Hostname: page-component-77f85d65b8-t6st2 Total loading time: 0 Render date: 2026-04-14T08:29:16.788Z Has data issue: false hasContentIssue false
  • English
  • Français

On wedge aerated water entry: experiment and theory

Published online by Cambridge University Press:  26 December 2025

Wencheng Wu Open the ORCID record for Wencheng Wu [Opens in a new window] ,
Longfei Xiao Open the ORCID record for Longfei Xiao [Opens in a new window] ,
Longbin Tao Open the ORCID record for Longbin Tao [Opens in a new window] ,
Yufeng Kou  and
Yiang Yang
Wencheng Wu
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Longfei Xiao*
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China SJTU-Sanya Yazhou Bay Institute of Deepsea Science and Technology, Sanya 572024, PR China
Longbin Tao
Affiliation:
College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, PR China
Yufeng Kou
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Yiang Yang
Affiliation:
Institute of Nuclear Science and Safety, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
Corresponding author: Longfei Xiao, xiaolf@sjtu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Pre-existing bubbles in the water play a critical role in influencing the impact pressure characteristics during the wedge water entry. This study experimentally and analytically investigates the effect of aeration on water-entry impact. A series of controlled drop tests were conducted using a wedge with a 20° deadrise angle at varying impact velocities and void fractions. Four classical pure water impact models (the Zhao & Faltinsen model (ZFM), original Logvinovich model (OLM), modified Logvinovich model (MLM) and generalised Wagner model (GWM)) were extended to account for the effect of aeration. These modifications accounted for compressibility effects, the time-dependent void fraction, three-dimensional flow corrections and area-averaged pressure calculations, resulting in four modified models (M-ZFM, M-OLM, M-MLM and M-GWM). This marks the first systematic theoretical extension of multiple classical water-entry models to aerated conditions. The proposed models demonstrated good agreement with experimental results, with the M-MLM providing accurate peak pressure predictions and M-GWM performing best in capturing the post-peak behaviours. The results indicated that the expansion velocity of the wetted surface varied spatially and closely matched the M-ZFM predictions. While the peak pressures decreased by up to 32.8 % in highly aerated water, the prolonged impact durations led to a comparable or slightly increased pressure impulse than that in pure water. This finding suggests that prolonged lower-magnitude impacts in aerated water may pose a greater risk to structural safety than short-duration high-magnitude impacts. These contributions offer new physical insight and validated tools relevant to marine engineering design in aerated environments.

JFM classification

Aerodynamics: Flow-structure interactions Multiphase and Particle-laden Flows: Multiphase flow

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1026 , 10 January 2026 , A7
Check for updates
Copyright
© The Author(s), 2025. Published by 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.)

