Skip to main content
Log in

Are breaking waves, bores, surges and jumps the same flow?

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

Abstract

The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps. Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.

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

Similar content being viewed by others

References

  1. Anguelova MD, Huq P (2012) Characteristics of bubble clouds at various wind speeds. J Geophys Res 117:C03036. doi:10.1029/2011JC007442

    Article  Google Scholar 

  2. Babb AF, Aus HC (1981) Measurements of air in flowing water. J Hydraul Div ASCE 107(12):1615–1630

    Google Scholar 

  3. Bacigaluppi P, Ricchiuto M, Bonneton P (2014) Upwind stabilized finite element modelling of non-hydrostatic wave breaking and run-up. Research Report INRIA, RR-8536, https://hal.inria.fr/hal-00990002v3

  4. Bakhmeteff BA (1912) O Neravnomernom Dwijenii Jidkosti v Otkrytom Rusle. (Varied Flow in Open Channel.) St Petersburg, Russia (in Russian)

  5. Bakhmeteff BA (1932) Hydraulics of open channels, 1st edn. McGraw-Hill, New York

    Google Scholar 

  6. Banner ML, Phillips OM (1974) On the incipient breaking of small scale waves. J Fluid Mech 65:647–656

    Article  Google Scholar 

  7. Banner ML, Melville WK (1976) On the separation of air flow over water waves. J Fluid Mech 77:825–891

    Article  Google Scholar 

  8. Banner ML, Peregrine DH (1993) Wave breaking in deep water. Annu Rev Fluid Mech 25:373–397

    Article  Google Scholar 

  9. Basco DR (1985) A qualitative description of wave breaking. J Waterw Port Coast Ocean Eng 111(2):171–188

    Article  Google Scholar 

  10. Battjes JA (1988) Surf-zone dynamics. Ann Rev Fluid Mech 20:257–293

    Article  Google Scholar 

  11. Bazin H (1865) Recherches Expérimentales sur la Propagation des Ondes. (‘Experimental Research on Wave Propagation.’) Mémoires présentés par divers savants à l’Académie des Sciences, Paris, France, Vol. 19, pp. 495–644 (in French)

  12. Bélanger JB (1841) “Notes sur l’Hydraulique.” (‘Notes on Hydraulic Engineering.’) Ecole Royale des Ponts et Chaussées, Paris, France, session 1841–1842, 223 pp (in French)

  13. Bjørkavåg M, Kalisch H (2011) Wave breaking in Boussinesq models for undular bores. Phys Lett A 375:1570–1578

    Article  Google Scholar 

  14. Blenkinsopp CE, Chaplin JR (2007) Void fraction measurements in breaking waves. Proc R Soc A 463:3151–3170. doi:10.1098/rspa.2007.1901

    Article  Google Scholar 

  15. Blenkinsopp CE, Chaplin JR (2010) Bubble size measurements in breaking waves using optical fiber phase detection probes. J Ocean Eng 35(2):388–401

    Article  Google Scholar 

  16. Blenkinsopp CE, Chaplin JR (2011) Void fraction measurements and scale effects in breaking waves in freshwater and seawater. Coast Eng 58:417–428

    Article  Google Scholar 

  17. Bombardelli FA (2012) Computational multi-phase fluid dynamics to address flows past hydraulic structures. Proceedings of 4th IAHR International Symposium on Hydraulic Structures, APRH—Associação Portuguesa dos Recursos Hídricos (Portuguese Water Resources Association), J. Matos, S. Pagliara & I. Meireles Eds., 9–11 February 2012, Porto, Portugal, Paper 2, 19 pages (CD-ROM)

  18. Bonmarin P (1989) Geometric properties of deep-water breaking waves. J Fluid Mech 209:405–433

    Article  Google Scholar 

  19. Boussinesq JV (1877) Essai sur la Théorie des Eaux Courantes. (‘Essay on the Theory of Water Flow.’) Mémoires présentés par divers savants à l’Académie des Sciences, Paris, France, Vol. 23, Série 3, No. 1, supplément 24, pp. 1–680 (in French)

  20. Bowyer PA (2001) Video measurements of near-surface bubble spectra. J Geophys Res 106(C7):14179–14190

    Article  Google Scholar 

  21. Bresse JA (1868) Cours de Mécanique Appliquée Professé à l’École Impériale des Ponts et Chaussées. (Course in Applied Mechanics lectured at the Pont-et-Chaussées Engineering School.) Gauthier-Villars, Paris, France, 586 p (in French)

  22. Brocchini M (2013) A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics. Proc R Soc A 469:20130496

    Article  Google Scholar 

  23. Brocchini M, Peregrine DH (2001) The dynamics of strong turbulence at free surfaces. Part 1. Description. J Fluid Mech 449:225–254

    Article  Google Scholar 

  24. Brocchini M, Peregrine DH (2001) The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions. J Fluid Mech 449:255–290

    Article  Google Scholar 

  25. Callaghan AH, Stokes MD, Deane GB (2014) The effect of water temperature on air entrainment, bubble plumes, and surface foam in a laboratory breaking-wave analog. J Geophys Res Ocean. doi:10.1002/2014JC010351

    Google Scholar 

  26. Carrica PM, Drew D, Bonetto F, Lahey RT Jr (1999) A polydisperse model for bubbly two-phase flow around a surface ship. Int J Multiph Flow 25:257–305

    Article  Google Scholar 

  27. Cartellier A, Achard JL (1991) Local phase detection probes in fluid/fluid two-phase flows. Rev Sci Instrum 62(2):279–303

