Pilot-wave hydrodynamics in a rotating frame: Exotic orbits

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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 multi-modal statistics,” J. Fluid Mech. 739, 444–464 (2014)].
Original languageEnglish
Article number082101
JournalPhysics of Fluids
Volume26
Number of pages17
ISSN1070-6631
DOIs
Publication statusPublished - 2014
CitationsWeb of Science® Times Cited: No match on DOI

ID: 98238824