The Modulation of an Unstable Baroclinic Wave Field

Abstract

Limit-cycle type oscillations of the amplitude of a baroclinic wave field, which has grown by instability on a background zonal flow, have been observed experimentally in a rotating cylinder containing two immiscible fluid layers, the upper one of which is driven by a differentially rotating contact lid. The experimental results are summarized and compared with previous speculations and theories on the origins of qualitatively similar long-period modulations occurring in the rotating annulus. Results from a truncated-spectral model are presented. The solutions reproduce the fundamental modulation characteristics for several different experimental configurations involving different distributions of the basic zonal potential vorticity gradients and hence different linear stability properties. The observed modulations are related to periodic transfers of energy between the wave field and the zonal flow. This process is primarily baroclinic, dominated by available potential energy transport fluctuations, but barotropic transfers also occur. The predicted wave field modulates in shape as well as amplitude and the motion cannot be characterized as either “tilted trough” or “amplitude” vacillation.