Stability of the steady three-dimensional lid-driven flow in a cube and the supercritical flow dynamics

The stability of the steady flow in a lid-driven cube is investigated by a collocation method making use of asymptotic solutions for the singular edges of the cavity up- and downstream of the moving wall. Owing to the rapid convergence of the method high-accuracy critical data are obtained. To determine the critical point subcritical growth rates of small perturbations are extrapolated to zero. We find the bifurcation to be of Hopf-type and slightly subcritical. Above the critical point, the oscillatory flow is symmetric with respect to the symmetric midplane of the cavity and characterized by nearly streamwise vortices in the boundary layer on the wall upstream of the moving wall. The oscillation amplitude grows slowly and seems to saturate. On a long time scale, however, the constant-amplitude oscillations are unstable. The periodic oscillations are interrupted by short bursts during which the oscillation amplitude grows substantially and the spatial structure of the oscillating streamwise vortices changes. Towards the end of each burst the mirror symmetry of the oscillatory flow is lost, the flow returns to the vicinity of the unstable steady state and the growth of symmetric oscillations starts again leading to an intermittent chaotic flow. (C) 2014 AIP Publishing LLC.