  In the present thesis, we are interested in the description of the dynamics
of flows on large scales. In this context, the fluids are governed by
rotational, weak compressibility and stratification effects, whose importance
is measured by adimensional numbers: the Rossby, Mach and Froude numbers. The
first part of the thesis is dedicated to the analysis of a 3D multi-scale
problem called the full Navier-Stokes-Fourier system where variations in
density and temperature are considered and in addition we take into account the
Coriolis, centrifugal and gravitational forces. We study, in the framework of
weak solutions, the combined incompressible and fast rotation limits in the
regime of small Mach, Froude and Rossby numbers and for general ill-prepared
initial data. In the case when the Mach number is of higher order than the
Rossby number, we prove that the limit dynamics is described by an
incompressible Oberbeck-Boussinesq type system. Conversely, when the Mach and
Rossby numbers have the same order of magnitude, we show convergence towards a
quasi-geostrophic type equation. Following "le fil rouge" of the asymptotic
analysis, in the second part of the thesis, we examine the effects of high
rotation for the 2D incompressible density-dependent Euler system. Now, the
main goal is to perform the singular limit in the fast rotation regime, showing
the convergence of the Euler equations to a quasi-homogeneous type system. The
proof of convergence of the two primitive problems towards the reduced models
is based on a compensated compactness argument. The key point is to use the
structure of the underlying system of Poincar\'e waves in order to identify
some compactness properties for suitable quantities. Compared to previous
results, our method enables to treat the whole range of parameters in the
multi-scale problem, and also to reach and go beyond the critical choice
$Fr=\sqrt{Ma}$.
