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.