Skip to main content
Log in

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

  • Original Article
  • Published:
Environmental Fluid Mechanics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. Source file golfbakonno2.avi contains surging, collapsing, plunging and spilling breakers at \(8,133,115\) and \(63\) s, respectively.

References

  1. Albert R, Albert I, Hornbaker D, Schiffer P, Barabási A-L (1997) Maximum angle of stability in wet and dry spherical granular media. Phys Rev E 56:6271–6274

    Article  Google Scholar 

  2. Batchelor GK (1967) An introduction to fluid dynamics, 635th edn. Cambridge University Press, London

    Google Scholar 

  3. Battjes J (1974) Surf similarity. Proc. \(14{\rm th}\) Coastal Eng. Conf., Copenhagen, Denmark, 466–480

  4. Bokhove O, Zwart V. Haveman MJ (2010) Fluid fascinations. Publication of stichting Qua Art Qua Science, University of Twente. The Hele–Shaw beach was revealed at the Qua Art Qua Science lecture by Bokhove and Zwart V on 17–01-2010, in a tribute to the late Prof. Peregrine. http://eprints.eemcs.utwente.nl/17393/

  5. Bokhove O, Van der Horn A, Van der Meer D, Zweers W, Thornton AR (2012) Breaking waves on a dynamic Hele-Shaw beach. Proc. Third Int. Symposium on Shallow Flows. http://eprints.eemcs.utwente.nl/21539/

  6. Calantoni J, Puleo JA, Holland KT (2006) Simulation of sediment motions using a discrete particle model in the inner surf and swash-zones. Cont Shelf Res 26:1987–2001

    Article  Google Scholar 

  7. Courrech du Pont S, Gondret P, Perrin B, Rabaud M (2003) Granular avalanches in fluids. Phys Rev Lett 90:044301–044311

    Article  Google Scholar 

  8. Doppler D, Gondret P, Loiseleux T, Meyer S, Rabaud M (2007) Relaxation dynamics of water-immersed granular avalanches. J Fluid Mech 577:161–181

    Article  Google Scholar 

  9. Garnier R, Dodd N, Falquez A, Calvete D (2010) Mechanisms controlling crescentic bar amplitude. J Geophys Res 115:F02007

    Google Scholar 

  10. Gagarina E, Van der Vegt JJW, Ambati VR, Bokhove O (2012) A Hamiltonian Boussinesq model with horizontally sheared currents. Third Int. Symp. on shallow flows Proc. June 4–6, Iowa. http://eprints.eemcs.utwente.nl/21540

  11. Gagarina E, Ambati VR, Van der Vegt JJW, Bokhove O (2013) Variational space-time (dis)continuous Galerkin finite element method for nonlinear water waves. Accepted with minor corrections J Comp Phys

  12. Gagarina E, Ambati VR, Van der Vegt JJW, Nurijanyan S, Bokhove O (2013) Variational time (dis)continuous Galerkin finite element method for nonlinear Hamiltonian systems. In preparation

  13. Galvin CJ (1968) Breaker type classification on three laboratory beaches. J Geophys Res 73:3651– 3659

    Google Scholar 

  14. Grimshaw R, Osaisai E (2013) Modelling the effect of bottom sediment on beach profiles and wave set-up. Ocean Modell 59–60:24–30

    Google Scholar 

  15. Hele-Shaw HS (1898) The flow of water. Nature 58:520–520

    Article  Google Scholar 

  16. Horn van der AJ (2012) Beach evolution and wave dynamics in a Hele-Shaw Geometry. MSc Thesis, Department of Physics, University of Twente

  17. Lamb H (1993) Hydrodynamics. Cambridge University Press, London

    Google Scholar 

  18. Lane EM, Restrepo JM (2007) Shoreface-connected ridges under the action of waves and currents. J Fluid Mech 582:23–52

    Article  Google Scholar 

  19. Lee AT, Ramos E, Swinney HL (2007) Sedimenting sphere in a variable-gap Hele-Shaw cell. J Fluid Mech 586:449–464

    Article  Google Scholar 

  20. McCall RT, Thiel de Vries JSM, Plant NG, van Dongeren AR, Roelvink JA, Thompson DM, Reniers AJHM (2010) Two-dimensional time dependent hurricane overwash and erosion modeling at Rosa Island. Coastal Eng 57:668–683

    Article  Google Scholar 

  21. Miles J (1977) On Hamilton’s principle for surface waves. J Fluid Mech 83:153–158

    Article  Google Scholar 

  22. Operational forecasting models 2013: Delft3D. Software platform including morphology of Deltares, The Netherlands. http://www.deltaressystems.com/hydro/product/621497/delft3d-suite Open Telemac-Mascaret: http://www.opentelemac.org/ XBeach: http://oss.deltares.nl/web/xbeach/

  23. Peregrine DH (1983) Breaking waves on beaches. Ann Rev Fluid Mech 15:149–178

    Article  Google Scholar 

  24. Plouraboué F, Hinch EJ (2002) Kelvin–Helmholtz instability on a Hele-Shaw cell. Phys Fluids 14:922–929

    Article  Google Scholar 

  25. Powell KA (1990) Predicting short term profile response for shingle beaches. HR Wallingford, Online Report

  26. Rajchenbach J, Lerouz A, Clamond D (2011) New standing solitary waves. Phys Rev Lett 107:024502

    Article  Google Scholar 

  27. Roelvink D, Reniers A, van Dongeren A, van Thiel de Vries J, McCall R, Lescinkski J (2009) Modelling storm impacts on beaches, dunes and barrier islands. Coastal Eng 56:1133–1152

    Article  Google Scholar 

  28. Rosenhead L (1963) Boundary layer theory. Oxford University Press, Oxford, p 688

    Google Scholar 

  29. Soulsby R (1997) Dynamics of marine sands. In: HR Wallingford. Thomas Telford (eds). p 249

  30. Vega JM, Knobloch E, Martel C (2001) Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio. Physica D 154:313–336

    Article  Google Scholar 

  31. Vella D, Mahadevan L (2005) The Cheerios effect. Am J Phys 73:817–825

    Article  Google Scholar 

  32. Williams J, Ruiz de Alegria-Arzaburu A (2012) Modelling gravel barrier profile response to combined waves and tides using XBeach: laboratory and fields results. Coastal Eng 63:62–80

    Article  Google Scholar 

  33. Wilson SK, Duffy BR (1998) On lubrication with comparable viscous and inertia forces. Q.J. Mech Appl Math 51:105–124

    Article  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Onno Bokhove.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Thornton, A.R., van der Horn, A.J., Gagarina, E. et al. Hele-Shaw beach creation by breaking waves: a mathematics-inspired experiment. Environ Fluid Mech 14, 1123–1145 (2014). https://doi.org/10.1007/s10652-014-9350-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-014-9350-7

Keywords

Navigation