There are two kinds of geophysical flow studies one can do. 2D simulations where you use models like shallow water equations. Then you deal with

• Velocity
• Reynolds number (which implies some viscosity)
• Froude number (or gravity)
• Rossby number (or Coriolis force from Earth's rotation)
• Total energy (so you know when it is in a statistically steady state)
• Density only if you add many layer
• Boundary conditions (only if it matters, can be avoided)

You can also do a 3D simulation, but often we use the Boussinesq equations, in which density is approximated as a passive scalar.

This is only the setup, but there is a rich set of phenomena one can aim to simulate with.