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Distinguishing Low-Dimensional Chaos from Random Noise in a Hydrodynamic Experiment

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Fluctuations and Sensitivity in Nonequilibrium Systems

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 1))

Abstract

Our experiments show that the circular Couette system undergoes a continuous transition from quasiperiodiс to weakly turbulent flow. The quasiperiodic flow is described by a phase space attractor of dimension 2.0. At the onset of turbulence broadband noise appears in the power spectrum, and with increasing Reynolds number the attractor dimension increases to about 2.5. Analysis of a model shows that the method used to determine the dimension of an attractor provides a way to distinguish between random and deterministic noise.

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References

  1. D. Ruelle and F. Takens: Comm. Math. Phys. 20, 167 (1971)

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  2. P.R. Fenstermacher, H.L. Swinney and J.P. Gollub: J.Fluid Mech. 94,103 (1979)

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  3. Reference [2] describes a system with radius ratio 0.875 and fluid height-to-gap ratio 20, as in the present experiments. Other routes to turbulence can be observed for different values of the control parameters.

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  4. A. Brandstater, J. Swift, H. Swinney, A. Wolf, D. Farmer, E. Jen, J. Crutchfield: Phys. Rev. Lett. 51, 1442 (1983)

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  5. A. Brandstater, J. Swift, H. Swinney, A. Wolf in: Turbulence and Chaotic Phenomena in Fluids ed. by T. Tatsumi, North-Holland, Amsterdam, 1984

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  6. A. Wolf, J. Swift, H. L. Swinney, J, Vastano: to be published

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  7. We use the term ‘random noise’ to describe nonperiodie behavior with a very large number of degrees of freedom

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Author information

Authors and Affiliations

  1. Department of Physics, University of Texas at Austin, Austin, TX, 78712, USA

    A. Brandstater & H. L. Swinney

Authors
  1. A. Brandstater
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  2. H. L. Swinney
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Editor information

Editors and Affiliations

  1. Department of Physics, Center for Studies in Statistical Mechanics, University of Texas, Austin, TX, 78712, USA

    Werner Horsthemke

  2. Center for Studies in Statistical Mechanics, University of Texas, Austin, TX, 78712, USA

    Dilip K. Kondepudi PhD

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Š 1984 Springer-Verlag Berlin Heidelberg

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Brandstater, A., Swinney, H.L. (1984). Distinguishing Low-Dimensional Chaos from Random Noise in a Hydrodynamic Experiment. In: Horsthemke, W., Kondepudi, D.K. (eds) Fluctuations and Sensitivity in Nonequilibrium Systems. Springer Proceedings in Physics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46508-6_17

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  • DOI: https://doi.org/10.1007/978-3-642-46508-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-46510-9

  • Online ISBN: 978-3-642-46508-6

  • eBook Packages: Springer Book Archive

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