    Article  Google Scholar 

  28. Cartmill J, Su M (1993) Bubble size distribution under saltwater and freshwater breaking waves. Dyn Atmos Oceans 20:25–31. doi:10.1016/0377-0265(93)90046-A

    Article  Google Scholar 

  29. Chachereau Y, Chanson H (2011) Bubbly flow measurements in hydraulic jumps with small inflow froude numbers. Int J Multiph Flow 37(6):555–564. doi:10.1016/j.ijmultiphaseflow.2011.03.012

    Article  Google Scholar 

  30. Chanson H (1996) Free-surface flows with near-critical flow conditions. Can J Civ Eng 23(6):1272–1284

    Article  Google Scholar 

  31. Chanson H (1997) Air bubble entrainment in free-surface turbulent shear flows. Academic Press, London

    Google Scholar 

  32. Chanson H (2004) The hydraulics of open channel flow: an introduction, 2nd edn. Butterworth-Heinemann, Oxford

    Google Scholar 

  33. Chanson H (2005) Air–water and momentum exchanges in unsteady surging waters: an experimental study. Exp Thermal Fluid Sci 30(1):37–47

    Article  Google Scholar 

  34. Chanson H (2007) Bubbly flow structure in hydraulic jump. Eur J Mech B/Fluids 26(3):367–384. doi:10.1016/j.euromechflu.2006.08.001

    Article  Google Scholar 

  35. Chanson H (2009) Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects. Environ Fluid Mech 9(2):125–142. doi:10.1007/s10652-008-9078-3

    Article  Google Scholar 

  36. Chanson H (2009) Development of the Bélanger equation and backwater equation by Jean-Baptiste Bélanger (1828). J Hydraul Eng ASCE 135(3):159–163. doi:10.1061/(ASCE)0733-9429(2009)135:3(159)

    Article  Google Scholar 

  37. Chanson H (2010) Undular tidal bores: basic theory and free-surface characteristics. J Hydraul Eng ASCE 136(11):940–944. doi:10.1061/(ASCE)HY.1943-7900.0000264

    Article  Google Scholar 

  38. Chanson H (2010) Unsteady turbulence in tidal bores: effects of bed roughness. J Waterw Port Coast Ocean Eng ASCE 136(5):247–256. doi:10.1061/(ASCE)WW.1943-5460.0000048

    Article  Google Scholar 

  39. Chanson H (2010) Convective transport of air bubbles in strong hydraulic jumps. Int J Multiph Flow 36(10):798–814. doi:10.1016/j.ijmultiphaseflow.2010.05.006

    Article  Google Scholar 

  40. Chanson H (2011) Turbulent shear stresses in hydraulic jumps and decelerating surges: an experimental study. Earth Surf Process Landf 36(2):180–189. doi:10.1002/esp.2031

    Article  Google Scholar 

  41. Chanson H (2012) Momentum considerations in hydraulic jumps and bores. J Irrig Drain Eng ASCE 138(4):382–385. doi:10.1061/(ASCE)IR.1943-4774.0000409

    Article  Google Scholar 

  42. Chanson H (2013) Hydraulics of aerated flows: Qui Pro Quo?. J Hydraul Res, IAHR. Invited Vision paper, 51(3): 223–243. doi: 10.1080/00221686.2013.795917

  43. Chanson H (2016) Atmospheric noise of a breaking tidal bore. J Acoust Soc Am 139(1):12–20. doi:10.1121/1.4939113

    Article  Google Scholar 

  44. Chanson H, Cummings PD (1994) Effects of plunging breakers on the gas contents in the oceans. Mar Technol Soc J 28(3):22–32

    Google Scholar 

  45. Chanson H, Gualtieri C (2008) Similitude and scale effects of air entrainment in hydraulic jumps. J Hydraul Res 46(1):35–44

    Article  Google Scholar 

  46. Chanson H, Montes JS (1995) Characteristics of undular hydraulic jumps. Experimental apparatus and flow patterns. J Hydraul Eng ASCE 121(2):129–144

    Article  Google Scholar 

  47. Chanson H, Aoki S, Maruyama M (2002) Unsteady air bubble entrainment and detrainment at a plunging breaker: dominant time scales and similarity of water level variations. Coast Eng 46(2):139–157

    Article  Google Scholar 

  48. Chanson H, Aoki S, Hoque A (2006) Bubble entrainment and dispersion in plunging jet flows: freshwater versus seawater. J Coast Res 22(3):664–677. doi:10.2112/03-0112.1

    Article  Google Scholar 

  49. Chanson H, Brattberg T (2000) Experimental study of the air–water shear flow in a hydraulic jump. Int J Multiph Flow 26(4):583–607

    Article  Google Scholar 

  50. Chanson H, Reungoat D, Simon B, Lubin P (2011) High-frequency turbulence and suspended sediment concentration measurements in the Garonne River Tidal Bore. Estuar Coast Shelf Sci 95(2–3):298–306. doi:10.1016/j.ecss.2011.09.012

    Article  Google Scholar 

  51. Chanson H, Toi YH (2015) Physical modelling of breaking tidal bores: comparison with prototype data. J Hydraul Res IAHR 53(2):264–273. doi:10.1080/00221686.2014.989458

    Article  Google Scholar 

  52. Chen G, Kharif C, Zaleski S, Li J (1999) Two-dimensional Navier–Stokes simulation of breaking waves. Phys Fluids 11(1):121–133

    Article  Google Scholar 

  53. Cheng J, Wang P (2015) Extracting turbulence under breaking waves in the surf zone. J Waterw Port Coast Ocean Eng. doi:10.1061/(ASCE)WW.1943-5460.0000307

