Skip to main content
Journal cover image

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

Publication ,  Journal Article
Lee, MW; Dowell, EH; Balajewicz, MJ
Published in: Communications in Nonlinear Science and Numerical Simulation
June 15, 2019

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.

Duke Scholars

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

June 15, 2019

Volume

71

Start / End Page

50 / 72

Related Subject Headings

  • Mathematical Physics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Lee, M. W., Dowell, E. H., & Balajewicz, M. J. (2019). A study of the regularized lid-driven cavity's progression to chaos. Communications in Nonlinear Science and Numerical Simulation, 71, 50–72. https://doi.org/10.1016/j.cnsns.2018.11.010
Lee, M. W., E. H. Dowell, and M. J. Balajewicz. “A study of the regularized lid-driven cavity's progression to chaos.” Communications in Nonlinear Science and Numerical Simulation 71 (June 15, 2019): 50–72. https://doi.org/10.1016/j.cnsns.2018.11.010.
Lee MW, Dowell EH, Balajewicz MJ. A study of the regularized lid-driven cavity's progression to chaos. Communications in Nonlinear Science and Numerical Simulation. 2019 Jun 15;71:50–72.
Lee, M. W., et al. “A study of the regularized lid-driven cavity's progression to chaos.” Communications in Nonlinear Science and Numerical Simulation, vol. 71, June 2019, pp. 50–72. Scopus, doi:10.1016/j.cnsns.2018.11.010.
Lee MW, Dowell EH, Balajewicz MJ. A study of the regularized lid-driven cavity's progression to chaos. Communications in Nonlinear Science and Numerical Simulation. 2019 Jun 15;71:50–72.
Journal cover image

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

June 15, 2019

Volume

71

Start / End Page

50 / 72

Related Subject Headings

  • Mathematical Physics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics