Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-22T17:59:43.091Z Has data issue: false hasContentIssue false
  • English
  • Français

Recurrent flows: the clockwork behind turbulence

Published online by Cambridge University Press:  06 June 2013

Predrag Cvitanović
Predrag Cvitanović*
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
*
†Email address for correspondence: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The understanding of chaotic dynamics in high-dimensional systems that has emerged in the last decade offers a promising dynamical framework to study turbulence. Here turbulence is viewed as a walk through a forest of exact solutions in the infinite-dimensional state space of the governing equations. Recently, Chandler & Kerswell (J. Fluid Mech., vol. 722, 2013, pp. 554–595) carry out the most exhaustive study of this programme undertaken so far in fluid dynamics, a feat that requires every tool in the dynamicist’s toolbox: numerical searches for recurrent flows, computation of their stability, their symmetry classification, and estimating from these solutions statistical averages over the turbulent flow. In the long run this research promises to develop a quantitative, predictive description of moderate-Reynolds-number turbulence, and to use this description to control flows and explain their statistics.

JFM classification

Instability: Instability Instability: Transition to turbulence Turbulent Flows: Turbulence theory
Type
Focus on Fluids
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 1 - 4
Copyright
©2013 Cambridge University Press 

References

Chandler, G. J. & Kerswell, R. R. 2013 Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow. J. Fluid Mech 722, 554–595.Google Scholar
Cvitanović, P., Artuso, R., Mainieri, R., Tanner, G. & Vattay, G. 2013 Chaos: Classical and Quantum. Niels Bohr Institute, ChaosBook.org.Google Scholar
Cvitanović, P. & Gibson, J. F. 2010 Geometry of turbulence in wall-bounded shear flows: periodic orbits. Phys. Scr. T 142, 014007.Google Scholar
Ezra, G. S., Richter, K., Tanner, G. & Wintgen, D. 1991 Semiclassical cycle expansion for the helium atom. J. Phys. B 24, L413–L420.Google Scholar
Gibson, J. F. 2013 Channelflow: a spectral Navier–Stokes simulator in C++. Tech Rep., University of New Hampshire, Channelflow.org.Google Scholar
Gibson, J. F., Halcrow, J. & Cvitanović, P. 2008 Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611, 107–130.CrossRefGoogle Scholar
Ginelli, F., Poggi, P., Turchi, A., Chate, H., Livi, R. & Politi, A. 2007 Characterizing dynamics with covariant Lyapunov vectors. Phys. Rev. Lett. 99, 130601.Google Scholar
Gutzwiller, M. C. 1990 Chaos in Classical and Quantum Mechanics. Springer.CrossRefGoogle Scholar
Hof, B., van Doorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F. 2004 Experimental observation of nonlinear travelling waves in turbulent pipe flow. Science 305, 1594–1598.CrossRefGoogle ScholarPubMed
Hopf, E. 1948 A mathematical example displaying features of turbulence. Commun. Pure Appl. Maths 1, 303–322.CrossRefGoogle Scholar
Kawahara, G. & Kida, S. 2001 Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291–300.Google Scholar
Kreilos, T. & Eckhardt, B. 2012 Periodic orbits near onset of chaos in plane Couette flow. Chaos 22, 047505.CrossRefGoogle ScholarPubMed
Moore, D. W. & Spiegel, E. A. 1966 A thermally excited nonlinear oscillator. Astrophys. J. 143, 871.Google Scholar
Orr, W. M. F. 1907 The stability or instability of the steady motions of a liquid. Part II: a viscous liquid. Proc. R. Irish Acad. A 27, 69–138.Google Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels. Proc. R. Soc. Lond. A 174, 935–982.Google Scholar
Ruelle, D. 1978 Statistical Mechanics, Thermodynamic Formalism. Addison-Wesley.Google Scholar
Viswanath, D. 2007 Recurrent motions within plane Couette turbulence. J. Fluid Mech. 580, 339–358.CrossRefGoogle Scholar
Willis, A. P., Cvitanović, P. & Avila, M. 2013 Revealing the state space of turbulent pipe flow by symmetry reduction. J. Fluid Mech. 721, 514–540.CrossRefGoogle Scholar