some problems about BackgroundVelocityField change with time

[Tinydog8]

Hello,
I'm trying to create a simulation with a background velocity field which will change with time(for example,ubg=sin(t)).I'm not sure that if ”BackgroundField“ takes the effect of non inertial reference system into account？or maybe I should use ”Forcing“ function in this situation？
Thanks in advance!

[glwagner]

BackgroundField doesn't change the frame of reference; it changes the meaning of the prognostic variables. I think U = sin(t) should be fine! But check out the equations in the docs to see if it's really the model you're looking for:

https://clima.github.io/OceananigansDocumentation/stable/physics/nonhydrostatic_model/

[Tinydog8]

BackgroundField doesn't change the frame of reference; it changes the meaning of the prognostic variables. I think U = sin(t) should be fine! But check out the equations in the docs to see if it's really the model you're looking for:

https://clima.github.io/OceananigansDocumentation/stable/physics/nonhydrostatic_model/

Thank you very much! If I defined the background velocity ubg changed with time, then the total velocity can be divided into u=v+ubg, v
is the resolved velocity. Take u into momentum equation, because the ubg change with time, there should have an additional term ∂(ubg)/∂t. But it seems not be mentioned in the document of "nonhydrostatic model", or maybe it is included in other terms? Thanks again！

[glwagner]

For sure, including a background field is not equivalent to simply substituting u = u_bg + u' into the momentum equations, and solving for u'.

I don't think you want to include the term ∂(ubg)/∂t. Consider: if you include that term, then the solution for the perturbation velocity is simply u = - u_bg, and you are back where you started.

Including a background field is only useful when we omit the "pure" background terms, and only include terms associated with background-perturbation interaction (right now we only include nonlinear advection terms and not potential nonlinear diffusion terms that would be associated with LES. This is a limitation.) One of the most important uses of BackgroundField is when we want to simulate periodic perturbations around a non-periodic flow (like Eady turbulence) in a periodic domain.

If you want dynamics that include both background dynamics and perturbation dynamics, then you should set your simulation up with forcing.

The docs just write down the equations that are solved when you use the background velocity. They don't explain why you want to solve that equation --- perhaps that's something we should add.

[Tinydog8]

Thanks a lot!！！！