I believe Oceananigans currently has the option to have curvilinear coordinates in the horizontal and a regular grid in the vertical. This has been used to solve the HydrostaticFreeSurfaceModel in spherical coordinates.

Using what is currently available, it seems like one could adapt this to create a HydrostaticFreeSurfaceModel and maybe IncompressibleModel that allows for topography that varies in one-dimension. We could use a curvlinear grid in the x-z plane that is build on terrain following coordinates over smooth topography and then use a regular grid for the y direction.

I think this model would be interesting in it's own right but if nothing else it could be used for comparison with immersed boundary methods that include topography, which I presume is an idea people have? Immersed boundary could be more powerful in that it would allow for two-dimensional topography.

Questions:

• If I define a terrain-following grid then what new code will need to adapted to do the above?
• Would this be as easy to do for the nonhydrostatic model as for the hydrostatic one?
• If we define a boundary-following shallow water model to deal with smooth coastlines, could we modify the ShallowWaterModel to evolve in this geometry? This is actually purely horizontal so maybe it would be easier?

I have not done anything towards these goals and simply testing the waters (pun intended) as to how easy/difficult and interesting, and people think of this.

@glwagner ?