ON WAVE INTERACTIONS .2. EXPLOSIVE RESONANT TRIADS IN FLUID-MECHANICS

This paper considers the occurrence of explosive resonant triads in fl uid mechanics. These are weakly nonlinear waves whose amplitudes becom e unbounded in finite time. Previous work is expanded to include inter facial flow systems with continuously varying basic velocities and den sities. The first paper in this series [10] discussed the surprisingly strong singular nature of explosive triads. Many of the problems to b e studied here will be found to have additional singularities, and the techniques for analyzing these difficulties will be developed. This w ill involve the concept of a critical layer in a fluid, a level at whi ch a wave phase speed equals the unperturbed fluid velocity in the dir ection of propagation. Examples of such waves in this context are pres ented.