Article purchase

Temporarily unavailable

References

Abrate, S. 2011 Hull slamming. Appl. Mech. Rev. 64 (6), 060803.10.1115/1.4023571CrossRefGoogle Scholar
Aghaei, A., Schimmels, S., Schlurmann, T. & Hildebrandt, A. 2020 Numerical investigation of the effect of aeration and hydroelasticity on impact loading and structural response for elastic plates during water entry. Ocean Engng 201, 107098.10.1016/j.oceaneng.2020.107098CrossRefGoogle Scholar
Baarholm, R. 2009 Experimental and theoretical study of three-dimensional effects on vertical wave-in-deck forces. Intl Conf. Offshore Mech. Arctic Engng 43468, 451–459.Google Scholar
Barjasteh, M., Zeraatgar, H. & Javaherian, M.J. 2016 An experimental study on water entry of asymmetric wedges. Appl. Ocean Res. 58, 292–304.10.1016/j.apor.2016.04.013CrossRefGoogle Scholar
Belden, J., Speirs, N.B., Hellum, A.M., Jones, M., Paolero, A.J. & Truscott, T.T. 2023 Water entry of cups and disks. J. Fluid Mech. 963, A14.10.1017/jfm.2023.330CrossRefGoogle Scholar
Belden, J., Speirs, N., Hellum, A., Loubimov, G. & Truscott, T.T. 2024 Water impact: when a sphere becomes flat. Phys. Rev. Lett. 133 (3), 034002.10.1103/PhysRevLett.133.034002CrossRefGoogle 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, 389–430.10.1017/S0022112009991571CrossRefGoogle Scholar
Bullock, G.N., Obhrai, C., Peregrine, D.H. & Bredmose, H. 2007 Violent breaking wave impacts. Part 1: results from large-scale regular wave tests on vertical and sloping walls. Coast. Engng 54 (8), 602–617.10.1016/j.coastaleng.2006.12.002CrossRefGoogle Scholar
Chuang, S.L. 1966 Slamming of rigid wedge-shaped bodies with various deadrise angles. Tech. Rep. No. 2268.10.21236/AD0643235CrossRefGoogle Scholar
Chuang, W.L. 2022 Experimental investigation on fluid kinematics and impact pressure of flat plate impacts on pure and aerated water. Ocean Engng 266, 112837.10.1016/j.oceaneng.2022.112837CrossRefGoogle Scholar
Cuomo, G., Shimosako, K. & Takahashi, S. 2009 Wave-in-deck loads on coastal bridges and the role of air. Coast. Engng 56 (8), 793–809.10.1016/j.coastaleng.2009.01.005CrossRefGoogle Scholar
Deane, G.B. & Stokes, M.D. 2002 Scale dependence of bubble creation mechanisms in breaking waves. Nature 418 (6900), 839–844.10.1038/nature00967CrossRefGoogle ScholarPubMed
Dias, F., Dutykh, D. & Ghidaglia, J.M. 2010 A two-fluid model for violent aerated flows. Comput. Fluids 39 (2), 283–293.10.1016/j.compfluid.2009.09.005CrossRefGoogle Scholar
Dobrovol’Skaya, Z.N. 1969 On some problems of similarity flow of fluid with a free surface. J. Fluid Mech. 36 (4), 805–829.10.1017/S0022112069001996CrossRefGoogle Scholar
Elhimer, M., El Malki Alaoui, A., Gabillet, C. & Jacques, N. 2022 Measurements of pressure during the forced water entry of a cone into pure and aerated water. J. Fluid. Struct. 113, 103605.10.1016/j.jfluidstructs.2022.103605CrossRefGoogle Scholar
Elhimer, M., Jacques, N., El Malki Alaoui, A. & Gabillet, C. 2017 The influence of aeration and compressibility on slamming loads during cone water entry. J. Fluid. Struct. 70, 24–46.10.1016/j.jfluidstructs.2016.12.012CrossRefGoogle Scholar
Ermanyuk, E.V. & Ohkusu, M. 2005 Impact of a disk on shallow water. J. Fluid. Struct. 20 (3), 345–357.10.1016/j.jfluidstructs.2004.10.002CrossRefGoogle Scholar
Fan, Y., Jain, U. & Van Der Meer, D. 2024 Air-cushioning below an impacting wave-structured disk: free-surface deformation and slamming load. Phys. Rev. Fluids 9 (1), 010501.10.1103/PhysRevFluids.9.010501CrossRefGoogle Scholar
Guo, Y., Xiao, L., Teng, X., Kou, Y. & Liu, J. 2020 Processing method and governing parameters for horizontal wave impact loads on a semi-submersible. Mar. Struct. 69, 102673.10.1016/j.marstruc.2019.102673CrossRefGoogle Scholar
Han, B., Li, H., Zhang, B., Zou, J. & Zhao, W. 2024 Experimental investigation of slamming characteristics of stiffened elastic wedges with different deadrise angles: Part I–Slamming pressure. Ocean Engng 303, 117728.10.1016/j.oceaneng.2024.117728CrossRefGoogle Scholar
Hong, Y., Wang, B. & Liu, H. 2021 Experimental and numerical study on hydrodynamic impact of a disk in pure and aerated water. Proc. Inst. Mech. Engng M 235 (1), 152–164.Google Scholar
Iafrati, A. 2016 Experimental investigation of the water entry of a rectangular plate at high horizontal velocity. J. Fluid Mech. 799, 637–672.10.1017/jfm.2016.374CrossRefGoogle Scholar
Jain, U., Gauthier, A.F., Lohse, D. & van der Meer, D. 2021 Air-cushioning effect and Kelvin–Helmholtz instability before the slamming of a disk on water. Phys. Rev. Fluids 6 (4), L042001.10.1103/PhysRevFluids.6.L042001CrossRefGoogle Scholar
Jain, U., Novaković, V., Bogaert, H. & van der Meer, D. 2022 On wedge-slamming pressures. J. Fluid Mech. 934, A27.10.1017/jfm.2021.1129CrossRefGoogle Scholar
von Karman, T. 1929 The impact on sea plane floats during landing. Tech. Rep. No. NACA-TN-321. Aerodynamical Institute 776 of the Technical High School, Aachen, 1929.Google Scholar
