The Nonlinear Critical Layer in a Slightly Stratified Shear Flow

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Abstract
An attempt is made in this paper to extend the nonlinear critical layer analysis, as developed for homogeneous shear flows by Benney and Bergeron [1] and Davis [2], to the case of a stratified shear flow. Although the analysis is restricted to small values of the Richardson number evaluated at the edge of the critical layer, it is definitely shown that buoyancy leads to the formation within the critical layer region of thin velocity and thermal boundary layers which tend to reduce the local Richardson number. We suggest that this result has considerable relevance to the phenomenon of clear air turbulence. As in the homogeneous case, no phase change of the disturbance takes place across the nonlinear critical layer.