Abstract
The aim of this article is not to study any practical design for a breakwater device nor to show the evidence of a particular event when waves break over a varying bathymetry, but to promote a paper showing an interesting idea of wave decomposition prior to impact, used in an experimental and numerical study published by Yasuda et al. (Proceedings 25th international conferences coastal engineering, pp 300–313, 1996) and Yasuda et al. (Coast Eng J 41(2): 269–280, 1999. We investigated the new type of breaker, proposed by Yasuda et al. (1996), by detailing several geometric aspects which lead to the unusual size and behavior of some very large plunging jets generated when waves break above some drastic changes of bathymetry. We thoroughly investigated all geometrical aspects of the breaking process, to propose a classification of the breaker types which were observed in our numerical results. We indicated the influences of the reef parameters (steps heights and lengths) on the subsequent breaking process. We also showed that the air entrainment was indeed much larger during the composite breaker occurrence.
Similar content being viewed by others
Data Availability Statement
Movies and pictures generated from the numerical simulations can be made available on reasonable request. The numerical tool used to generate the simulations is an open-source tool, available from: https://notus-cfd.org/. Source code available from: https://git.notus-cfd.org/notus/notus.
Notes
Notus CFD code: http://www.notus-cfd.org is developed in the I2M Laboratory.
References
Bacigaluppi, P., Ricchiuto, M., Bonneton, P.: Implementation and evaluation of breaking detection criteria for a hybrid boussinesq model. Water Waves 2, 207–241 (2020)
Battjes, J.A.: Surf-zone dynamics. Ann. Rev. Fluid Mech. 20, 257–293 (1988)
Blenkinsopp, C.E., Chaplin, J.R.: Void fraction measurements in breaking waves. Proc. R. Soc. A Math. Phys. Eng. Sci. 463(2088), 3151–3170 (2007)
Blenkinsopp, C.E., Chaplin, J.R.: The effect of relative crest submergence on wave breaking over submerged slopes. Coast. Eng. 55(12), 967–974 (2008)
Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)
Bryan, C.: Biggest teahupoo ever, shot on the phantom camera. All images were shot by Chris Bryan using the Phantom HD Gold camera. WWW.CHRISBRYANFILMS.COM. Video available via Youtube: https://www.youtube.com/watch?v=7woVTuN8k3c (2011)
Chang, K.-A., Hsu, T.-J., Liu, P.L.-F.: Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle. Coast. Eng. 44, 13–36 (2001)
Cooker, M.J., Peregrine, D.H., Vidal, C., Dold, J.W.: The interaction between a solitary wave and a submerged semicircular cylinder. J. Fluid Mech. 215, 1–22 (1990)
Deborde, J., Milcent, T., Lubin, P., Glockner, S.: Simulations of the interaction of solitary waves and elastic structures with a fully Eulerian method. Water Waves 2, 433–466 (2020)
Deike, L.: Mass transfer at the ocean–atmosphere interface: the role of wave breaking, droplets, and bubbles. Ann. Rev. Fluid Mech. 54(1), 191–224 (2022)
Desmons, F.: étude numérique du déferlement de vagues capillo-gravitaires. Ph.D. thesis, Université de Bordeaux, retrieved from https://tel.archives-ouvertes.fr/tel-03204107 (2021)
Desmons, F., Coquerelle, M.: A generalized high-order momentum preserving (homp) method in the one-fluid model for incompressible two phase flows with high density ratio. J. Comput. Phys. 437, 110322 (2021)
Galvin, C.J.: Breaker type classification on three laboratory beaches. J. Geophys. Res. 73, 3651–3659 (1968)
Goda, K.: A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. J. Comput. Phys. 30(1), 76–95 (1979)
