Hysteresis and the Transition between Axisymmetric Flow and Wave Flow in the Baroclinic Annulus

Abstract

A numerical model is used to determine the transitions between axisymmetric flow and wave flow in the rotating, differentially heated annulus experiments of Fein for both rigid lid and free surface cases. For most of the transitions, the technique of computing a steady axisymmetric flow and then testing its linear stability to wave disturbances results in good agreement with the experiments. Nonlinear calculations with a single azimuthal wave accurately predict the observed hysteresis in the transition for large differential heating rates in the free surface case. Specifically, it is demonstrated that, in the experimentally observed hysteresis region, the Navier-Stokes equations support two stable equilibria for the same values of the external parameters. The hysteresis occurs in conjunction with a jump in wave amplitude as the rotation rate is slowly varied. Analysis of the longitudinal mean states and the linear and nonlinear waves indicates that the jump in amplitude is due to destabilization of the mean flow by the wave because of the reduction of the mean upper-level jet and the lower dissipation in the nonlinear wave. The reduction of the mean jet, which is due to the lowering of the thermal wind by baroclinic energy transfer, results in a smaller barotropic wave energy sink. Some implications for the study of the dynamics of the Earth's atmosphere are discussed.