Transition to complex dynamics in the cubic lid-driven cavity

The onset of time dependence in the cubic lid-driven cavity is surprisingly complicated, given the simplicity of the geometry and the modest value of the Reynolds number at which it occurs. The onset is characterized by finite-amplitude oscillations that appear to be stable for long times, but are subjected to intermittent bursts at irregular times during which the reflection symmetry about the spanwise midplane is broken. The complex dynamics are shown to be intimately related to the subcritical nature of the instability of the steady basic state. We use a spectral collocation numerical technique, solving both in the full three-dimensional space and in the symmetric subspace, and use selective frequency damping and Arnoldi iterations about the unstable basic state to determine its bifurcations. Edge tracking is also used to investigate a number of time-dependent saddle states. Putting all this together, we show that the complex dynamics are organized by two successive Hopf bifurcations, the first of which is shown to be subcritical. All local states are unstable in the full space at higher Reynolds numbers, leading to the intermittent bursting behavior.