Resonant Interactions Between Unstable and Neutral Baroclinic Waves: Part I

Abstract

Resonant interactions between a finite-amplitude marginally unstable and two neutral baroclinic waves are investigated in a quasi-geostrophic two-layer model on the beta plane. The three wave-amplitudes are taken of comparable magnitude, a scaling assumption which permits the problem to be carried out only near the minimum critical shear required for instability. It is shown, using a numerical approach, that in the absence of dissipation the finite-amplitude state exhibits a long-period oscillation of the individual wave-amplitudes and of the total energy in the wave field. The neutral waves alter the phase shift between the unstable wave in the upper and lower layer and, therefore, affect the energy exchange with the mean flow. In the region F<10.5, where F represents the internal rotational Froude number, depending on the initial conditions, it is possible to transfer within an oscillation all of the energy available in the mean field to one of the neutral waves. In the region F>10.5, irrespective of the initial conditions, all of the available energy is transferred to both neutral waves.