On Radiating Instabilities and Resonant Overreflection

Abstract

Shear instabilities can result in waves being radiated far from the seat of instability. This phenomenon, and its opposite extreme, the trapping of instabilities, can be described and interdistinguished by linear theory for slowly growing instabilities only. To describe strong instabilities which radiate, laboratory and numerical studies are needed. Linear theory can better describe the somewhat similar phenomenon of “resonant overreflection,” which for a constant incident wave is characterized by linear rather than exponential growth in fine. The energy budget of sustained radiation, or overreflection, from a shear layer does not necessarily involve net removal of energy from the neighborhood of the shear layer.