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  • Letter
  • Open Access

Experimental observation of parabolic wakes in thin plates

Janez Rus*, Aleksi Bossart, Benjamin Apffel, Matthieu Malléjac, and Romain Fleury†

  • *Contact author: janez.rus@tum.de
  • †Contact author: romain.fleury@epfl.ch
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Phys. Rev. Research 6, L032027 – Published 2 August, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032027

Abstract

Wakes are medium perturbations created by a moving object, such as wave patterns behind boats, or wingtip vortices following an aircraft. Here, we report about an experimental study of an uncharted form of parabolic wakes occurring in media with the group velocity twice larger than the phase velocity, as opposed to the conventional case of Kelvin wakes. They are formed by moving a laser spot on a thin plate, which excites a unique wake pattern made of confocal parabolas, due to the quadratic dispersion of the zero-order flexural Lamb mode. If the spatial dimensions are rescaled by the perturbation velocity and material constant, we obtain a single universal wake with constant parabolic focal lengths. We demonstrate an evanescent regime above the critical frequency where the wave components oscillate exclusively in the direction parallel to the perturbation path, with an opening angle of 90∘. We define a dimensionless number, analogous to Froude and Mach numbers, which determines whether or not the complete parabolic wake pattern will be excited by the moving source. Finally, we generalize the physics of wake shapes to arbitrary dispersion relations.

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Phys. Rev. Research 6, L032027– Published 2 August, 2024
  • Received 7 February 2024
  • Accepted 3 July 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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