Discussion
Which problem do spherical coordinates create at the poles?
Answer: D
All meridians converge at the pole, so the longitudinal grid spacing shrinks to zero and the permissible time step collapses with it. Numerical models handle this with filtering, reduced grids or entirely different meshes such as the cubed sphere or icosahedral grids. The Coriolis parameter reaches a finite maximum of twice the rotation rate, gravity is perfectly well defined, and the pressure gradient is computable given a suitable representation of the field.
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