A Stability Study of Axisymmetric Flows in a Rotating Annulus

Abstract

A stability of axisymmetric flows in the rotating fluid annulus with respect to the wave perturbations is studied by the numerical time integration of linearized hydrodynamic equations. Firstly, two steady axisymmetric flows are established by integrating nonlinear Boussinesq equations. One (Case (C)) is supposed to be located in the upper symmetric regime and the other (Case (B)) in the wave regime. Then, the stability of the two axisymmetric flows with respect to the wave disturbance with an assumed zonal wave number is examined by integrating a system of linearized perturbation equations as an initial value problem. The axisymmetric flow for Case (B) is shown to be unstable with respect to the disturbance with a wave number 8. The developed wave is essentially similar to the classical Eady wave. Near the upper and lower boundaries, the structure of the wave is modified to form the Ekman layer balance. Energetics of the developed wave is also discussed.