Bursting dynamics due to a homoclinic cascade in Taylor-Couette flow

J. Abshagen, Juan Lopez, F. Marques, G. Pfister

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

Transitions between regular oscillations and bursting oscillations that involve a bifurcational process which culminates in the creation of a relative periodic orbit of infinite period and infinite length are investigated both experimentally and numerically in a short-aspect-ratio Taylor-Couette flow. This bifurcational process is novel in that it is the accumulation point of a period-adding cascade at which the mid-height reflection symmetry is broken. It is very rich and complex, involving very-low-frequency states arising via homoclinic and heteroclinic dynamics, providing the required patching between states with very different dynamics in neighbouring regions of parameter space. The use of nonlinear dynamical systems theory together with symmetry considerations has been crucial in interpreting the laboratory experimental data as well as the results from the direct numerical simulations. The phenomenon corresponds to dynamics well beyond the first few bifurcations from the basic state and so is beyond the reach of traditional hydrodynamic stability analysis, but it is not fully developed turbulence where a statistical or asymptotic approach could be employed. It is a transitional phenomenon, where the phase dynamics of the large-scale structures (jets of angular momentum emanating from the boundary layer on the rotating inner cylinder) becomes complicated. Yet the complicated phase dynamics remains accessible to an analysis of its space - time characteristics and a comprehensive mechanical characterization emerges. The excellent agreement between the experiments and the numerical simulations demonstrates the robustness of this complex bifurcation phenomenon in a physically realized system with its inherent imperfections and noise. Movies are available with the online version of the paper.

Original languageEnglish (US)
Pages (from-to)357-384
Number of pages28
JournalJournal of Fluid Mechanics
Volume613
DOIs
StatePublished - 2008

Fingerprint

Couette flow
cascades
flow stability
Nonlinear dynamical systems
oscillations
very low frequencies
Angular momentum
Direct numerical simulation
System theory
direct numerical simulation
dynamical systems
aspect ratio
Aspect ratio
boundary layers
broken symmetry
Boundary layers
Orbits
Turbulence
Hydrodynamics
angular momentum

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

Bursting dynamics due to a homoclinic cascade in Taylor-Couette flow. / Abshagen, J.; Lopez, Juan; Marques, F.; Pfister, G.

In: Journal of Fluid Mechanics, Vol. 613, 2008, p. 357-384.

Research output: Contribution to journalArticle

Abshagen, J. ; Lopez, Juan ; Marques, F. ; Pfister, G. / Bursting dynamics due to a homoclinic cascade in Taylor-Couette flow. In: Journal of Fluid Mechanics. 2008 ; Vol. 613. pp. 357-384.
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