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Faraday pilot-wave dynamics: modelling and computation

Published online by Cambridge University Press:  31 July 2015

Paul A. Milewski ,
Carlos A. Galeano-Rios ,
André Nachbin  and
John W. M. Bush
Paul A. Milewski*
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
Carlos A. Galeano-Rios
Affiliation:
IMPA/National Institute of Pure and Applied Mathematics, Est. D. Castorina, 110, Rio de Janeiro, RJ 22460-320, Brazil
André Nachbin
Affiliation:
IMPA/National Institute of Pure and Applied Mathematics, Est. D. Castorina, 110, Rio de Janeiro, RJ 22460-320, Brazil
John W. M. Bush
Affiliation:
Department of Mathematics, MIT, Cambridge, MA, USA
*
†Email address for correspondence: [email protected]
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Abstract

A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field. This system represents the first known example of a pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory. We here develop a fluid model of pilot-wave hydrodynamics by coupling recent models of the droplet’s bouncing dynamics with a more realistic model of weakly viscous quasi-potential wave generation and evolution. The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect and walker–walker interactions.

JFM classification

Waves/Free-surface Flows: Capillary waves Drops and Bubbles: Drops Waves/Free-surface Flows: Faraday waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 778 , 10 September 2015 , pp. 361 - 388
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Copyright
© 2015 Cambridge University Press 

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