Multi-mode spatio-temporal instability in non-Boussinesq convection

It is shown that nonlinear (non-Boussinesq) fluid property variations caused by large temperature differences between the walls of a vertical channel are responsible for the appearance of physically distinct types of instability in mixed convection flows: the previously known shear and new buoyancy-induced instabilities. Shear instability dominates the forced convection regimes, while the buoyancy instability prevails in nearly natural convection states. The most challenging situation requiring elaborate theoretical analysis and numerical verification arises in a mixed convection regime where both instabilities compete, forming a wide variety of possible flow patterns. Each of the instabilities is found to undergo the transition from a convective state (when disturbances grow and propagate away from their source) to absolute (when disturbances grow and occupy the complete flow domain). A number of regions in a complete parameter space corresponding to qualitatively different flow scenarios are identified, and accurate boundaries separating them are computed. Various patterns are illustrated by the direct evaluation of the Fourier integrals representing disturbances.