[btrettel]

Fluid dynamicist here. The word "compressible" has multiple meanings and this might be confusing you. You don't need compressible flows in the sense of high Mach numbers. There are other models where the flow is variable density, but thermodynamic and hydrodynamic pressure are decoupled to remove the pressure waves that make high Mach number flows hard. There's also the Boussinesq approximation for buoyancy when the density varies only a small amount. I'm not particularly familiar with atmospheric models, but I'm sure they don't use the high Mach number form. "Incompressible" methods are common for the second class of model I mentioned, though how to use them so might not be obvious.