Numerical study of transition in lid-driven flow in cavities with a semicircular round bottom

In this article, three-dimensional lid-driven flows in cavities with a semicircular round bottom are studied. We have first focused on lid-driven flow in a semicircular cavity with a unit square moving lid and height 1/2. The critical Reynolds number Recr for the transition from steady flow to unsteady one has been obtained. Based on the averaged velocity field in one cycle of fluid flow motion, the flow difference between the averaged one and velocity field, called oscillation mode, at several time instances in such cycle shows an almost identical pattern for several Reynolds numbers close to Recr. This similarity indicates the oscillation mode associated with the Hopf bifurcation originated at Re less than Recr. For lid-driven flow in a cavity with a semicircular round bottom and height one, its oscillation mode shows a periodic change of local secondary flows associated with Hopf bifurcation and pairs of Taylor-G & ouml;rtler-like vortices are obtained.