Pilot-wave hydrodynamics in a rotating frame: Exotic orbits

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

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


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,".

Original languageEnglish (US)
Article number082101
JournalPhysics of Fluids
Issue number8
StatePublished - Aug 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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