Pilot-wave hydrodynamics in a rotating frame: Exotic orbits

Oza, Anand U.; Harris, Daniel M.; Rosales, Rodolfo R.; Bush, John W. M.,; Wind-Willassen, Øistein

doi:10.1063/1.4891568

Title: Pilot-wave hydrodynamics in a rotating frame: Exotic orbits

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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)].

Authors:

Oza, Anand U.; Harris, Daniel M.; Rosales, Rodolfo R.; Bush, John W. M., ^[1]; Wind-Willassen, Øistein ^[2]

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States)
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kongens Lyngby (Denmark)

Publication Date:: Fri Aug 15 00:00:00 EDT 2014

OSTI Identifier:: 22311240

Resource Type:: Journal Article

Journal Name:: Physics of Fluids (1994)

Additional Journal Information:: Journal Volume: 26; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-6631

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCELERATION; CHAOS THEORY; COMPARATIVE EVALUATIONS; DIAGRAMS; DROPLETS; FLUIDS; HYDRODYNAMICS; INSTABILITY; INTEGRO-DIFFERENTIAL EQUATIONS; MATHEMATICAL SOLUTIONS; ORBITS; SIMULATION; STATISTICS; TRAJECTORIES

Citation Formats


                    Oza, Anand U., Harris, Daniel M., Rosales, Rodolfo R., Bush, John W. M.,, and Wind-Willassen, Øistein. Pilot-wave hydrodynamics in a rotating frame: Exotic orbits.  United States: N. p., 2014. 
        Web.  doi:10.1063/1.4891568.

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                    Oza, Anand U., Harris, Daniel M., Rosales, Rodolfo R., Bush, John W. M.,, & Wind-Willassen, Øistein. Pilot-wave hydrodynamics in a rotating frame: Exotic orbits.  United States.  https://doi.org/10.1063/1.4891568

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                    Oza, Anand U., Harris, Daniel M., Rosales, Rodolfo R., Bush, John W. M.,, and Wind-Willassen, Øistein. 2014.  
        "Pilot-wave hydrodynamics in a rotating frame: Exotic orbits".  United States.  https://doi.org/10.1063/1.4891568.

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@article{osti_22311240,

  title        = {Pilot-wave hydrodynamics in a rotating frame: Exotic orbits},

  author       = {Oza, Anand U. and Harris, Daniel M. and Rosales, Rodolfo R. and Bush, John W. M., and Wind-Willassen, Øistein},

  abstractNote = {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)].},

  doi          = {10.1063/1.4891568},

  url          = {https://www.osti.gov/biblio/22311240},
  journal      = {Physics of Fluids (1994)},

  issn         = {1070-6631},

  number       = 8,

  volume       = 26,

  place        = {United States},

  year         = {Fri Aug 15 00:00:00 EDT 2014},

  month        = {Fri Aug 15 00:00:00 EDT 2014}

}

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