Görtler vortices in compressible mixing layers (Q2709178)

Experiments 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 [\textit{S. R. Otto}, \textit{T. L. Jackson} and \textit{F. Q. Hu} [J. Fluid Mech. 315, 85-103 (1996; Zbl 0874.76019)]. This paper investigated the roles of compressibility and heating in determining the streamwise fate of Görtler vortices in these situations. NEWLINENEWLINENEWLINEHere the development of disturbances is monitored downstream, and curves of neutral stability are plotted for compressible mixing layers. The effect of changing the Mach number and free-stream temperatures is studied in detail. It is found that, for certain parameter regimes, modes can occur within convexly curved, or `stable' mixing layers; these `thermal modes' have no counterpart within incompressible mixing layers. The large Görtler number analysis allows to verify numerical results, and derive a very simple condition which yields information about the parameter ranges in 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.