Hopf Bifurcation of the Unsteady Regularized Driven Cavity Flow

A numerical simulation of the unsteady incompressible flow in the unit cavity is performed by using a Chebyshev-Tau approximation for the space variables. The high accuracy of the spectral methods and the condensed distribution of the Chebyshev-collocation points near the boundary enable us to obtain reliable results for high Reynolds numbers with a moderate number of modes. It is found that the flow converges to a stationary state for Reynolds numbers (Re) up to 10,000; for Reynolds numbers larger than a critical value 10,000 < Re 1 < 10,500 and less than another critical value 15,000 < Re 2 < 15,500, the flow becomes periodic in time which indicates a Hoph bifurcation; the flow loses time periodicity for Re > Re 2. c 1991 Acsdemc Press, Inc.