Flow patterns near codimension-2 bifurcation in non-Boussinesq mixed convection

Realistic nonlinear (non-Boussinesq) fluid property variations with temperature (expressed, for example, by the Sutherland formulae for viscosity and thermal conductivity and by the ideal gas equation of state for the density) are shown to lead to a rich variety of flow instability phenomena in the classical problem of mixed convection in a differentially heated vertical channel. The instabilities are caused by competing buoyancy and shear effects. One of the most complicated and interesting flow regimes arises when two instability modes bifurcate simultaneously at the so-called codimension-2 point. It is shown that such a situation can be modelled successfully by coupled cubic complex Landau-type equations derived using a weakly nonlinear stability theory. In this paper the unfoldings of one of the double Hopf bifurcations detected in non-Boussinesq mixed convection are investigated. The complete set of resulting flow patterns is studied as functions of governing physical parameters. This paper complements a general classification of unfoldings of codimension-2 bifurcations and interprets the results obtained for the model dynamical system from the physical point of view.