THE ROLE OF NONLINEAR CRITICAL LAYERS IN BOUNDARY-LAYER-TRANSITION

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops w hen initially linear spatially growing instability waves evolve downst ream in nominally two-dimensional laminar boundary layers. The first n onlinear reaction takes place locally within a so-called 'critical lay er', with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of the se waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equat ion or a pair of integro-differential equations with quadratic to quar tic-type nonlinearities. The physical implications of these equations are discussed.