    Google Scholar 

  54. Christensen ED, Walstra D-J, Emerat N (2002) Vertical variation of the flow across the surf zone. Coast Eng 45:169–198

    Article  Google Scholar 

  55. Cienfuegos R, Barthélemy E, Bonneton P (2010) Wave-breaking model for boussinesq-type equations including roller effects in the mass conservation equation. J Waterw Port Coast Ocean Eng 136(1):10–26

    Article  Google Scholar 

  56. Cipriano RJ, Blanchard DC (1981) Bubble and aerosol spectra produced by a laboratory ‘breaking wave’. J Geophys Res 86(C9):8085–8092

    Article  Google Scholar 

  57. Clift R, Grace JR, Weber ME (1978) Bubbles, drops, and particles. Academic Press, San Diego

    Google Scholar 

  58. Coakley DB, Haldeman PM, Morgan DG, Nicolas KR, Penndorf DR, Wetzel LB, Weller CS (2001) Electromagnetic scattering from large steady breaking waves. Exp Fluids 30(5):479–487. doi:10.1007/s003480000220

    Article  Google Scholar 

  59. Cointe R, Tulin MP (1994) A theory of steady breakers. J Fluid Mech 216:1–20

    Article  Google Scholar 

  60. Cox DT, Shin S (2003) Laboratory measurements of void fraction and turbulence in the Bore Region of surf zone waves. J Eng Mech ASCE 129(10):1197–1205

    Article  Google Scholar 

  61. Crowe CT, Schwarzkopf JD, Sommerfeld M, Tsuji Y (2011) Multiphase flows with droplets and particles, 2nd edn. Boca Raton, CRC Press

    Book  Google Scholar 

  62. D’Alessandro F, Tomasicchio GR (2008) The BCI criterion for the initiation of breaking process in Boussinesq-type equations wave models. Coast Eng 55:1174–1184

    Article  Google Scholar 

  63. Dabiri D, Gharib M (1997) Experimental investigation of the vorticity generation within a spilling water wave. J Fluid Mech 330:113–139

    Article  Google Scholar 

  64. Dahl PH, Jessup AT (1995) On bubble clouds produced by breaking waves: an event analysis of ocean acoustic measurements. J Geophys Res 100(C3):5007–5020. doi:10.1029/94JC03019

    Article  Google Scholar 

  65. Darcy HPG, Bazin H (1865) Recherches Hydrauliques. (Hydraulic Research.) Imprimerie Impériales, Paris, France, Parties 1ère et 2ème (in French)

  66. Deane G (1997) Sound generation and air entrainment by breaking waves in the surf zone. J Acoust Soc Am 102(5):2671–2689. doi:10.1121/1.420321

    Article  Google Scholar 

  67. Deane G, Stokes MD (2002) Scale dependence of bubble creation mechanisms in breaking waves. Nature 418:839–844

    Article  Google Scholar 

  68. Derakhti M, Kirby JT (2014) Bubble entrainment and liquid–bubble interaction under unsteady breaking waves. J Fluid Mech 761:464–506. doi:10.1017/jfm.2014.637

    Article  Google Scholar 

  69. Docherty NJ, Chanson H (2012) Physical modelling of unsteady turbulence in breaking tidal bores. J Hydraul Eng ASCE 138(5):412–419. doi:10.1061/(ASCE)HY.1943-7900.0000542

    Article  Google Scholar 

  70. Drazen DA, Melville WK, Lenain L (2008) Inertial scaling of dissipation in unsteady breaking waves. J Fluid Mech 611:307–332

    Article  Google Scholar 

  71. Drew DA (1983) Mathematical modeling of two-phase flow. Annu Rev Fluid Mech 1983(15):261–291

    Article  Google Scholar 

  72. Drew DA, Passman SL (1999). Theory of Multicomponent Fluids. Applied Mathematical Sciences, Vol. 135, Springer: New York, doi:10.1007/b97678

  73. Duncan JH (1981) An experimental investigation of breaking waves produced by a towed hydrofoil. Proc R Soc Lond A 377:331–348

    Article  Google Scholar 

  74. Duncan JH (2001) Spilling breakers. Annu Rev Fluid Mech 33:519–547

    Article  Google Scholar 

  75. Esmaeeli A, Tryggvason G (1996) An inverse energy cascade in two-dimensional low Reynolds number bubbly flows. J Fluid Mech 314:315–330

    Article  Google Scholar 

  76. Falvey HT (1990) Cavitation in chutes and spillways. US Bureau of Reclamation Engineering Monograph, No. 42, Denver, Colorado, USA

  77. Farahani RJ, Dalrymple RA (2014) Three-dimensional reversed horseshoe vortex structures under broken solitary waves. Coast Eng 91:261–279

    Article  Google Scholar 

  78. Favre H (1935) Etude Théorique et Expérimentale des Ondes de Translation dans les Canaux Découverts. (‘Theoretical and Experimental Study of Travelling Surges in Open Channels.’) Dunod, Paris, France (in French)

  79. Führboter A (1970). Air entrainment and energy dissipation in breakers. 12th International Conference on Coastal Engineering. https://journals.tdl.org/icce/index.php/icce/article/view/2628

  80. Furgerot L, Mouaze D, Tessier B, Perez L, Haquin S (2013) Suspended Sediment Concentration in Relation to the Passage of a Tidal Bore (Sée River Estuary, Mont Saint Michel, NW France). Proc. Coastal Dynamics 2013, Arcachon, France, 24–28 June, pp. 671–682

