On Resonant Interactions Between Unstable and Neutral Baroclinic Waves

Abstract

Abstract Resonant interactions between a marginally unstable baroclinic wave and one or two pairs of neutral waves in a rotating, two-layer zonal Row model are studied. Analyses based on a multiple scaling technique are carried out for inviscid flow on a beta plane, inviscid flow on an f-plane, and slightly viscous flow on an f-plane. It is assumed that the neutral waves are of smaller order in amplitude than the unstable wave, and the flow domain is taken to be zonally periodic so that zonal wavelengths are discrete. In this and other respects, the theory differs from an earlier study by Loesch (1974a,b) and avoids a number of difficulties inherent in that work. For an inviscid beta plane flow, the evolution of a wave triad is governed by a certain parameter N2N3/U. If this is negative, the neutral waves are unable to grow substantially larger in amplitude than their respective initial amplitudes, despite which they have a disproportionately large effect on the evolution of the unstable wave. If O<N2N3/U...