INTERACTION OF OBLIQUE INSTABILITY WAVES WITH A NONLINEAR PLANE-WAVE

This paper is concerned with the downstream evolution of a resonant tr iad of initially non-interacting linear instability waves in a boundar y layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude obliqu e modes that form a subharmonic standing wave in the spanwise directio n. The growth rates are small and there is a well-defined common criti cal layer for these waves. As in Goldstein & Lee (1992), the wave inte raction takes place entirely within this critical layer and is initial ly of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. H owever, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can b ecome nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the p arametric-resonance effects and occurs on a much shorter streamwise sc ale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage - even as the growt h rate of the fundamental approaches zero - and the subharmonic eventu ally becomes large enough to influence the fundamental which causes bo th waves to evolve on the same shorter streamwise scale.