Title: Hopf Bifurcation of the Unsteady Regularized Driven Cavity Flow

Author: Jie Shen

Status: J. Comput. Phys. 95, 228, 245, 1991

Abstract:

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 10000; for Reynolds numbers larger
than a critical value $10000<Re1<10500$ and less than another critical
value $15000<Re2<16000$, the flow becomes periodic in time which
indicates a Hopf bifurcation; the flow loses time periodicity for
$Re\ge Re2$.