We study a triple singular limit for the scaled barotropic Navier-Stokes
system modeling the motion of a rotating, compressible, and viscous fluid,
where the Mach and Rossby numbers are proportional to a small parameter, while
the Reynolds number becomes infinite. If the fluid is confined to an infinite
slab bounded above and below by two parallel planes, the limit behavior is
identified as a purely horizontal motion of an incompressible inviscid fluid,
the evolution of which is described by an analogue of the Euler system