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Large-scale vertical vorticity generated by two crossing surface waves

Vladimir M. Parfenyev* and Sergey S. Vergeles

  • Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia

  • *parfenius@gmail.com
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Phys. Rev. Fluids 5, 094702 – Published 30 September, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.094702

Abstract

We demonstrate that two surface waves propagating at a small angle 2θ to each other generate large-scale (compared to the wavelength) vertical vorticity owing to hydrodynamic nonlinearity in a viscous fluid. The horizontal geometric structure of the induced flow coincides with the structure of the Stokes drift in an ideal fluid, but its steady-state amplitude is larger and it penetrates deeper into the fluid volume as compared to the Stokes drift. In an unbounded fluid, the steady-state amplitude and penetration depth are increased by the factor of 1/sinθ and the evolution time of the induced flow can be estimated as 1/(4νk2sin2θ), where ν is the fluid kinematic viscosity and k is the wave number. Also, we study how the finite depth of the fluid and a thin insoluble liquid film that possibly covers the fluid surface due to contamination effect the generation of large-scale vorticity and discuss the physical consequences of this phenomenon in the context of recent experiments.

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Outline

Information

Phys. Rev. Fluids 5, 094702– Published 30 September, 2020
  • Received 14 May 2020
  • Accepted 14 September 2020
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