Numerical investigation of instability of an annular rotating cavity

A direct two-dimensional numerical simulation has been performed to study the transition flow in an annual rotating cavity. The spectral collocation method based on the Chebyshev polynomial is used to solve the incompressible Navier-Stokes equation. The time scheme is semi-implicit and second-order accurate; it corresponds to a combination of the second-order backward differentiation formula for the viscous diffusion term and the Adams-Bashforth scheme for the non-linear terms. The method uses a projection scheme to maintain the incompressibility constrain. The numerical computations, performed for an annular cavity of the aspect ratio L=2 and 5 and for the curvature parameters Rm=(R1+R0)/(R1-R0)=5, exhibit instability structures in the form of circular rolls. These structures are in good agreement with the other investigations, both experimental and theoretical