The inviscid secondary instability of fully nonlinear longitudinal vortex structures in growing boundary layers

Abstract

The inviscid instability of a longitudinal vortex structure within a steady boundary layer is investigated. The instability has a wavelength comparable with the boundary layer thickness so that a quasi-parallel approach to the instability problem can be justified. The generalization of the Rayleigh equation to such a flow is obtained and solved for the case when the vortex structure is induced by curvature. Two distinct modes of instability are found; these modes correspond with experimental observations on the breakdown process for Goertler vortices.