  The focus of this study is to understand the evolution of instability in
centrifugal buoyancy-induced flow in a rotating system. The problem is of
interest in atmospheric flows as well as in engineering applications. In this
study, we perform direct numerical simulations (DNS) by solving the
compressible Navier-Stokes equations and multi-dimensional stability analyses
by using a forced DNS approach. We systematically and independently vary the
Rayleigh and Mach numbers. The heat transfer by thermal conduction is used as
base flow and maintained as a reference state, upon which the growth of small
perturbations is investigated. It is found that the critical wavenumber
obtained from the linear stability analysis at the onset of convection has a
much shorter wavelength than the one that eventually appears in the non-linear
regime. Further, the investigations show that compressibility effects lead to a
reduction of the growth rate of the dominant mode, and it modifies the overall
formation of convection cells in the cavity.
