Analysis of instability patterns in non-Boussinesq mixed convection using a direct numerical evaluation of disturbance integrals

Abstract

The Fourier integrals representing linearised disturbances arising from an initially localised source are evaluated numerically for natural and mixed convection flows between two differentially heated plates. The corresponding spatio-temporal instability patterns are obtained for strongly non-Boussinesq high-temperature convection of air and are contrasted to their Boussinesq counterparts. A drastic change in disturbance evolution scenarios is found when a large cross-channel temperature gradient leads to an essentially nonlinear variation of the fluid’s transport properties and density. In particular, it is shown that non-Boussinesq natural convection flows are convectively unstable while forced convection flows can be absolutely unstable. These scenarios are opposite to the ones detected in classical Boussinesq convection. It is found that the competition between two physically distinct instability mechanisms which are due to the action of the shear and the buoyancy are responsible for such a drastic change in spatio-temporal characteristics of instabilities. The obtained numerical results confirm and complement semi-analytical conclusions of [Suslov SA. Spatio-temporal instabilities in non-Boussinesq convection. Teor Comp Fluid Dyn 2007;21(4):271–290] on the absolute/convective instability transition in non-Boussinesq mixed convection. Generic features of the chosen numerical approach are discussed and its advantages and shortcomings are reported.