  81. Galinat S, Risso F, Masbernat O, Guiraud P (2007) Dynamics of drop breakup in inhomogeneous turbulence at various volume fractions. J Fluid Mech 578:85–94. doi:10.1017/S0022112007005186

    Article  Google Scholar 

  82. Gemmrich J (2010) Strong turbulence in the wave crest region. J Phys Oceanogr 40:583–595. doi:10.1175/2009JPO4179.1

    Article  Google Scholar 

  83. Gemmrich JR, Farmer DM (2004) Near-surface turbulence in the presence of breaking waves. J Phys Oceanogr 34:1067–1086

    Article  Google Scholar 

  84. Gomez-Gesteira M, Rogers BD, Dalrymple RA, Crespo AJC (2010) State-of-the-art of classical SPH for free-surface flows. J Hydraul Res 48(S1):6–27. doi:10.1080/00221686.2010.9641242

    Article  Google Scholar 

  85. Govender K, Mocke GP, Alport MJ (2002) Video-imaged surf zone wave and roller structures and flow fields. J Geophys Res 107(C7):3072. doi:10.1029/2000JC000755

    Article  Google Scholar 

  86. Gualtieri C, Chanson H (2010) Effect of Froude number on bubble clustering in a hydraulic jump. J Hydraul Res IAHR 48(4):504–508

    Article  Google Scholar 

  87. Haller MC, Catalán PA (2010) Remote sensing of wave roller lengths in the laboratory. J Geophys Res 114:C07022. doi:10.1029/2008JC005185

    Google Scholar 

  88. Henderson FM (1966) Open channel flow. MacMillan Company, New York

    Google Scholar 

  89. Hinze JO (1955) Fundamentals of the hydrodynamic mechanism of slitting in dispersion processes. J Am Inst Chem Eng 1:289–295

    Article  Google Scholar 

  90. Hoque A, Aoki S-I (2005) Distributions of void fraction under breaking waves in the surf zone. Ocean Eng 32:1829–1840

    Article  Google Scholar 

  91. Hornung HG, Willert C, Turner S (1995) The flow field downstream of a hydraulic jump. J Fluid Mech 287:299–316

    Article  Google Scholar 

  92. Hoyt JW, Sellin RHJ (1989) Hydraulic jump as ‘mixing layer’. J Hydraul Eng ASCE 115(12):1607–1614

    Article  Google Scholar 

  93. Hubbard DW, Griffin OM, Peltzer RD (1987) Foam generation and air entrainment near a free surface. Naval Research Laboratory Memorandum Report 6038, Washington D.C., USA

  94. Hwung HH, Chyan JM, Chung YC (1992) Energy dissipation and air bubbles mixing inside surf zone. Proceedings of 23rd International Conference on Coastal Engineering, ASCE, Venice, Italy, Vol. 1, Chap. 22, pp. 308–321

  95. Iafrati A (2009) Numerical study of the effects of the breaking intensity on wave breaking flows. J Fluid Mech 622:371–411

    Article  Google Scholar 

  96. Iafrati A (2011) Energy dissipation mechanisms in wave breaking processes: spilling and highly aerated plunging breaking events. J Geophys Res 116:C07024. doi:10.1029/2011JC007038

    Article  Google Scholar 

  97. Jansen PCM (1986) Laboratory observations of the kinematics in the aerated region of breaking waves. Coast Eng 9:453–477

    Article  Google Scholar 

  98. Kalvoda PM, Xu L, Wu J (2003) Macrobubble clouds produced by breaking wind waves: a laboratory study. J Geophys Res 108(C6):3207. doi:10.1029/1999JC000265

    Article  Google Scholar 

  99. Katz Y, Horev E, Wygnanski I (1992) The forced turbulent wall jet. J Fluid Mech 242:577–609

    Article  Google Scholar 

  100. Kazolea M, Delis AI, Synolakis CE (2014) Numerical treatment of wave breaking on unstructured finite volume approximations for extended Boussinesq-type equations. J Comput Phys 271:281–305

    Article  Google Scholar 

  101. Kimmoun O, Branger H (2007) A particle image velocimetry investigation on laboratory surf-zone breaking waves over a sloping beach. J Fluid Mech 588:353–397

    Article  Google Scholar 

  102. Kiger KT, Duncan JH (2012) Air-entrainment mechanisms in plunging jets and breaking waves. Ann Rev Fluid Mech 44:563–596

    Article  Google Scholar 

  103. Kennedy AB, Chen Q, Kirby JT, Dalrymple RA (2000) Boussinesq modeling of wave transformation, breaking and run-up. I: one dimension. ASCE. J Waterw Port Coast Ocean Eng 126(1):48–56

    Article  Google Scholar 

  104. Koch C, Chanson H (2008) Turbulent mixing beneath an undular bore front. J Coast Res 24(4):999–1007. doi:10.2112/06-0688.1

    Article  Google Scholar 

  105. Koch C, Chanson H (2009) Turbulence measurements in positive surges and bores. J Hydraul Res IAHR 47(1):29–40. doi:10.3826/jhr.2009.2954

    Article  Google Scholar 

  106. Kucukali S, Chanson H (2008) Turbulence measurements in hydraulic jumps with partially-developed inflow conditions. Exp Thermal Fluid Sci 33(1):41–53. doi:10.1016/j.expthermflusci.2008.06.012

    Article  Google Scholar 

  107. Labourasse E, Lacanette D, Toutant A, Lubin P, Vincent S, Lebaigue O, Caltagirone J-P, Sagaut P (2007) Towards large eddy simulation of isothermal two-phase flows: governing equations and a priori tests. Int J Multiph Flow 33(1):1–39

