Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T08:42:12.679Z Has data issue: false hasContentIssue false
  • English
  • Français

Violent breaking wave impacts. Part 3. Effects of scale and aeration

Published online by Cambridge University Press:  16 January 2015

H. Bredmose ,
G. N. Bullock  and
A. J. Hogg
H. Bredmose*
Affiliation:
DTU Wind Energy, Nils Koppels Allé Building 403, DK-2800 Kgs. Lyngby, Denmark
G. N. Bullock
Affiliation:
School of Marine Science and Engineering, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK
A. J. Hogg
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of scale and aeration on violent breaking wave impacts with trapped and entrained air are investigated both analytically and numerically. By dimensional analysis we show that the impact pressures for Froude scaled conditions prior to the impact depend on the scale and aeration level. The Bagnold–Mitsuyasu scaling law for the compression of an air pocket by a piston of incompressible water is rederived and generalised to 3D air pockets of arbitrary shape. Numerical results for wall pressure, force and impulse are then presented for a flip-through impact, a low-aeration impact and a high-aeration impact, for nine scales and five levels of initial aeration. Two of these impact types trap a pocket of air at the wall. Among the findings of the paper is that for fixed initial aeration, impact pressures from the flip-through impact broadly follow Froude scaling. This is also the case for the two impact types with trapped air pockets for impact pressures below 318 kPa, while impact pressures above this value broadly follow the Bagnold–Mitsuyasu scaling law with full-scale pressures greater than those predicted by the Froude law. For all impact types, the effect of aeration is found to reduce the maximum impact pressure, maximum force and impulse. Good agreement with the asymptotic model of Peregrine & Thais (J. Fluid Mech., vol. 325, 1996, pp. 377–397) is found for the flip-through impact pressure and a fair agreement is found for the low- and high-aeration impacts. Based on the numerical results, a modified scaling curve that combines Froude scaling and the Bagnold–Mitsuyasu law is suggested. The practical implications of the findings are discussed and attention is drawn to the limitations of physical model tests.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 765 , 25 February 2015 , pp. 82 - 113
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrahamsen, B. C. & Faltinsen, O. M. 2011 The effect of air leakage and heat exchange on the decay of entrapped air pocket slamming oscillations. Phys. Fluids 23, 102107.CrossRefGoogle Scholar
Abrahamsen, B. C. & Faltinsen, O. M. 2012 The natural frequency of the pressure oscillations inside a water-wave entrapped air pocket on a rigid wall. J. Fluids Struct. 35, 200–212.CrossRefGoogle Scholar
Abrahamsen, B. C. & Faltinsen, O. M. 2013 Scaling of entrapped gas pocket slamming events at dissimilar Euler number. J. Fluids Struct. 40, 246–256.CrossRefGoogle Scholar
Bagnold, R. A. 1939 Interim report on wave-pressure research. Proc. Inst. Civ. Engrs 12, 201–226.Google Scholar
Blackmore, P. A. & Hewson, P. J. 1984 Experiments on full-scale wave impact pressures. Coast. Engng 8, 331–346.CrossRefGoogle Scholar
Blenkinsopp, C. E. & Chaplin, J. R.2007a Validity of small-scale physical models involving breaking waves. In Proceedings of the 22nd International Workshop on Water Waves and Floating Bodies, Plitvice, Croatia. IWWWFB.Google Scholar
Blenkinsopp, C. E. & Chaplin, J. R. 2007b Void fraction measurements in breaking waves. Proc. R. Soc. Lond. A 463 (2088), 3151–3170.Google Scholar
Blenkinsopp, C. & Chaplin, J. R. 2011 Void fraction measurements and scale effects in breaking waves in fresh water and sea water. Coast. Engng 58 (5), 417–428.CrossRefGoogle Scholar
Bogaert, H., Kaminski, M. L., Léonard, S. & Brosset, L.2010 Sloshing and scaling: results from the Sloshel project. In Proceedings of the 20th International Offshore and Polar Engineering Conference, Beijing, China, June 2010, pp. 88–97. ISOPE.Google Scholar
