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Laboratory study of the wave-induced mean flow and set-down in unidirectional surface gravity wave packets on finite water depth

R. Calvert1,2, C. Whittaker3, A. Raby4, P. H. Taylor5, A. G. L. Borthwick2, and T. S. van den Bremer1

  • 1Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
  • 2School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United Kingdom
  • 3Department of Civil and Environmental Engineering, University of Auckland, Auckland 1010, New Zealand
  • 4School of Engineering, University of Plymouth, Plymouth PL4 8AA, United Kingdom
  • 5Faculty of Engineering and Mathematical Sciences, University of Western Australia, Crawley WA 6009, Australia

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Phys. Rev. Fluids 4, 114801 – Published 22 November, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.114801

Abstract

The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modeling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wave packets that is valid for all water depths, relative to both the length of the wave and the length of the wave packet. To validate this solution, we carry out particle tracking velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wave packets, finding good agreement. The extraction technique is able to deal with small background motion and subharmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wave-packet scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.

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Phys. Rev. Fluids 4, 114801– Published 22 November, 2019
  • Received 10 May 2019
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