Adds a validation example that can use both a NonhydrostaticModel and HydrostaticFreeSurfaceModel with an implicit surface. The solution of the hydrostatic model here isn't very good since the physics are inherently non-hydrostatic, but the main purpose here is to test that the model works in the sense that it produces what we would expect it to produce. After this is merged I intend to add a SplitExplicit hydrostatic model to the same script in #5351.

cc @simone-silvestri

Should be easy to make the dynamics hydrostatic by using a large aspect ratio

Should be easy to make the dynamics hydrostatic by using a large aspect ratio

Right, I was kind of avoiding doing that because we also want to test the nonhydrostatic capabilities of PerturbationAdvection, but there's no reason we can't do both. So I made the validation script very flexible, and as it is it runs three cases: a very flat (i.e. hydrostatic physics) hill with the nonhydrostatic model + free surface, the same setup with a hydrostatic implicit free surface model, and a steep hill with a nonhydrostatic model with rigid lid. Hey there are respectively:

I'm not super familiar with hydrostatic physics, so it'd be good to have a second set of eyes in these examples, but the animations look reasonable to me when taking into consideration the limitations of each model.

@simone-silvestri do you mind taking a look at this validation? After we merge this I'd like your work in #5351 to it

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✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 68.89%. Comparing base (85ba915) to head (6e29156).
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##             main    #5359      +/-   ##
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- Coverage   74.01%   68.89%   -5.12%     
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  Files         400      400              
  Lines       22875    22153     -722     
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- Hits        16930    15263    -1667     
- Misses       5945     6890     +945     

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@simone-silvestri do you mind taking a look at this validation? After we merge this I'd like your work in #5351 to it

Sorry was on vacation for a while. Looks good!