Braeunig, J.-P., Braeunig, J.-P., Brosset, L., Dias, F. & Ghidaglia, J.-M.2009 Phenomenological study of liquid impacts through 2D compressible two-fluid numerical simulations. In Proceedings of the International Offshore and Polar Engineering Conference, pp. 21–29. ISOPE.Google Scholar
Bredmose, H. & Bullock, G. N.2008 Scaling of wave impact pressures in trapped air pockets. In Proceedings of the 23rd International Workshop on Water Waves and Floating Bodies, Jeju, Korea. IWWWFB.Google Scholar
Bredmose, H., Hunt-Raby, A., Jayaratne, R. & Bullock, G. N. 2010 The ideal flip-through impact: experimental and numerical investigation. J. Engng Maths 67, 115–136, special commemorative volume for Howell Peregrine.CrossRefGoogle Scholar
Bredmose, H., Peregrine, D. H. & Bullock, G. N. 2009 Violent breaking wave impacts. Part 2. Modelling the effect of air. J. Fluid Mech. 641, 389–430.CrossRefGoogle Scholar
Brosset, L., Mravak, Z., Kaminski, M., Collins, S. & Finnigan, T.2009 Overview of Sloshel project. In Proceedings of the 19th International Offshore and Polar Engineering Conference, Osaka, Japan, June 2009, pp. 115–124. ISOPE.Google Scholar
Bullock, G. & Bredmose, H.2010 Breaking wave impacts on coastal structures. In Proceedings of the 5th Annual Conference on Advances in Computing and Technology, 27th January, School of Computing, Information Technology and Engineering, University of East London, pp. 17–26.Google Scholar
Bullock, G., Obhrai, C., Müller, G., Wolters, G., Peregrine, D. H. & Bredmose, H. 2003 Field and laboratory measurements of wave impacts. In Proceedings of the 3rd Coastal Structures Conference, ASCE.Google Scholar
Bullock, G. N., Crawford, A. R., Hewson, P. J., Walkden, M. J. A. & Bird, P. A. D. 2001 The influence of air and scale on wave impact pressures. Coast. Engng 42, 291–312.CrossRefGoogle Scholar
Bullock, G. N., Obhrai, C., Peregrine, D. H. & Bredmose, H. 2007 Violent breaking wave impacts. Part I. Results from large scale regular wave tests on vertical and sloping walls. Coast. Engng 54 (8), 602–617.CrossRefGoogle Scholar
Chan, E. S. & Melville, W. K. 1988 Deep-water plunging wave pressures on a vertical plane wall. Proc. R. Soc. Lond. A 417, 95–131.Google Scholar
Cooker, M. J. 2002 Liquid impact, kinetic energy loss and compressibility: Lagrangian, Eulerian and acoustic viewpoints. J. Engng Maths 44, 259–276.CrossRefGoogle Scholar
Cooker, M. J. & Peregrine, D. H. 1990 Computation of violent wave motion due to waves breaking against a wall. In Proceedings of the 22nd International Conference on Coastal Engineering, pp. 164–176. ASCE.Google Scholar
Cooker, M. J. & Peregrine, D. H. 1991 Violent motion as near-breaking waves meet a vertical wall. In Breaking Waves, IUTAM Symp., Sydney 1990 (ed. Banner, M. L. & Grimshaw, R. H. J.), pp. 291–297. IUTAM, Springer.Google Scholar
Cooker, M. J., Vidal, C., Dold, J. W. & Peregrine, D. H. 1990 The interaction between a solitary wave and a submerged semicircular cylinder. J. Fluid Mech. 215, 1–22.CrossRefGoogle Scholar
Cuomo, G., Allsop, W., Bruce, T. & Pearson, J. 2010a Breaking wave loads at vertical sea walls and breakwaters. Coast. Engng 57, 424–439.CrossRefGoogle Scholar
Cuomo, G., Allsop, W. & Takahashi, S. 2010b Scaling wave impact pressures on vertical walls. Coast. Engng 57, 604–609.CrossRefGoogle Scholar
Cuomo, G., Shimosako, K. & Takahashi, S. 2009 Wave-in-deck loads on coastal bridges and the role of air. Coast. Engng 56, 793–809.CrossRefGoogle Scholar
Deane, G. B. & Stokes, M. D. 2002 Scale dependence of bubble creation mechanisms in breaking waves. Nature 418 (6900), 839–844.CrossRefGoogle ScholarPubMed
Dold, J. W. 1992 An efficient surface integral algorithm applied to unsteady gravity waves. J. Comput. Phys. 103, 90–115.CrossRefGoogle Scholar
Dold, J. W. & Peregrine, D. H. 1986 An efficient boundary-integral method for steep unsteady water waves. In Numer. Meth. for Fluid Dynamics II (ed. Morton, K. W. & Baines, M. J.), pp. 671–679. Oxford University Press.Google Scholar
Fenton, J. D. 1988 The numerical solution of steady water wave problems. Comput. Geosci. 14 (3), 357–368.CrossRefGoogle Scholar
