In two-phase flows of steam, when the velocity is between the equilibrium and frozen speeds of sound, the system is fundamentally unstable. Because any disturbance of the system, e.g. imposition of a small supercooling on the fluid, will cause condensation, the resulting heat release will accelerate the flow and increase the supercooling and thus move the system further from thermodynamic equilibrium. But in high-speed flows of a two-phase mixture, dynamic changes affect the thermodynamic equilibrium within the fluid, leading to phase change, and the heat release resulting from condensation disturbs the flow further and can also cause the disturbances to be amplified at other Mach numbers. To investigate the existence of instabilities in such flows, the behaviour of small perturbations of the system has been examined using stability theory. It is found that, although the amplification rate is highest between the equilibrium and frozen speeds of sound, such flows are temporally unstable at all Mach numbers.

In experiments, Plesniak, Mehta & Johnson (1994) have noted that curved two-stream mixing layers are susceptible to centrifugal instabilities under the condition that the slower of the streams curves towards the faster one; this condition is analogous to the concave curvature condition for the stability of the flow over a plate. The modes which arise manifest themselves as vortices aligned with the dominant flow direction. Previous numerical and analytical work has elucidated the structure of these vortices within incompressible mixing layers; Otto, Jackson & Hu (1996). In this paper we go on to investigate the rôles of compressibility and heating in determining the streamwise fate of Görtler vortices within these situations.The development of the disturbances is monitored downstream and curves of neutral stability are plotted. The effect of changing the Mach number and free-stream temperatures is studied in detail. It is found that for certain parameter régimes modes can occur within convexly curved, or ‘stable’ mixing layers; these ‘thermal modes’ have no counterpart within incompressible mixing layers. By making use of a large Görtler number analysis we are able to verify our numerical results, and derive a very simple condition which yields information about the parameter ranges for which certain modes are likely to occur. As an aside this method can be used to show that no degree of wall cooling will allow sustained growth of Görtler vortices within boundary layers over convex plates.

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