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Intermittency and transition to chaos in the cubical lid-driven cavity flow
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-Poincar\'e-Hopf bifurcation
at a critical Reynolds number = 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.Comment: Accepted for publication in Fluid Dynamics Researc
The lid-driven square cavity flow : From stationary to time periodic and chaotic
Ranging from Re=100 to Re=20,000, several computational experiments are conducted, Re being the Reynolds number. The primary vortex stays put, and the longterm dynamic behavior of the small vortices determines the nature of the solutions. For low Reynolds numbers, the solution is stationary; for moderate Reynolds numbers, it is time periodic. For high Reynolds numbers, the solution is neither stationary nor time periodic: the solution becomes chaotic. Of the small vortices, the merging and the splitting, the appearance and the disappearance, and, sometime, the dragging away from one corner to another and the impeding of the merging - these mark the route to chaos. For high Reynolds numbers, over weak fundamental frequencies appears a very low frequency dominating the spectra - this very low frequency being weaker than clear-cut fundamental frequencies seems an indication that the global attractor has been attained. The global attractor seems reached for Reynolds numbers up to Re=15,000. This is the lid-driven square cavity flow; the motivations for studying this flow are recalled in the Introduction
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