The growth and nonlinear evolution of helical perturbations in a swirling jet model

Abstract

The growth and nonlinear evolution of a helical perturbation is investigated in a simplified swirling jet model, consisting of a line vortex along the axis surrounded by a jet shear layer with both azimuthal and streamwise vorticity. Inviscid Lagrangian vortex dynamics simulations demonstrate the mechanisms of vorticity concentration, reorientation, and stretching, as well as the nonlinear interaction and competition between a centrifugal Rayleigh instability and a Kelvin-Helmholtz instability feeding on both components of the base flow vorticity. The nonlinear evolution resulting from the interaction of these two instabilities allows for very different flow behaviors to emerge, depending on whether the helical perturbation wave and the vortex lines of the jet shear layer wind around the jet axis in the same or in opposite directions. Large-scale vortex helices evolve that can contain azimuthal vorticity either of the same or of opposite sign to that initially present in the jet shear layer. These different evolutions are triggered by the differences in the direction of the strain field set up by the evolving large-scale helix. In both cases, the generation of both signs of azimuthal vorticity due to the centrifugal Rayleigh instability allows for the possibility of unlimited growth of the helix circulation, in the absence of viscous diffusion.