Stability of Unstably Stratified Shear Flow in a Channel Under Non-Boussinesq Conditions

We investigate the linear stability of unstably strati ed Poiseuille ow between two horizontal parallel plates under non-Boussinesq conditions. It is shown, that Squire's transformation can be used to reduce the three-dimensional stability problem to an equivalent two-dimensional one. The eigenvalue problem, consisting of the generalized Orr-Sommerfeld equations, is solved numerically using an integral Chebyshev pseudospectral method. The in uence of the non-Boussinesq e ects on stability is studied. The dependence of the critical Rayleigh number on the Reynolds number and temperature di erence parameter is obtained. As in the Boussinesq case, results show that the most unstable mode is that of longitudinal rolls. However, in contrast to the Boussinesq case, the rolls are highly distorted for large temperature di erences. In addition, the critical Rayleigh number increases with the increase of the temperature di erence and is independent of the Reynolds number. Appeared in ACTA Mechanica, 112, 37-58 (1995)