On the resonant interaction of neutral disturbances in two inviscid shear flows

Abstract

The second-order resonant interaction of two disturbances which are neutrally stable on a linear basis is investigated for cases when the mean flow is, first, an inviscid, homogeneous jet and, secondly, a stably stratified, antisymmetric shear layer for which the linear eigen-solutions are regular. For the former case, the periodic nature of the neutral disturbances is unaffected by the interaction. For the latter, the interaction can lead to an O(ε^½) temporal growth rate of one disturbance, where ε is a characteristic disturbance amplitude.