  In this article our goal is to study the singular limits for a scaled
barotropic Euler system modelling a rotating, compressible and inviscid fluid,
where Mach number $=\epsilon^m $, Rossby number $=\epsilon $ and Froude number
$=\epsilon^n $ are proportional to a small parameter $\epsilon\rightarrow 0$.
The fluid is confined to an infinite slab, the limit behaviour is identified as
the incompressible Euler system. For \emph{well--prepared} initial data, the
convergence is shown on the life span time interval of the strong solutions of
the target system, whereas a class of generalized \emph{dissipative solutions}
is considered for the primitive system. The technique can be adapted to the
compressible Navier--Stokes system in the subcritical range of the adiabatic
exponent $\gamma$ with $1<\gamma\leq\frac{3}{2}$, where the weak solutions are
not known to exist.
