Oscillatory instability of a three-dimensional lid-driven flow in a cube

A series of time-dependent three-dimensional (3D) computations of a lid-driven flow in a cube with no-slip boundaries is performed to find the critical Reynolds number corresponding to the steady-oscillatory transition. The computations are done in a fully coupled pressure-velocity formulation on 104(3), 152(3), and 200(3) stretched grids. Grid-independence of the results is established. It is found that the oscillatory instability of the flow sets in via a subcritical symmetry-breaking Hopf bifurcation at Re(cr)approximate to 1914 with the nondimensional frequency omega=0.575. Three-dimensional patterns in the steady and oscillatory flow regimes are compared with the previously studied two-dimensional configuration and a three-dimensional model with periodic boundary conditions imposed in the spanwise direction. (C) 2010 American Institute of Physics. [doi:10.1063/1.3487476]