In experiments, Plesniak, Mehta & Johnson (1994) have noted that curved two
-stream mixing layers are susceptible to centrifugal instabilities under th
e condition that the slower of the streams curves towards the faster one; t
his condition is analogous to the concave curvature condition for the stabi
lity 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 incom
pressible mixing layers; Otto, Jackson & Hu (1996). In this paper we go on
to investigate the roles of compressibility and heating in determining the
streamwise fate of Gortler vortices within these situations.
The development of the disturbances is monitored downstream and curves of n
eutral stability are plotted. The effect of changing the Mach number and fr
ee-stream temperatures is studied in detail. It is found that for certain p
arameter regimes modes can occur within convexly curved, or 'stable' mixing
layers; these 'thermal modes' have no counterpart within incompressible mi
xing layers. By making use of a large Gortler number analysis we are able t
o verify our numerical results, and derive a very simple condition which yi
elds information about the parameter ranges for which certain modes are lik
ely to occur. As an aside this method can be used to show that no degree of
wall cooling will allow sustained growth of Gortler vortices within bounda
ry layers over convex plates.