Numerical Simulation of Unsteady Driven Cavity Flow

A numerical study is performed on the flow of an incompressible fluid driven in a square cavity. The behavior of unsteady flows beyond the first Hopf bifurcation is investigated. The first Hopf bifurcation is localized at Re cr1 =7987±0.2% with the fundamental frequency f B =0.4519, in good agreement with the previous studies. A secondary Hopf bifurcation occurs at Re cr2 =9575±3%, which generates a quasi-periodic solution with two incommensurable frequencies f B and f H , up to the annihilation of f B at Re cr3 =10975±2%. While quasi-periodic flow is observed for Re cr2 ≤ Re ≤ Re cr3 on this solution branch, another branch of the periodic solution with fundamental frequency f L (< f H ) appears for Re ≥ Re cr1' =9310±2% (< Re cr2 ) via a subcritical Hopf bifurcation. Bistable periodic solutions with fundamental frequencies f H and f L coexist for Re cr3 ≤ Re up to about 18400, which is the highest Re computed in the present study.