Numerical Analysis of the Stability and Non-Uniqueness of Spherical Couette Flow

Numerical study of the non-linear axisymmetric viscous flow in a spherical layer is presented. The boundary spheres may rotate with constant but different angular velocities about the same axis. The flow is governed by a non-linear boundary value problem of the Navier-Stokes equations. The solution of this problem is found by the method of stabilization. The unknown functions are represented as series of Legendre associated functions with the coefficients depending on z and t. Two different procedures are used for non-linear terms computation. The numerical results show the existence of several different types of steady state flows in the same supercritical regions of the similarity parameters. The stability curves of the basic flow in the (Re ₁ , δ) and (Re ₁ , Re ₂ )-planes are obtained.