Interactions between Long and Synoptic-Scale Waves. Part I: Instability of a Nonzonal Flow

Abstract

The interactions between long and synoptic-scale waves are studied as a two time-scale process. In the frame of reference of a long wave, a long wave varies slowly compared with the period of synoptic-scale waves. The long wave can spatially modulate the synoptic-scale waves whose fluxes will then show variations with the same wavelength as the long wave. These eddy fluxes can then alter the initial long wave on the slower time scale, making the interactions nonlinear. The assumption is made that the synoptic-scale waves have the structure ofthe most unstable normal modes; so in Part I, the instabilities of a wavy flow in a two-level j3-plane channel are studied. The derived analyticalsolution is simple, and appears more amenable to physical interpretation than previously derived analytical and numerical solutions The solution can be understood in terms of eddies and their local growth rate. In Part11, we will examine the effect of these synoptic-eddy fluxes on a long wave.