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arXiv · 1607.05126

Intermittency and transition to chaos in the cubical lid-driven cavity flow

Jean-Christophe Loiseau·Jean-Christophe Robinet·Emmanuel Leriche
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Abstract

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 $Re_c$ = 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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Jean-Christophe Loiseau, Jean-Christophe Robinet, Emmanuel Leriche. 2016-07-18. Intermittency and transition to chaos in the cubical lid-driven cavity flow. https://doi.org/10.1088/0169-5983%2F48%2F6%2F061421

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