Stability Analysis for Flows in Rotating Spherical Layers (Linear Theory)

Abstract

We present a technique and the results of linear stability analysis for the viscous incompressible flows in an annulus between two concentric coaxial spheres, of which the outer remains stationary while the inner is rotated. We show that the characteristics of the main flow instability strongly depend on the layer thickness, qualitatively as well quantitatively. The critical perturbation for the main flow in a thin layer is monotonic and has the form of a system of ring vortices covering the entire flow region from one pole to the other; the vortices are axisymmetric but nonsymmetric about the equatorial plane. The critical perturbation in a thick layer is nonmonotonic, three-dimensional, and nonsymmetric about the equatorial plane. The shape of the critical perturbation depends on the layer thickness. A comparison with the experimental data is carried out.