  We study the singular limit of a rotating compressible fluid described by a
scaled barotropic Navier-Stokes system, where the Rossby number, the Mach
number and the Froude number tend to 0 in a particular mutual rate while the
Reynolds number tends to infinity. The inviscid planar Euler system is
identified as the limit problem. The proof is based on the application of the
method of relative entropies and careful analysis of oscillatory integrals
describing the propagation of Rossby-acoustic waves.