    Article  Google Scholar 

  108. Lakehal D, Liovic P (2011) Turbulence structure and interaction with steep breaking waves. J Fluid Mech 674:522–577. doi:10.1017/jfm.2011.3

    Article  Google Scholar 

  109. Lamarre E, Melville WK (1991) Air entrainment and dissipation in breaking waves. Nature 351:469–472. doi:10.1038/351469a0

    Article  Google Scholar 

  110. Lamarre E, Melville WK (1992) Instrumentation for the measurement of void-fraction in breaking waves: laboratory and field results. IEEE J Ocean Eng 17(2):204–215. doi:10.1109/48.126977

    Article  Google Scholar 

  111. Lamarre E, Melville WK (1994) Void-fraction measurements and sound-speed fields in bubble plumes generated by breaking waves. J Acoust Soc Am 95(3):1317–1328. doi:10.1121/1.408572

    Article  Google Scholar 

  112. Leandro J, Carvalho R, Chachereau Y, Chanson H (2012) Estimating void fraction in a hydraulic jump by measurements of pixel intensity. Exp Fluids 52(5):1307–1318. doi:10.1007/s00348-011-1257-1

    Article  Google Scholar 

  113. Leifer I, Caulliez G, de Leeuw G (2006) Bubbles generated from wind-steepened breaking waves: 2. Bubble plumes, bubbles, and wave characteristics. J Geophys Res 111:C06021. doi:10.1029/2004JC002676

    Google Scholar 

  114. Leng X, Chanson H (2015) Turbulent advances of a breaking bore: preliminary physical experiments. Exp Thermal Fluid Sci 62:70–77. doi:10.1016/j.expthermflusci.2014.12.002

    Article  Google Scholar 

  115. Leng X, Chanson H (2015) Breaking bore: physical observations of roller characteristics. Mech Res Commun 65:24–29. doi:10.1016/j.mechrescom.2015.02.008

    Article  Google Scholar 

  116. Leng X, Chanson H (2016) Coupling between free-surface fluctuations, velocity fluctuations and turbulent reynolds stresses during the upstream propagation of positive surges, bores and compression waves. Environ Fluid Mech 16(4):695–719. doi:10.1007/s10652-015-9438-8

    Article  Google Scholar 

  117. Lennon JM, Hill DF (2006) Particle image velocimetry measurements of undular and hydraulic jumps. J Hydraul Eng 132(12):1283–1294

    Article  Google Scholar 

  118. Lighthill J (1978) Waves in fluids. Cambridge University Press, Cambridge

    Google Scholar 

  119. Lim H-J, Chang K-A, Huang Z-C, Na B (2015) Experimental study on plunging breaking waves in deep water. J Geophys Res Oceans 120:2007–2049. doi:10.1002/2014JC010269

    Article  Google Scholar 

  120. Lin C, Hwung HH (1992) External and internal flow fields of plunging breakers. Exp Fluids 12:229–237

    Google Scholar 

  121. Lin JC, Rockwell D (1995) Evolution of a quasi-steady breaking wave. J Fluid Mech 302:29–44

    Article  Google Scholar 

  122. Loewen MR, O’Dor MA, Skafel MG (1996) Bubbles entrained by mechanically generated breaking waves. J Geophys Res: Oceans 101(C9):20759–20769

    Article  Google Scholar 

  123. Longuet-Higgins MS (1973) A model of flow separation at a free surface. J. Fluid Mech 57(1):129–148

    Article  Google Scholar 

  124. Longuet-Higgins MS, Turner JS (1974) An ‘entraining plume’ model of a spilling breaker. J. Fluid Mech 63(1):1–20

    Article  Google Scholar 

  125. Lubin P, Vincent S, Abadie S, Caltagirone J-P (2006) Three-dimensional large eddy simulation of air entrainment under plunging breaking waves. Coast Eng 53(8):631–655

    Article  Google Scholar 

  126. Lubin P, Glockner S (2015) Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments. J Fluid Mech 767:364–393. doi:10.1017/jfm.2015.62

    Article  Google Scholar 

  127. Ma G, Shi F, Kirby JT (2011) A polydisperse two-fluid model for surf zone bubble simulation. J Geophys Res 116:C05010

    Google Scholar 

  128. Madsen PA (1981) A model for a turbulent bore. Ph.D. Thesis, Tech. Univ. of Denmark, Inst. of Hydrodynamics and Hyd. Eng., Copenhagen, Denmark, 149 pages. (also Series Paper No. 28, Tech. Univ. of Denmark, Inst. of Hydrodyamics and Hyd. Eng., Copenhager, Denmark, 149 pages.)

  129. Melville WK (1996) The role of surface-wave breaking in air–sea interaction. Annu Rev Fluid Mech 28:279–321

    Article  Google Scholar 

  130. Melville WK, Veron F, White CJ (2002) The velocity field under breaking waves: coherent structures and turbulence. J Fluid Mech 454:203–233

    Article  Google Scholar 

  131. Miller RL (1972) Study of air entrainment in breaking waves. Am Geophys Union Trans EOS 53:426

    Google Scholar 

  132. Miller RL (1976) Role of vortices in surf zone prediction: sedimentation and wave forces. In Beach and Nearshore Sedimentation, Edited by Richard A. Davis, Jr. and R. L. Ethington, 24: 92–114

