The formation of ordered vortex structures from unstable oscillations in the boundary layer

Abstract

The results of an asymptotic approach to the propagation of comparatively large amplitude perturbations in a boundary layer are described. The properties of the non-linear process being considered are established using the Benjamin-Ono equation. The behaviour of the periodic solution of this equation as a function of the magnitude of the arbitrary constants is analysed. A comparison with available experimental data shows that a description of the basic regularities following from them can be achieved within the framework of the asymptotic theory. It is concluded from this that the development of Tollmin-Schlichting waves with an increasing amplitude in the boundary layer leads to the formation of ordered vortex structures of the soliton type.