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Faraday pilot-wave dynamics: modelling and computation

2015; Cambridge University Press; Volume: 778; Linguagem: Inglês

10.1017/jfm.2015.386

1469-7645

Paul A. Milewski, Carlos A. Galeano-Rios, André Nachbin, John W. M. Bush,

Nonlinear Dynamics and Pattern Formation

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.