  133. Monahan EC (1993) Occurrence and evolution of acoustically relevant sub-surface bubble plumes and their associated, remotely monitorable, surface whitecaps”. In: Kerman BR (ed) Natural physical sources of underwater sound. Kluwer, Dordrecht, pp 503–517

    Chapter  Google Scholar 

  134. Moraga FJ, Carrica PM, Drew DA, Lahey RT Jr (2008) A sub-grid air entrainment model for breaking bow waves and naval surface ships. Comput Fluids 37:281–298

    Article  Google Scholar 

  135. Mori N, Suzuki T, Kakuno S (2007) Experimental study of air bubbles and turbulence characteristics in the surf zone. J Geophys Res 112:C05014. doi:10.1029/2006JC003647

    Google Scholar 

  136. Mori N, Kakuno S (2008) Aeration and bubble measurements of coastal breaking waves. Fluid Dyn Res 40:616–626

    Article  Google Scholar 

  137. Mossa M, Tolve U (1998) Flow visualization in bubbly two-phase hydraulic jump. J Fluids Eng, ASME 120:160–165

    Article  Google Scholar 

  138. Mouaze D, Chanson H, Simon B (2010) Field measurements in the tidal bore of the Sélune River in the Bay of Mont Saint Michel (September 2010). Hydraulic Model Report No. CH81/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia

  139. Murzyn F, Chanson H (2009) Free-surface fluctuations in hydraulic jumps: experimental observations. Exp Thermal Fluid Sci 33(7):1055–1064. doi:10.1016/j.expthermflusci.2009.06.003

    Article  Google Scholar 

  140. Murzyn F, Mouaze D, Chaplin JR (2005) Optical fibre probe measurements of bubbly flow in hydraulic jumps. Intl J Multiph Flow 31(1):141–154

    Article  Google Scholar 

  141. Musumeci RE, Svendsen IA, Veeramony J (2005) The flow in the surf zone: a fully nonlinear Boussinesq-type of approach. Coast Eng 52:565–598. doi:10.1016/j.coastaleng.2005.02.007

    Article  Google Scholar 

  142. Nadaoka K, Hino M, Koyano Y (1989) Structure of the turbulent flow field under breaking waves in the surf zone. J Fluid Mech 204:359–387

    Article  Google Scholar 

  143. Oguz HN, Prosperetti A, Kolaini AR (1995) Air entrapment by a falling mass of water. J Fluid Mech 294:181–207

    Article  Google Scholar 

  144. Ohtsu, I., Yasuda, Y., and Gotoh, H. (2001). Hydraulic condition for undular-jump formations. J Hydraul Res IAHR, 39(2), 203–209. Discussion: 2002 40 (3), 379–384

  145. Okamoto T, Basco DR (2006) The relative trough Froude number for initiation of wave breaking: theory experiments and numerical model confirmation. Coast Eng 53:675–690

    Article  Google Scholar 

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

    Article  Google Scholar 

  147. Peregrine DH, Svendsen IA (1978) Spilling breakers, bores and hydraulic jumps. Proc Int Conf Coast Eng 30:540–550

    Article  Google Scholar 

  148. Prosperetti A (1988) Bubble-related ambient noise in the ocean. J Acoust Soc Am 84(3):1042–1054

    Article  Google Scholar 

  149. Rajaratnam N (1962) An experimental study of air entrainment characteristics of the hydraulic jump. J Inst Eng India 42(7):247–273

    Google Scholar 

  150. Rajaratnam, N. (1965). The Hydraulic Jump as a Wall Jet. Jl of Hyd. Div., ASCE, Vol. 91, No. HY5, pp. 107–132. Discussion: Vol. 92, No. HY3, pp. 110–123 & Vol. 93, No. HY1, pp. 74–76

  151. Rao NSL, Kobus HE (1971) Characteristics of self-aerated free-surface flows. Water and waste water/current research and practice, vol 10. Eric Schmidt Verlag, Berlin

    Google Scholar 

  152. Rapp RJ, Melville WK (1990) Laboratory measurements of deep-water breaking waves. Philos Trans R Soc Lond Ser A 331:735–800. doi:10.1098/rsta.1990.0098

    Article  Google Scholar 

  153. Resch FJ, Leutheusser HJ (1972) Le Ressaut Hydraulique: mesure de Turbulence dans la Région Diphasique. Jl La Houille Blanche 1(4):279–293 (in French)

    Article  Google Scholar 

  154. Reungoat D, Chanson H, Caplain B (2014) Sediment processes and flow reversal in the undular tidal bore of the Garonne River (France). Environ Fluid Mech 14(3):591–616. doi:10.1007/s10652-013-9319-y

    Article  Google Scholar 

  155. Reungoat D, Chanson H, Keevil CE (2015) Field Measurements of Unsteady Turbulence in a Tidal Bore: the Garonne River in October 2013. J Hydraul Res IAHR. doi:10.1080/00221686.2015.1021717

    Google Scholar 

  156. Rojas G, Loewen MR (2010) Void fraction measurements beneath plunging and spilling breaking waves. J Geophys Res 115:C08001. doi:10.1029/2009JC005614

    Article  Google Scholar 

  157. Rouse H, Siao TT, Nagaratnam S (1959) Turbulence characteristics of the hydraulic jump. Trans ASCE 124:926–950

    Google Scholar 

  158. Ryabenko, A.A. (1990). Conditions favorable to the existence of an undulating jump. Gidrotekhnicheskoe Stroitel’stvo, No. 12, pp. 29–34 (in Russian). (Translated in Hydrotechnical Construction, 1990, Plenum Publ., pp. 762–770)

