Non-Boussinesq Convection in a Tall Cavity Near the Codimension-2 Point

By means of weakly nonlinear analysis, we investigate the interaction between two physically distinct instability modes arising in the non-Boussinesq convection flow in a differentially heated tall vertical air-filled cavity. It is shown that in the neighborhood of the codimention-2 point the primary parallel flow becomes unstable due to both shear and buoyant disturbances. The flow dynamics is modeled by a system of the two coupled Landau equations. Different possible instability wave patterns are found, and the parameter regions of their existence are discussed. Energy analysis of the interacting instability modes is also presented.