Convective and absolute instabilities in non-Boussinesq mixed convection

Abstract

[Abstract]: The problem of non-Boussinesq mixed convection in a vertical channel formed by two differentially heated infinite plates is investigated and the complete convective/absolute instability boundary is computed for a wide range of physical parameters. A physical insight into the mechanisms causing instabilities is given. In particular, it is shown that the appearance of absolute instability is always dictated by a flow reversal within a channel, however existence of the flow reversal does not exclude the possibility of convective instability. It is also shown that fluid's nonlinear transport property variations have a dramatic effect on the structure and complexity of spatio-temporal instabilities of the co-existing buoyancy and shear modes as the temperature difference across the channel increases. The validity of the stability results obtained using the procedure described in (J. Comp. Phys.212, 188-217) is assessed using the method of steepest descent.