The nonlinear evolution of the inviscid secondary instability of streamwise vortex structures

Abstract

The weakly nonlinear evolution of an inviscid marginally unstable wave growing on a boundary layer supporting a streamwise vortex structure is investigated. The nonlinear growth of the wave is found to be controlled by the diffusion layer located at the edge of the critical layer associated with the wave. The evolution equation is found to depend on the upstream history of the wave and the solution of the equation suggests th at the wave either restructures the mean state so as to make it stable or develops a singularity at a finite distance downstream of the point of neutral stability.