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.
- capillary waves
- Faraday waves
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- Department of Mathematical Sciences - Head of Department
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Centre for Networks and Collective Behaviour
- Water Innovation and Research Centre (WIRC)
- Centre for Mathematical Biology
Person: Research & Teaching