| Abstract: | A class of non-linear instabilities of a vertically sheared zonal flow is discussed. This is a type of baroclinic instability that lies outside the purview of a linear eigenmode analysis of baroclinic instability problems. The form taken by the instability is that of an ensemble of three neutral Rossby waves whose amplitudes are slowly modified by their mutual non-linear interactions. For a triad of small amplitude, these interactions introduce a weak, vertical variation of phase to the structure of the individual waves. This allows the generation of rectified heat fluxes and an exchange of energy with the mean flow.This instability exhibits explosive growth and spans a range of horizontal wavenumbers that exceeds the range that is unstable in the corresponding linear model. It is shown that the type of instability discussed can only occur when the model used admits unstable eigenmodes as well as neutral Rossby waves.The mechanism for the non-linear instability discussed here is believed to be fairly general and should exist also in the context of a horizontally sheared flow where it would take the form of a barotropic instability. |
