Forced Waves in a Baroclinic Shear Flow. Part I: Undamped Evolution near the Baroclinic Instability Threshold

Abstract

The properties of forced waves in a two-layer baroclinic fluid are considered. The mean shear is taken to be just smaller than the critical value required for baroclinic instability. A nonlinear evolution equation is derived for the response of the system to weak forcing at a frequency close to resonance. A steady solution exists but under certain circumstances is unstable, in which case the wave undergoes a vacillation cycle, exchanging energy periodically with the mean flow. In general, the wave performs either a small-amplitude vacillation about the steady solution or a larger vacillation akin to that arising from the instability. Which type of solution is chosen depends on forcing amplitude, frequency and initial conditions.