Pilot-wave hydrodynamics in a rotating frame: Exotic orbits
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Bush_Pilot-wave.pdf
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Author(s)
Oza, Anand Uttam
Wind-Willassen, Øistein
Harris, Daniel Martin
Rosales, Rodolfo R.
Bush, John W. M.
Date Issued
August 2014
Journal
Physics of Fluids
Publisher
American Institute of Physics (AIP)
Citation
Oza, Anand U., Øistein Wind-Willassen, Daniel M. Harris, Rodolfo R. Rosales, and John W. M. Bush. “Pilot-Wave Hydrodynamics in a Rotating Frame: Exotic Orbits.” Physics of Fluids 26, no. 8 (August 2014): 082101. © 2014 AIP.
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Author's final manuscript
Abstract
We present the results of a numerical investigation of droplets walking on a rotating vibrating fluid bath. The drop's trajectory is described by an integro-differential equation, which is simulated numerically in various parameter regimes. As the forcing acceleration is progressively increased, stable circular orbits give way to wobbling orbits, which are succeeded in turn by instabilities of the orbital center characterized by steady drifting then discrete leaping. In the limit of large vibrational forcing, the walker's trajectory becomes chaotic, but its statistical behavior reflects the influence of the unstable orbital solutions. The study results in a complete regime diagram that summarizes the dependence of the walker's behavior on the system parameters. Our predictions compare favorably to the experimental observations of Harris and Bush [“Droplets walking in a rotating frame: from quantized orbits to multimodal statistics,” J. Fluid Mech.739, 444–464 (2014)].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1063/1.4891568
