Journal
FLUID DYNAMICS RESEARCH
Volume 48, Issue 6, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0169-5983/48/6/061421
Keywords
lid-driven cavity; global instability; intermittency; chaos
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Transition from steady state to intermittent chaos in the cubical lid-driven cavity flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov-Poincare-Hopf bifurcation at a critical Reynolds number Re-c. = 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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