Rotating compressible fluids under strong stratification

We consider the Navier–Stokes system written in the rotational frame describing the motion of a compressible viscous fluid under strong stratification. The asymptotic limit for low Mach and Rossby numbers and large Reynolds number is studied on condition that the Froude number characterizing the degree of stratification is proportional to the Mach number. We show that, at least for the well prepared data, the limit system is the same as for the problem without stratification—a variant of the incompressible planar Euler system.