A Multi-scale Limit of a Randomly Forced Rotating 3-D Compressible Fluid

We study a singular limit of a scaled compressible Navier-Stokes-Coriolis system driven by both a deterministic and stochastic forcing terms in three dimensions. If the Mach number is comparable to the Froude number with both proportional to say ɛ≪1, whereas the Rossby number scales like ɛm for m>1 large, then we show that any family of weak martingale solution to the 3-D randomly forced rotating compressible equation (under the influence of a deterministic centrifugal force) converges in probability, as ɛ→0, to the 2-D incompressible Navier-Stokes system with a corresponding random forcing term.