Wave Overreflection and Shear Instability

Abstract

Abstract It is shown that the necessary conditions for the instability of unstratified plane-parallel shear flow, rotating barotropic flows and rotating baroclinic flows are also sufficient conditions for the existence of propagating waves (essentially Rossby waves) and their overreflection (reflection coefficient exceeds 1 in magnitude) from critical levels (where flow speed and phase speed are equal). The identification of the unstable modes with overreflected waves is strongly suggested and allows greater insight into the meaning of various theorems such as Rayleigh’s inflection point theorem. The present results also suggest an important distinction between instabilities associated with, redistribution such as Bénard convective instability and instabilities, such as those we are concerned with, associated with the self-excitation of waves.