A study of the regularized lid-driven cavity's progression to chaos

Michael W. Lee, Earl H. Dowell, Maciej Balajewicz

Research output: Contribution to journalArticle

Abstract

Computational simulations of a two-dimensional incompressible regularized lid-driven cavity flow were performed and analyzed to identify the dynamic behavior of the flow through multiple bifurcations which ultimately result in Eulerian chaotic flow. Semi-implicit, pseudo-spectral numerical simulations were performed at Reynolds numbers from 1000 to 25,000. Poincaré maps were used to identify transitions as the Reynolds number increased from stable-laminar flow to periodic flow, periodic flow to quasi-periodic flow, quasi-periodic flow to chaotic flow, and a sudden, brief return from chaotic flow to periodic flow. The first critical Reynolds number, near 10,250, is found in agreement with existing literature. An additional bifurcation is observed near a Reynolds number of 15,500. A power spectrum analysis, in which the novel concepts of frequency shredding and power capacity are introduced, was performed with the conclusion that no further bifurcations occurred at Reynolds numbers above 15,500 even though Eulerian chaos was not formally observed until Reynolds numbers above 18,000. While qualitative changes in the fluid flow's attractor were apparent from trajectories in the phase space, mechanisms by which such changes can occur were apparent from power spectra of flow time histories. The novel power spectrum analysis may also serve as a new approach for characterizing multi-scale nonlinear dynamical systems.

Original languageEnglish (US)
Pages (from-to)50-72
Number of pages23
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume71
DOIs
StatePublished - Jun 15 2019

Fingerprint

Lid-driven Cavity
Progression
Chaos theory
Chaos
Reynolds number
Power spectrum
Power Spectrum
Spectrum analysis
Spectrum Analysis
Power Analysis
Bifurcation
Nonlinear dynamical systems
Laminar flow
Driven Cavity Flow
Flow of fluids
Computational Simulation
Semi-implicit
Flow Time
Trajectories
Nonlinear Dynamical Systems

Keywords

  • Bifurcation
  • Cavity flows
  • Chaos
  • Nonlinear flows

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

Cite this

A study of the regularized lid-driven cavity's progression to chaos. / Lee, Michael W.; Dowell, Earl H.; Balajewicz, Maciej.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 71, 15.06.2019, p. 50-72.

Research output: Contribution to journalArticle

Lee, Michael W. ; Dowell, Earl H. ; Balajewicz, Maciej. / A study of the regularized lid-driven cavity's progression to chaos. In: Communications in Nonlinear Science and Numerical Simulation. 2019 ; Vol. 71. pp. 50-72.
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