Rossby wave packet interactions

Abstract

A mechanism is proposed whereby planetary zonal flows can be generated by the resonant interaction of Rossby wave packets whose amplitudes are slowly varying functions of both space and time. Equations are derived describing the long-time behaviour of a resonantly interacting triad. At the first closure certain properties analogous to those already known for discrete waves are deduced. At the second closure, in the particular case when one of the members of the triad is a zonal flow, it is shown that the sideband resonance mechanism can cause energy to be gained or lost by this zonal flow. It is also shown that a single Rossby wave packet can exchange energy with a zonal flow with weak shear. In the final section a resonant quarter mechanism for producing zonal flows is discussed. A numerical estimate of the acceleration of a zonal current from a zero initial state gives values of a few km/day per day.