Weakly non-linear instability of non-parallel shear flows

A spectral theory proposed by Plaschko and Hussain [Phys. Fluids A 27, 1603 (1984)] for the downstream evolution of non-linearly interacting waves in a non-parallel shear how is further developed and extended so that it can provide dominant contributions to the non-linear terms by subharmonic components at frequencies omega/n (n = 2,3,4,...), where omega is a given frequency of the fundamental mode. The results are consistent with the experimental observations. The theory also is generalized to take into account three-dimensional disturbances acting on three-dimensional base flows with or without spanwise variations. (C) 1997 Elsevier Science Ltd.