Gortler vortices in curved mixing layers and their effect on the inherent instabilities

摘要

Curved mixing layers are known to be inherently unstable to short wavelength travelling waves (due to the layer's inflectional nature) and longitudinal vortex structures (due to the change in circulation); these are akin to Gortler vortices. We shall discuss the latter through their linear evolution and subsequent nonlinear growth. Depending on the size of the instability and other parameters this may cause the flow to breakdown. This manifests itself as large jets in the neighbourhood of the centre line of the mixing layer. Prior to the actual breakdown, the flow becomes inflectional in the spanwise coordinate and has additional structure in the normal direction. One is compelled to solve the Rayleigh stability equation with variation in the underlying state in more than one variable; this requires a sophisticated numerical method to solve the resulting partial differential eigenvalue problem. The presence of the vortices and their effect on the intrinsic travelling waves are discussed, with a view to using their existence to control these waves.