On the stability of generalized thermal shear flows

A mathematical stability analysis is carried out for the physical situation where a horizontal layer of an incompressible inviscid heat conducting fluid incorporates a differential streaming in the horizontal direction and density variations in the vertical direction. The entire system is situated between two horizontal boundaries of different but uniform temperature, the temperature of the lower boundary being higher than that of the upper one. Temperature variations and streaming are continuous functions of the vertical coordinate everywhere in the flow. A marginal state solution of the governing equations is obtained and analyzed. It is shown that nonoscillatory modes, if they exist, are unstable.