VACILLATING FLOWS BETWEEN TWO DIFFERENTIALLY ROTATING CONCENTRIC SPHERES

Pu Zhang (U. K.) and Keke Zhang (U. K.)

Abstract

Time-dependent flows between two concentric spheres driven by a rotating inner sphere with a fixed outer sphere are investigated using fully three-dimensional numerical simulations without imposing spatial symmetries. The inner sphere has a periodically varying angular velocity which temporally modulates otherwise the steady flow results in a time-dependent vacillating flow. Two different cases are considered. The first case concerns with the rotation of the inner sphere modulated around a nonzero mean and the second case is for a periodically oscillating inner sphere. The temporally modulated flow is characterized by vacillation between various flow configurations which are usually dependent upon the initial condition used in a numerical simulation. However, the non-uniqueness of the flow is removed when the amplitude of modulation is sufficiently large.

Keywords and phrases: vacillation, spherical Couette flows.