Hattori, M., Arami, A. & Yui, T. 1994 Wave impact pressure on vertical walls under breaking waves of various types. Coast. Engng 22 (1–2), 79–114.CrossRefGoogle Scholar
Jayaratne, R., Hunt-Raby, A., Bullock, G. N. & Bredmose, H. 2008 Individual violent overtopping events: new insights. In Proceedings of the 31st Coastal Engineering Conference, ASCE.Google Scholar
Kimmoun, O., Ratouis, A. & Brosset, L.2010 Sloshing and scaling: experimental study in a wave canal at two different scales. In Proceedings of the 20th International Offshore and Polar Engineering Conference, Beijing, China, June 2010, pp. 33–43. ISOPE.Google Scholar
Korobkin, A. A. 2006 Two-dimensional problem of the impact of a vertical wall on a layer of partially aerated liquid. J. Appl. Mech. Tech. Phys. 47 (5), 643–653.CrossRefGoogle Scholar
Lafeber, W., Bogaert, H. & Brosset, L.2012 Elementary loading processes (ELP) involved in breaking wave impacts: findings from the Sloshel project. In Proceedings of the 22nd International Offshore and Polar Engineering Conference, Rhodes, Greece, June 2012, pp. 265–276. ISOPE.Google Scholar
LeVeque, R. J. 2002 Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.CrossRefGoogle Scholar
Lugni, C., Brocchini, M. & Faltinsen, O. M. 2006 Wave loads: the role of flip-through. Phys. Fluids 18, 122101.CrossRefGoogle Scholar
Lugni, C., Brocchini, M. & Faltinsen, O. M. 2010a Evolution of the air cavity in a depressurized wave impact. II. The dynamic flow field. Phys. Fluids 22, 056102.Google Scholar
Lugni, C., Miozzi, M., Brocchini, M. & Faltinsen, O. M. 2010b Evolution of the air cavity in a depressurized wave impact. I. The kinematic flow field. Phys. Fluids 22, 056101.Google Scholar
Lundgren, H.1969 Wave shock forces: an analysis of deformations and forces in the wave and the foundation. In Proceedings Symposium ‘Research on Wave Action’, Delft, The Netherlands, March 1969, vol. 2. WL Delft, Rijkswaterstaat en TU Delft.Google Scholar
Mitsuyasu, H. 1966 Shock pressure of breaking wave. In Proceedings of the 10th International Conference Coastal Engineering, Tokyo, pp. 268–283. ASCE.Google Scholar
Oumeraci, H. 1994 Review and analysis of vertical breakwater failures – lessons learned. Coast. Engng 22, 3–29.CrossRefGoogle Scholar
Peregrine, D. H., Bredmose, H., Bullock, G. N., Hunt, A. & Obhrai, C. 2006 Water wave impact on walls and the role of air. In Proceedings of the 30th International Conference on Coastal Engineering, San Diego (ed. Smith, J. M.), pp. 4494–4506. ASCE.Google Scholar
Peregrine, D. H. & Kalliadasis, S. 1996 Filling flows, cliff erosion and cleaning flows. J. Fluid Mech. 310, 365–374.CrossRefGoogle Scholar
Peregrine, D. H. & Thais, L. 1996 The effect of entrained air in violent water wave impacts. J. Fluid Mech. 325, 377–397.CrossRefGoogle Scholar
Plumerault, L.-R., Astruc, D. & Maron, P. 2012 The influence of air on the impact of a plunging breaking wave on a vertical wall using a multifluid model. Coast. Engng 62, 62–74.CrossRefGoogle Scholar
Scott, J. C. 1975 The role of salt in white-cap persistence. Deep-Sea Res. 22, 653–657.Google Scholar
Slauenwhite, D. E. & Johnson, B. D. 1999 Bubble shattering: differences in bubble formation in fresh water and seawater. J. Geophys. Res. Oceans 104 (C2), 3265–3275.CrossRefGoogle Scholar
Takahashi, S., Tanimoto, K. & Miyanaga, S. 1985 Uplift wave forces due to compression of enclosed air layer and their similitude law. Coast. Engng Japan 28, 191–206.CrossRefGoogle Scholar
Tanaka, M., Dold, J. W., Lewy, M. & Peregrine, D. H. 1987 Instability and breaking of a solitary wave. J. Fluid Mech. 135, 235–248.CrossRefGoogle Scholar
Topliss, M. E., Cooker, M. J. & Peregrine, D. H.1992 Pressure oscillations during wave impact on vertical walls. In Proceedings of the 23rd International Conference on Coastal Engineering, Venice, vol. 2, pp. 1639–1650. ASCE.Google Scholar
Wood, D., Peregrine, D. H. & Bruce, T. 2000 Wave impact on a wall using pressure–impulse theory. I: Trapped air. ASCE J. Waterway Port Coastal Ocean Engng 126 (4), 182–190.CrossRefGoogle Scholar