Environmental Fluid Mechanics

, Volume 14, Issue 5, pp 1123–1145 | Cite as

Hele-Shaw beach creation by breaking waves: a mathematics-inspired experiment

  • Anthony R. Thornton
  • Avraham J. van der Horn
  • Elena Gagarina
  • Wout Zweers
  • Devaraj van der Meer
  • Onno Bokhove
Original Article


Fundamentals of nonlinear wave-particle interactions are studied experimentally in a Hele-Shaw configuration with wave breaking and a dynamic bed. To design this configuration, we determine, mathematically, the gap width which allows inertial flows to survive the viscous damping due to the side walls. Damped wave sloshing experiments compared with simulations confirm that width-averaged potential-flow models with linear momentum damping are adequately capturing the large scale nonlinear wave motion. Subsequently, we show that the four types of wave breaking observed at real-world beaches also emerge on Hele-Shaw laboratory beaches, albeit in idealized forms. Finally, an experimental parameter study is undertaken to quantify the formation of quasi-steady beach morphologies due to nonlinear, breaking waves: berm or dune, beach and bar formation are all classified. Our research reveals that the Hele-Shaw beach configuration allows a wealth of experimental and modelling extensions, including benchmarking of forecast models used in the coastal engineering practice, especially for shingle beaches.


Hele-Shaw cell Laboratory experiments Mathematical design Shingle beaches Potential flow and shallow water simulations 



We acknowledge Gert-Wim Bruggert for technical assistance and dr. Boudewijn de Smeth from the International Institute for Geo-Information Science and Earth Observation in Twente for lending technical equipment. Financial support came from the MultiScale Mechanics and Physics of Fluids groups of Stefan Luding and Detlef Lohse (University of Twente), respectively; the Stichting Free Flow Foundation; and, the Geophysical Fluid Dynamics Program at the Woods Hole Oceanographic Institution, where O.B. did some of the work.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Anthony R. Thornton
    • 1
    • 3
  • Avraham J. van der Horn
    • 2
  • Elena Gagarina
    • 3
  • Wout Zweers
    • 4
  • Devaraj van der Meer
    • 2
  • Onno Bokhove
    • 3
    • 5
  1. 1.Department of Mechanical EngineeringUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of PhysicsUniversity of TwenteEnschedeThe Netherlands
  3. 3.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  4. 4.FabLab Saxion HogeschoolEnschedeThe Netherlands
  5. 5.School of MathematicsUniversity of LeedsLeedsUnited Kingdom

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