CRITICAL LAYER AND NONLINEAR EVOLUTION OF DISTURBANCES WEAKLY SUPERCRITICAL SHEAR FLOWS

In this paper an attempt is made to classify the possible scenarios of the nonlinear evolution of free weakly-unstable shear flows of a nearly inviscid (Re much greater than 1) fluid with respect to two-dimensional perturbations in the presence of a critical laver. The analysis is carried out on the basis of results obtained both by these authors and by other workers, It is shown that the character of the weakly-nonlinear evolution of an initially small perturbation is closely associated with the presence and type of neutral mode singularity at the critical level, and these signatures can be used as the basis for a classification of the scenarios.