  159. Russell SO, Sheehan GJ (1974) Effect of entrained air on cavitation damage. Can J Civil Eng 1:97–107

    Article  Google Scholar 

  160. Salter ME, Nilsson ED, Butcher A, Bilde M (2014) On the seawater temperature dependence of the sea spray aerosol generated by a continuous plunging jet. J Geophys Res Atmos. doi:10.1002/2013JD021376

    Google Scholar 

  161. Schäffer HA, Madsen PA, Deigaard R (1993) A Boussinesq model for waves breaking in shallow water. Coast Eng 20:185–202

    Article  Google Scholar 

  162. Shi F, Kirby JT, Ma G (2010) Modeling quiescent phase transport of air bubbles induced by breaking waves. Ocean Model 35:105–117

    Article  Google Scholar 

  163. Simpson JH, Fisher NR, Wiles P (2004) Reynolds Stress and TKE Production in an Estuary with a tidal bore. Estuar Coast Shelf Sci 60(4):619–627

    Article  Google Scholar 

  164. Stoker JJ (1957) Water waves. The mathematical theory with applications. New York, Interscience Publishers

    Google Scholar 

  165. Stokes MD, Deane GB (1999) A new optical instrument for the study of bubbles at high void fractions within breaking waves. IEEE J Ocean Eng 24(3):300–311

    Article  Google Scholar 

  166. Stokes D, Deane G, Vagle S, Farmer D (2002) Measurements of large bubbles in open-ocean whitecaps. Gas Transf Water Surf, pp. 279–284. doi:10.1029/GM127p0279

  167. Svendsen IA (1984) Wave heights and set-up in a surf zone. Coast Eng 8:303–329

    Article  Google Scholar 

  168. Svendsen IA (1984) Mass flux and undertow in a surf zone. Coast Eng 8:347–365

    Article  Google Scholar 

  169. Taylor G (1934) The formation of emulsions in definable field of flow. Proc R Soc A 146:501–523

    Article  Google Scholar 

  170. Thorpe SA (1982) On the clouds of bubbles formed by breaking wind-waves in deep water, and their role in air–sea gas transfer. Philos Trans R Soc Lond A 304:155–210. doi:10.1098/rsta.1982.0011

    Article  Google Scholar 

  171. Tissier M, Bonneton P, Marche F, Lannes D (2012) A new approach to handle wave breaking in fully non-linear Boussinesq models. Coast Eng 67:54–66

    Article  Google Scholar 

  172. Tonelli M, Petti M (2009) Hybrid finite volume-finite difference scheme for 2DH improved Boussinesq equations. Coast Eng 56:609–620

    Article  Google Scholar 

  173. Treske A. (1994). Undular bores (favre-waves) in open channels—experimental studies. J Hydraul Res, IAHR, Vol. 32, No. 3, pp. 355–370. Discussion: Vol. 33, No. 3, pp. 274–278

  174. Tricker RAR (1965) Bores, breakers waves and wakes. American Elsevier Publ. Co., New York

    Google Scholar 

  175. Vagle S, Farmer DM (1998) A comparison of four methods for bubble size and void fraction measurements. IEEE J Ocean Eng 23(3):211–222. doi:10.1109/48.701193

    Article  Google Scholar 

  176. Véron F (2015) Ocean spray. Annu Rev Fluid Mech 47:507–538. doi:10.1146/annurev-fluid-010814-014651

    Article  Google Scholar 

  177. Violeau D, Rogers BD (2016) Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future. J Hydraul Res. doi:10.1080/00221686.2015.1119209

    Google Scholar 

  178. Wang H, Chanson H (2015) Air entrainment and turbulent fluctuations in hydraulic jumps. Urban Water J 12(6):502–518. doi:10.1080/1573062X.2013.847464

    Article  Google Scholar 

  179. Wang H, Murzyn F, Chanson H (2014) Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps. Exp Fluids 55(11):1–16. doi:10.1007/s00348-014-1847-9

    Article  Google Scholar 

  180. Wang H, Murzyn F, Chanson H (2015) Interaction between free-surface, two-phase flow and total pressure in hydraulic jump. Exp Thermal Fluid Sci 64:30–41. doi:10.1016/j.expthermflusci.2015.02.003

    Article  Google Scholar 

  181. Wang P, Yao Y, Tulin MP (1995) An efficient numerical tank for non-linear water waves, based on the multi-subdomain approach with BEM. Int J Numer Methods Fluids 20(12):1315–1336

    Article  Google Scholar 

  182. Wanninkhof R, Asher WE, Ho DT, Sweeney C, McGillis WR (2009) Advances in quantifying air–sea gas exchange and environmental forcing. Annu Rev Fluid Mech 1:213–244

    Google Scholar 

  183. Wolanski E, Williams D, Spagnol S, Chanson H (2004) Undular tidal bore dynamics in the Daly Estuary, Northern Australia. Estuar Coast Shelf Sci 60(4):629–636

    Article  Google Scholar 

  184. Wood IR (1991) Air entrainment in free-surface flows. IAHR hydraulic structures design manual No. 4, hydraulic design considerations. Balkema Publ, Rotterdam

    Google Scholar 

  185. Zhang G, Wang H, Chanson H (2013) Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements. Environ Fluid Mech 13(2):189–204. doi:10.1007/s10652-012-9254-3

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank their students, former students and co-workers for their work and input. The financial support of the Australian Research Council (Grant DP120100481) is acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pierre Lubin.

Appendices

Appendix 1

See Table 4.