Gourlay, M.R.: Wave transformation on a coral reef. Coast. Eng. 23(1), 17–42 (1994)
Gourlay, M.R.: Wave set-up on coral reefs. 1. set-up and wave-generated flow on an idealised two dimensional horizontal reef. Coast. Eng. 27(3), 161–193 (1996)
Gourlay, M.R.: Wave set-up on coral reefs. 2. set-up on reefs with various profiles. Coast. Eng. 28(1), 17–55 (1996)
Gourlay, M.R., Colleter, G.: Wave-generated flow on coral reefs-an analysis for two-dimensional horizontal reef-tops with steep faces. Coast. Eng. 52(4), 353–387 (2005)
Hara, M., Yasuda, T., Sakakibara, Y.: Characteristics of a solitary wave breaking caused by a submerged obstacle. Coast. Eng. Proc. 1(23), 253–266 (1992)
Helluy, P., Gollay, F., Grilli, S.T., Seguin, N., Lubin, P., Caltagirone, J.-P., Vincent, S., Drevard, D., Marcer, R.: Numerical simulations of wave breaking. Math. Model. Numer. Anal. 39(3), 591–608 (2005)
Hsiao, S.-C., Lin, T.-C.: Tsunami-like solitary waves impinging and overtopping an impermeable seawall: experiment and rans modeling. Coast. Eng. 57, 1–18 (2010)
Huang, C.-J., Chang, H.-H., Hwung, H.-H.: Structural permeability effects on the interaction of a solitary wave and a submerged breakwater. Coast. Eng. 49(1), 1–24 (2003)
Kalisch, H., Ricchiuto, M., Bonneton, P., Colin, M., Lubin, P.: Introduction to the special issue on breaking waves. Eur. J. Mech. B Fluids 73, 1–5 (2019)
Kazolea, M., Delis, A.I., Synolakis, C.E.: Numerical treatment of wave breaking on unstructured finite volume approximations for extended boussinesq-type equations. J. Comput. Phys. 271, 281–305 (2014)
Kazolea, M., Ricchiuto, M.: On wave breaking for boussinesq-type models. Ocean Model. 123, 16–39 (2018)
Kiger, K.T., Duncan, J.H.: Air-entrainment mechanisms in plunging jets and breaking waves. Ann. Rev. Fluid Mech. 44, 563–596 (2012)
Lee, J.-J., Skjelbreia, J.E., Raichlen, F.: Measurements of velocities in solitary waves. J. Waterw. Port Coast. Ocean Div. WW2(108), 200–218 (1982)
Liu, P.L.-F., Cheng, Y.: A numerical study of the evolution of a solitary wave over a shelf. Phys. Fluids 13(6), 1660–1667 (2001)
Losada, M.A., Vidal, C., Medina, R.: Experimental study of the evolution of a solitary wave at an abrupt junction. J. Geophys. Res. Oceans 94(C10), 14557–14566 (1989)
Lubin, P.: Large eddy simulation of plunging breaking waves. Ph.D. thesis, Université Bordeaux I, in English (2004)
Lubin, P., Chanson, H.: Are breaking waves, bores, surges and jumps the same flow? Environ. Fluid Mech. 17, 47–77 (2017)
Lubin, P., Chanson, H., Glockner, S.: Large eddy simulation of turbulence generated by a weak breaking tidal bore. Environ. Fluid Mech. 10(5), 587–602 (2010)
Lubin, P., Glockner, S.: Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments. J. Fluid Mech. 767, 364–393 (2015)
Lubin, P., Glockner, S., Kimmoun, O., Branger, H.: Numerical study of the hydrodynamics of regular waves breaking over a sloping beach. Eur. J. Mech. B Fluids 30(6), 552–564 (2011)
Lubin, P., Lemonnier, H.: Propagation of solitary waves in constant depths over horizontal beds. Multiph. Sci. Technol. 16(1–3), 237–248 (2004)
Lubin, P., Vincent, S., Abadie, S., Caltagirone, J.-P.: Three-dimensional large eddy simulation of air entrainment under plunging breaking waves. Coast. Eng. 53(8), 631–655 (2006)
Lubin, P., Vincent, S., Caltagirone, J.-P.: On the Navier–Stokes equations simulation of the head-on collision between two surface solitary waves. C. R. Mécanique 333(4), 351–357 (2005)
Massel, S.R., Gourlay, M.R.: On the modelling of wave breaking and set-up on coral reefs. Coast. Eng. 39(1), 1–27 (2000)
