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

TL;DR

This study numerically investigates the transition from steady flow to intermittent chaos in a cubical lid-driven cavity, identifying bifurcation points and mechanisms leading to complex flow behavior.

Contribution

It provides the first detailed analysis of the bifurcation and transition to chaos in three-dimensional lid-driven cavity flow, highlighting the roles of centrifugal instability and energy extraction mechanisms.

Findings

Flow experiences an Andronov-Poincaré-Hopf bifurcation at Re=1914.

Unstable mode originates from centrifugal instability of the primary vortex.

Flow transitions from steady state to intermittent chaos via a primary limit cycle.

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-Poincar\'e-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.