The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral - Archive ouverte HAL
Article Dans Une Revue Chaos: An Interdisciplinary Journal of Nonlinear Science Année : 2018

The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral

Résumé

Millimetric droplets may walk across the surface of a vibrating fluid bath, propelled forward by their own guiding or “pilot” wave field. We here consider the interaction of such walking droplets with a submerged circular pillar. While simple scattering events are the norm, as the waves become more pronounced, the drop departs the pillar along a path corresponding to a logarithmic spiral. The system behavior is explored both experimentally and theoretically, using a reduced numerical model in which the pillar is simply treated as a region of decreased wave speed. A trajectory equation valid in the limit of weak droplet acceleration is used to infer an effective force due to the presence of the pillar, which is found to be a lift force proportional to the product of the drop’s walking speed and its instantaneous angular speed around the post. This system presents a macroscopic example of pilot-wave-mediated forces giving rise to apparent action at a distance.

Dates et versions

hal-02429465 , version 1 (06-01-2020)

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Citer

Daniel Harris, P.-T. Brun, Adam Damiano, Luiz Faria, John Bush. The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018, 28 (9), pp.096105. ⟨10.1063/1.5031022⟩. ⟨hal-02429465⟩
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