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.