Linear Stability of Equatorial Zonal Flows

Abstract

The instability of zonally and temporally invariant, equatorial, zonal flow is found to be tied directly to the presence of critical layers within the fluid. Insight into the mechanism of instability can, therefore, be gained through the use of the ideas of wave over-reflection. For idealized flows, where it can be directly applied, over-reflection successfully predicts the phase speed and wavelength of the most unstable waves. In complex flows, where application is difficult, the character of the energy exchanges is consistent with the ideas of over-reflection. Whereas at the scales of the tropical instability waves, instability arises by extracting energy from the background state through varying mixes of baroclinic, barotropic, and Kelvin-Helmholtz mechanisms (depending upon the details of the flow), the importance of the critical layer as the root of instability suggests that attempting to classify the instability through these energy conversions is misleading.