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

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:
; ; ;  [1] ;  [2]
  1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States)
  2. Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kongens Lyngby (Denmark)
Publication Date:
OSTI Identifier:
22311240
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
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