Table 4 Breaking waves, bores, surges and jumps: flow analogies in the literature

Appendix 2: Basic momentum and energy considerations for bores and jumps

A bore is an abrupt rise in water depth (Fig. 1) and its front may be analysed as a hydraulic jump in translation [41, 118, 174]. In a system of reference in translation with the bore front, the integral form of the continuity and momentum equations gives a relationship between the cross-section area upstream and downstream of the roller, A1 and A2 respectively, and the upstream Froude number Fr1 [114]

$${Fr_{1}^{2} = \frac{ 1}{ 2} \times \frac{{A_{ 2} }}{{A_{ 1} }} \times \frac{{B_{ 1} }}{B} \times \left( {\left( { 2- \frac{B'}{B}} \right) + \frac{B'}{B} \times \frac{{A_{ 2} }}{{A_{ 1} }}} \right) + \frac{{A_{ 2} }}{{A_{ 2} - A_{ 1} }} \times \frac{{F_{\text{fric}} - W \times { \sin }\theta }}{{\rho \times g \times \frac{{A_{1}^{2} }}{B}}}}$$
(9)

where Fr1 is the bore Froude number: Fr = (U + V1)/(g × A1/B1)1/2, V is the cross-sectional averaged velocity positive downstream as shown in Fig. 1, U is the bore celerity positive upstream, the channel cross-sectional area A measured perpendicular to the flow direction, ρ is the water density, g is the gravity acceleration, Ffric is the friction force, W is the weight force, θ the angle between the bed slope and horizontal, and the subscripts 1 and 2 refer to the flow conditions immediately before and after the bore roller respectively (Fig. 1). In Eq. (9), B and B′ are characteristic widths functions of the bathymetry:

$${\text{B}} = \frac{{{\text{A}}_{2} - {\text{A}}_{1} }}{{{\text{d}}_{2} - {\text{d}}_{1} }}$$
(10)
$$B^{\prime} = \frac{{\int\limits_{{A_{1} }}^{{A_{2} }} {\int {\rho \times g \times \left( {d_{2} - z} \right) \times dA} } }}{{\frac{1}{2} \times \rho \times g \times \left( {d_{2} - d_{1} } \right)^{2} }}$$
(11)

with d the flow depth (Fig. 1b). For a smooth rectangular horizontal channel, Eq. (9) yields to the Bélanger equation:

$$\frac{{{\text{d}}_{2} }}{{{\text{d}}_{1} }} = \frac{1}{2} \times \left( {\sqrt {1 + 8 \times {\text{Fr}}_{1}^{2} } - 1} \right)\;\;{\text{Smooth }}\;{\text{horizontal }}\;{\text{rectangular }}\;{\text{channel}}$$
(12)

where d1 and d2 are respectively the upstream and downstream flow depth, and Fr1 simplifies into: Fr1 = (U + V1)/(g × d1)1/2 (Fig. 1). First presented in 1841 [12, 36], Eq. (12) is inappropriate in an irregular channel [41]. The roller height hr is in first approximation: hr = d2 − d1 and Eq. (12) may rewritten as:

$${\text{Fr}}_{1}^{2} = \frac{1}{2} \times \left( {\frac{{{\text{d}}_{2} - {\text{d}}_{1} }}{{{\text{d}}_{1} }}} \right)^{2} + \frac{3}{2}\frac{{{\text{d}}_{2} - {\text{d}}_{1} }}{{{\text{d}}_{1} }}\;{\text{Smooth}}\;{\text{ horizontal }}\;{\text{rectangular}}\;{\text{ channel}}$$
(13)

Note that the above development (Eq. 9, 12 and 13) assumes implicitly that the bore celerity is uniform and the roller shape two-dimensional. Field and laboratory observations suggested that these assumptions are simplistic [114].

The application of the energy principle across the bore roller gives an expression of the energy dissipation [4, 21]:

$$\Delta {\text{E}} = {\text{d}}_{1} + \frac{{\left( {{\text{V}}_{1} + {\text{U}}} \right)^{2} }}{{{\text{2}} \times {\text{g}}}} - \left( {{\text{d}}_{{\text{2}}} {\text{ + }}\frac{{\left( {{\text{V}}_{{\text{2}}} {\text{ + U}}} \right)^{{\text{2}}} }}{{{\text{2}} \times {\text{g}}}}} \right)$$
(14)

assuming hydrostatic pressure upstream and downstream. For a smooth horizontal rectangular channel, the rate of energy dissipation becomes [5]:

$$\frac{{\Delta {\text{E}}}}{{{\text{E}}_{1} }} = \frac{{\left( {\sqrt {1 + 8 \times {\text{Fr}}_{1}^{2} } - 3} \right)^{3} }}{{16 \times \left( {\sqrt {1 + 8 \times {\text{Fr}}_{1}^{2} } - 1} \right) \times \left( {1 + \frac{1}{2} \times {\text{Fr}}_{1}^{2} } \right)}}$$
(15)

where E1 = d1 + (V1 + U)2/(2 × g). The rate of energy dissipation ranges from 0 for Fr1 = 1 to more than 70 % for Fr1 > 9 [32, 88]. The power dissipated in the bore is:

$${P_{d} = \rho \times g \times \left( {V_{ 1} + U} \right) \times d_{ 1} \times L \times {{\Delta }}E}$$
(16)

where L is the transverse length of the bore roller.In the above equations, the solution for a stationary hydraulic jump is obtained for U = 0.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lubin, P., Chanson, H. Are breaking waves, bores, surges and jumps the same flow?. Environ Fluid Mech 17, 47–77 (2017). https://doi.org/10.1007/s10652-016-9475-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-016-9475-y

Keywords

Navigation