Abstract: Viscous incompressble flow between two concentric rotating spheres is simulated numerically by the spectral Galerkin method,in which the eigenfunctions of Stokes operator are used as basis functions.Model systems similiar to Lorenz's system are presented.The existence of attractor and the stability of model systems are obtained.

Key words: Navier Stokes equation, Spectral method, Stokes operator, Bifurcation, Attractor