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Chaotic dynamics of falling disks

Nature volume 388, pages 252–254 (1997)Cite this article

Abstract

The study of the motion of flat bodies falling in a viscous mediumdates back at least to Newton1 and Maxwell2, and is relevant to problems in meteorology3, sedimentology4, aerospace engineering1 and chemical engineering5,6,7,8. More recent theoretical studies9,10,11,12 have emphasized the role played by deterministic chaos, although many experimental studies1,5,6,7,8,13,14 were performed before the development of such ideas. Here we report experimental observations of the dynamics of disks falling in water/glycerol mixtures. We find four distinct types of motion, which are mapped out in a ‘phase diagram’. The apparently complex behaviour can be reduced to a series of one-dimensional maps, which display a discontinuity at the crossover from periodic to chaotic motion. This discontinuity leads to an unusual intermittency transition15, not previously observed experimentally, between the two behaviours.

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Figure 1: Trajectories of falling disks, obtained by imaging from the side using a video camera; the digitized images were measured, and computer-drawn images are shown.
Figure 2: Phase diagram showing the dynamical behaviour of the disks as a function of the two parameters I* (dimensionless moment of inertia) and Re (Reynold's number).
Figure 3: Iteration maps of falling disks, constructed as follows.

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Acknowledgements

We thank D. T. Walker for providing the video equipment. This work was supported in part by the NSF REU Program.

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Authors and Affiliations

  1. *Department of Physics, Colorado State University, Fort Collins, 80523, Colorado, USA

    Stuart B. Field

  2. †Department of Physics, The University of Michigan, Ann Arbor, 48109-1120, Michigan, USA

    M. Klaus, M. G. Moore & Franco Nori

  3. ‡Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, 78712, Texas, USA

    M. G. Moore

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  1. Stuart B. Field
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Correspondence to Stuart B. Field.

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Field, S., Klaus, M., Moore, M. et al. Chaotic dynamics of falling disks. Nature 388, 252–254 (1997). https://doi.org/10.1038/40817

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