Compressibility Effects on the Linear-stability of Centrifugal Buoyancy-induced Flow

TL;DR

This paper investigates how compressibility influences the linear stability and convection patterns in centrifugal buoyancy-driven flows using DNS and stability analysis, revealing that compressibility reduces growth rates and alters convection cell formation.

Contribution

It introduces a combined DNS and stability analysis approach to study compressibility effects on centrifugal buoyancy-induced flow stability, which is novel in this context.

Findings

Critical wavenumber is shorter in nonlinear regime than linear stability predicts.

Compressibility reduces the growth rate of dominant convection modes.

Compressibility modifies convection cell formation in the flow.

Abstract

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.