Nonlinear centrifugal instabilities in curved free shear layers

Curved free shear layers exist in many engineering problems involving complex flow geometries, such as the backward facing step flow, flows with wall injection, the flow inside side-dump combustors, or flows generated by vertical axis wind turbines, among others. Most of the studies involving centrifugal instabilities have been focused on wall flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers resulting from the imbalance between centrifugal effects and radial pressure gradients, are generated. Curved free shear layers, however, did not receive sufficient attention. An examination of the stability characteristics and the flow structures associated with curved free shear flows should provide a better understanding of these complex flow problems. In this work, we study the development of Görtler vortices inside a curved shear layer in both the incompressible and compressible regimes using a numerical solution to a parabolized form of the Navier-Stokes equations, in the assumption that the streamwise wavenumber associated with the vortex flow is much smaller than the crossstream wavenumbers. Various results consisting of contour plots of centrifugal instabilites in crossflow planes, and energy and streak amplitude distributions along the streamwise direction are reported and discussed. In addition, we conduct a biglobal stability analysis to study the growth rates and the eigenmodes associated with these flows.