Abstract
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 \(\varepsilon \ll 1\), whereas the Rossby number scales like \(\varepsilon ^m\) 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 \(\varepsilon \rightarrow 0\), to the 2-D incompressible Navier–Stokes system with a corresponding random forcing term.
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