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Damping of surface waves by a floating viscoplastic plate

Xuemeng Wang and Neil J. Balmforth

  • Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2

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Phys. Rev. Fluids 7, 123302 – Published 13 December, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.123302

Abstract

A theoretical model is presented to explore how surface waves in an inviscid fluid layer are damped by the bending stresses induced in a overlying floating film of yield-stress fluid. The model applies in the long-wavelength limit, combining the shallow-water equations for the inviscid fluid with a theory for the bending of a thin viscoplastic plate described by the Herschel-Bulkley constitutive law. An exploration of the energetics captured by the model suggests that waves decay to rest in finite time, a result that is confirmed using a combination of approximate, numerical and asymptotic solutions to the model equations. In the limit that the plate behaves like a perfectly plastic material, the sloshing motions take the form of triangular waves with bending restricted to narrow viscoplastic hinges.

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Phys. Rev. Fluids 7, 123302– Published 13 December, 2022
  • Received 29 September 2022
  • Accepted 23 November 2022
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