Mayer, R.H., Kriebel, D.L.: Wave runup on composite-slope and concave beaches. In: Proceedings of 24th International Conference Coastal Engineering, pp. 2325–2339 (1994)
Mutsuda, H., Yasuda, T.: Numerical simulation of turbulent air-water mixing layer within surf-zone. In: Proceedings of 27th International Conference Coastal Engineering, pp. 755–768 (2000)
Owkes, M., Desjardins, O.: A mesh-decoupled height function method for computing interface curvature. J. Comput. Phys. 281, 285–300 (2015)
Peregrine, D.H.: Breaking waves on beaches. Annu. Rev. Fluid Mech. 15, 149–178 (1983)
Popinet, S.: An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228(16), 5838–5866 (2009)
Popinet, S.: Numerical models of surface tension. Ann. Rev. Fluid Mech. 50(1), 49–75 (2018)
Robertson, B., Hall, K., Zytner, R., Nistor, I.: Breaking waves: review of characteristic relationships. Coast. Eng. J. 55(1), 13500021–135000240 (2013)
Seabra-Santos, F.J., Renouard, D.P., Temperville, A.M.: Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle. J. Fluid Mech. 176, 117–134 (1997)
Svendsen, I.A.: Analysis of surf zone turbulence. J. Geophys. Res. 92(C5), 5115–5124 (1987)
Svendsen, I.A., Putrevu, U.: Surf-zone Hydrodynamics, Advances in Coastal and Ocean Engineering, vol. 2, pp. 1–78. World Scientific, Singapore (1996)
Whitam, G.B.: Linear and Non-linear Waves. Wiley-Interscience Publication, New York (1974)
Wroniszewski, P.A., Verschaeve, C.G.J., Pedersen, K.G.: Benchmarking of Navier–Stokes codes for free surface simulations by means of a solitary wave. Coast. Eng. 91, 1–17 (2014)
Xu, J.Y., Liu, S.X., Li, J.X., Jia, W.: Experimental study of wave propagation characteristics on a simplified coral reef. J. Hydrodyn. 32, 385–397 (2020)
Yasuda, T., Hara, M.: Breaking and reflection of a steep solitary wave caused by a submerged obstacle. Coast. Eng. Proc. 1(22), 923–934 (1990)
Yasuda, T., Mutsuda, H., Mizutani, N.: Kinematics of overturning solitary waves and their relations to breaker types. Coast. Eng. 29, 317–346 (1997)
Yasuda, T., Mutsuda, H., Mizutani, N., Matsuda, H.: Relationships of plunging jet size to kinematics of breaking waves with spray and entrained air bubbles. Coast. Eng. J. 41(2), 269–280 (1999)
Yasuda, T., Mutsuda, H., Oya, A., Tada, A., Fukumoto, T.: A new type breaker forming a giant jet and its decaying properties. In: Proceedings 25th International Conferences Coastal Engineering, pp. 300–313 (1996)
Acknowledgements
This study was carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the “Investments for the future” Programme IdEx Bordeaux-SysNum (ANR-10-IDEX-03-02). The authors wish to thank the Aquitaine Regional Council for the financial support towards a 432-processor cluster investment, located in the I2M laboratory. This work was granted access to the HPC resources of CINES, under allocation A0012A06104 made by GENCI (Grand Equipement National de Calcul Intensif). Computer time for this study was also provided by the computing facilities MCIA (Mésocentre de Calcul Intensif Aquitain) of the Université de Bordeaux and of the Université de Pau et des Pays de l’Adour.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all the authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Desmons, F., Lubin, P. Numerical Simulations of Waves Breaking over a Rectangular Submerged Reef Consisting of a Double Step: Analogies with massive Natural Wave Breaking over Abrupt Bathymetries. Water Waves 4, 379–407 (2022). https://doi.org/10.1007/s42286-022-00067-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42286-022-00067-3