Transition to complex dynamics in the cubic lid-driven cavity

Juan Lopez, Bruno Welfert, Ke Wu, Jason Yalim

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The onset of time dependence in the cubic lid-driven cavity is surprisingly complicated, given the simplicity of the geometry and the modest value of the Reynolds number at which it occurs. The onset is characterized by finite-amplitude oscillations that appear to be stable for long times, but are subjected to intermittent bursts at irregular times during which the reflection symmetry about the spanwise midplane is broken. The complex dynamics are shown to be intimately related to the subcritical nature of the instability of the steady basic state. We use a spectral collocation numerical technique, solving both in the full three-dimensional space and in the symmetric subspace, and use selective frequency damping and Arnoldi iterations about the unstable basic state to determine its bifurcations. Edge tracking is also used to investigate a number of time-dependent saddle states. Putting all this together, we show that the complex dynamics are organized by two successive Hopf bifurcations, the first of which is shown to be subcritical. All local states are unstable in the full space at higher Reynolds numbers, leading to the intermittent bursting behavior.

Original languageEnglish (US)
Article number074401
JournalPhysical Review Fluids
Volume2
Issue number7
DOIs
StatePublished - Jul 1 2017

Fingerprint

Lid-driven Cavity
Complex Dynamics
Reynolds number
Unstable
Arnoldi
Reflectional symmetry
Bursting
Hopf bifurcation
Time Dependence
Saddle
Numerical Techniques
Collocation
Burst
Hopf Bifurcation
Irregular
Simplicity
Damping
Bifurcation
Subspace
Oscillation

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Modeling and Simulation

Cite this

Transition to complex dynamics in the cubic lid-driven cavity. / Lopez, Juan; Welfert, Bruno; Wu, Ke; Yalim, Jason.

In: Physical Review Fluids, Vol. 2, No. 7, 074401, 01.07.2017.

Research output: Contribution to journalArticle

@article{3df49fbc6eed420987954a961ca57a71,
title = "Transition to complex dynamics in the cubic lid-driven cavity",
abstract = "The onset of time dependence in the cubic lid-driven cavity is surprisingly complicated, given the simplicity of the geometry and the modest value of the Reynolds number at which it occurs. The onset is characterized by finite-amplitude oscillations that appear to be stable for long times, but are subjected to intermittent bursts at irregular times during which the reflection symmetry about the spanwise midplane is broken. The complex dynamics are shown to be intimately related to the subcritical nature of the instability of the steady basic state. We use a spectral collocation numerical technique, solving both in the full three-dimensional space and in the symmetric subspace, and use selective frequency damping and Arnoldi iterations about the unstable basic state to determine its bifurcations. Edge tracking is also used to investigate a number of time-dependent saddle states. Putting all this together, we show that the complex dynamics are organized by two successive Hopf bifurcations, the first of which is shown to be subcritical. All local states are unstable in the full space at higher Reynolds numbers, leading to the intermittent bursting behavior.",
author = "Juan Lopez and Bruno Welfert and Ke Wu and Jason Yalim",
year = "2017",
month = "7",
day = "1",
doi = "10.1103/PhysRevFluids.2.074401",
language = "English (US)",
volume = "2",
journal = "Physical Review Fluids",
issn = "2469-990X",
publisher = "American Physical Society",
number = "7",

}

TY - JOUR

T1 - Transition to complex dynamics in the cubic lid-driven cavity

AU - Lopez, Juan

AU - Welfert, Bruno

AU - Wu, Ke

AU - Yalim, Jason

PY - 2017/7/1

Y1 - 2017/7/1

N2 - The onset of time dependence in the cubic lid-driven cavity is surprisingly complicated, given the simplicity of the geometry and the modest value of the Reynolds number at which it occurs. The onset is characterized by finite-amplitude oscillations that appear to be stable for long times, but are subjected to intermittent bursts at irregular times during which the reflection symmetry about the spanwise midplane is broken. The complex dynamics are shown to be intimately related to the subcritical nature of the instability of the steady basic state. We use a spectral collocation numerical technique, solving both in the full three-dimensional space and in the symmetric subspace, and use selective frequency damping and Arnoldi iterations about the unstable basic state to determine its bifurcations. Edge tracking is also used to investigate a number of time-dependent saddle states. Putting all this together, we show that the complex dynamics are organized by two successive Hopf bifurcations, the first of which is shown to be subcritical. All local states are unstable in the full space at higher Reynolds numbers, leading to the intermittent bursting behavior.

AB - The onset of time dependence in the cubic lid-driven cavity is surprisingly complicated, given the simplicity of the geometry and the modest value of the Reynolds number at which it occurs. The onset is characterized by finite-amplitude oscillations that appear to be stable for long times, but are subjected to intermittent bursts at irregular times during which the reflection symmetry about the spanwise midplane is broken. The complex dynamics are shown to be intimately related to the subcritical nature of the instability of the steady basic state. We use a spectral collocation numerical technique, solving both in the full three-dimensional space and in the symmetric subspace, and use selective frequency damping and Arnoldi iterations about the unstable basic state to determine its bifurcations. Edge tracking is also used to investigate a number of time-dependent saddle states. Putting all this together, we show that the complex dynamics are organized by two successive Hopf bifurcations, the first of which is shown to be subcritical. All local states are unstable in the full space at higher Reynolds numbers, leading to the intermittent bursting behavior.

UR - http://www.scopus.com/inward/record.url?scp=85035323807&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035323807&partnerID=8YFLogxK

U2 - 10.1103/PhysRevFluids.2.074401

DO - 10.1103/PhysRevFluids.2.074401

M3 - Article

AN - SCOPUS:85035323807

VL - 2

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 7

M1 - 074401

ER -