On the Behavior of Large-Amplitude Baroclinic Waves

Abstract

We discuss the evolution of baroclinic waves which develop as instabilities of a two-layer fluid contained in a rapidly rotating cylinder and driven by differential rotation of the upper contact lid. Laboratory ex- periments were carried out by slowly increasing the system Rossby number Ro[ =ω/(2Ω] at various values of the internal Froude number F[=(4ω²L/gHΔp/p. We found previously that the flow was axisymmetric if Ro was small enough but that non-axisymmetric wave motions appeared spontaneously at certain critical Rossby numbers, depending on geometry, Ekman number, and F. For nearly critical values the waves are steady, but as Ro becomes large (and before the flow becomes turbulent) either amplitude or frequency modulation (vacillation) of the wave envelope is observed. In this paper we give some details of these observed modulations. Frequency-amplitude vacillation appears to be due to a nonlinear, quasi-geostrophic wave selection process which possesses limit cycle solutions. The amplitude vacillations observed in our experiments do not appear to be due to theoretically predicted modulations from simple non- linear mean-field or radial-mode-mixing models but to a higher order (perhaps barotropic) instability of the primary baroclinic wave. The wave amplitudes, relative to the basic flow, are generally small and much of the observed qualitative behavior can be inferred from the linear stability diagrams.