The fully nonlinear development of Goertler vortices in growing boundary layers

A combination of asymptotic and numerical methods is used to study the fully nonlinear development of small-wavelength Goertler vortices in a growing boundary layer. It is shown that the vortices spread out across the boundary layer, effectively driving the boundary layer, and that the mean flow adjusts so as to make the large-amplitude vortices locally neutral. In the region where the vortices exist, the mean flow is found to have a square-root profile, and the vortex velocity field can be written in closed form. The region of vortex activity is shown to ultimately include almost all of the original boundary layer and much of the free stream.