Intermittency and transition to chaos in the cubical lid-driven cavity flow
Résumé
Transition from steady state to intermittent chaos in the cubical lid-driven flow is investigated
numerically. Fully three-dimensional stability analyses have revealed that the flow experiences
an Andronov-Poincaré-Hopf bifurcation at a critical Reynolds number Rec = 1914. As for the
2D-periodic lid-driven cavity flows, the unstable mode originates from a centrifugal instability of
the primary vortex core. A Reynolds-Orr analysis reveals that the unstable perturbation relies
on a combination of the lift-up and anti lift-up mechanisms to extract its energy from the base
flow. Once linearly unstable, direct numerical simulations show that the flow is driven toward
a primary limit cycle before eventually exhibiting intermittent chaotic dynamics. Though only
one eigenpair of the linearized Navier-Stokes operator is unstable, the dynamics during the
intermittencies are surprisingly well characterized by one of the stable eigenpairs.
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