may have bettern numerical properties than implementing it yourself.

[peitianyi23-sudo]

Got it! I will look into it :)