Khabakhpasheva, T.I., Korobkin, A.A. & Malenica, S. 2013 Fluid impact onto a corrugated panel with trapped gas cavity. Appl. Ocean Res. 39, 97–112.10.1016/j.apor.2012.10.005CrossRefGoogle Scholar
Korobkin, A. 2004 Analytical models of water impact. Eur. J. Appl. Math. 15 (6), 821–838.10.1017/S0956792504005765CrossRefGoogle Scholar
Korobkin, A.A. 2006 Two-dimensional problem of the impact of a vertical wall on a layer of a partially aerated liquid. J. Appl. Mech. Tech. Phys. 47, 643–653.10.1007/s10808-006-0100-6CrossRefGoogle Scholar
Lin, M.C. & Shieh, L.D. 1997 Simultaneous measurements of water impact on a two-dimensional body. Fluid Dyn. Res. 19 (3), 125.10.1016/S0169-5983(96)00033-0CrossRefGoogle Scholar
Logvinovich, G.V. 1972 Hydrodynamics of Free-Boundary Flows [M]. Israel Program for Scientific Translations.Google Scholar
Lu, W., Wu, X. & Zha, R. 2024 Numerical study on the motion characteristics of free fall lifeboats entering calm water and rough sea. Phys. Fluids 36 (9), 097102.10.1063/5.0220575CrossRefGoogle Scholar
Ma, Z.H., Causon, D.M., Qian, L., Mingham, C.G., Mai, T., Greaves, D. & Raby, A. 2016 Pure and aerated water entry of a flat plate. Phys. Fluids 28 (1), 016104.10.1063/1.4940043CrossRefGoogle Scholar
Mai, T., Mai, C., Raby, A. & Greaves, D.M. 2019 Aeration effects on water-structure impacts: Part 1. Drop plate impacts. Ocean Engng 193, 106600.10.1016/j.oceaneng.2019.106600CrossRefGoogle Scholar
Manjula, R. & Sannasiraj, S.A. 2019 Response of a slender cylindrical member under breaking wave impact. J. Hydrodyn. 31, 345–357.10.1007/s42241-019-0002-8CrossRefGoogle Scholar
Melville, W.K. 1996 The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech. 28, 279–321.10.1146/annurev.fl.28.010196.001431CrossRefGoogle Scholar
Miller, S.T., Jasak, H., Boger, D.A., Paterson, E.G. & Nedungadi, A. 2013 A pressure-based, compressible, two-phase flow finite volume method for underwater explosions. Comput. Fluids 87, 132–143.10.1016/j.compfluid.2013.04.002CrossRefGoogle Scholar
Peregrine, D.H. & Thais, L. 1996 The effect of entrained air in violent water wave impacts. J. Fluid Mech. 325, 377–397.10.1017/S0022112096008166CrossRefGoogle Scholar
Peters, I.R., van der Meer, D. & Gordillo, J.M. 2013 Splash wave and crown breakup after disc impact on a liquid surface. J. Fluid Mech. 724, 553–580.10.1017/jfm.2013.160CrossRefGoogle Scholar
Plumerault, L.-R., Astruc, D., Villedieu, P. & Maron, P. 2012 A numerical model for aerated-water wave breaking. Intl J. Numer. Meth. Fluids 69 (12), 1851–1871.10.1002/fld.2667CrossRefGoogle Scholar
Pumphrey, H.C. & Elmore, P.A. 1990 The entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539–567.10.1017/S0022112090003378CrossRefGoogle Scholar
Saurel, R. & Abgrall, R. 1999 A simple method for compressible multifluid flows. SIAM J. Sci. Comput. 21 (3), 1115–1145.10.1137/S1064827597323749CrossRefGoogle Scholar
Semenov, Y.A. & Iafrati, A. 2006 On the nonlinear water entry problem of asymmetric wedges. J. Fluid Mech. 547, 231–256.10.1017/S0022112005007329CrossRefGoogle Scholar
Shan, M., Xiao, L., Kou, Y., Wu, W. & Li, K. 2025 Wave run-up and secondary load cycle on a rounded square column in focused waves. Phys. Fluids 37 (2), 023369.10.1063/5.0254550CrossRefGoogle Scholar
Silberman, E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29 (8), 925–933.10.1121/1.1909101CrossRefGoogle Scholar
Tassin, A., Jacques, N., El Malki Alaoui, A., Nême, A. & Leblé, B. 2010 Assessment and comparison of several analytical models of water impact. Intl J. Multiphys. 4 (2), 125–140.10.1260/1750-9548.4.2.125CrossRefGoogle Scholar
Verhagen, J.H.G. 1967 The impact of a flat plate on a water surface. J. Ship Res. 11 (04), 211–223.10.5957/jsr.1967.11.4.211CrossRefGoogle Scholar
Wagner, H. 1932 Über stoß-und gleitvorgänge an der oberfläche von flüssigkeiten. ZAMM 12 (4), 193–215.10.1002/zamm.19320120402CrossRefGoogle Scholar
Wang, J. & Faltinsen, O. 2017 Improved numerical solution of Dobrovol’skaya’s boundary integral equations on similarity flow for uniform symmetrical entry of wedges. Appl. Ocean Res. 66, 23–31.10.1016/j.apor.2017.05.006CrossRefGoogle Scholar
Wen, X., Qu, Q., Liu, P. & Hu, T. 2024 A general solution for the water entry of an arbitrary curved wedge. Ships Offshore Struc. 1–17. https://www.tandfonline.com/doi/full/10.1080/17445302.2024.2403182Google Scholar
Wu, J. 2000 Bubbles produced by breaking waves in fresh and salt waters. J. Phys. Oceanogr. 30 (7), 1809–1813.10.1175/1520-0485(2000)030<1809:BPBBWI>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Wu, W., Liu, M., Xiao, L., Shan, M., Kou, Y., Li, K. & Guo, J. 2024 Experimental study of wave impact pressure impulse and characteristic pressure on the fixed four-rounded-square-column array in focused waves. Ocean Engng 311, 118829.10.1016/j.oceaneng.2024.118829CrossRefGoogle Scholar
Wu, W., Xiao, L., Kou, Y. & Liu, M. 2025 Research on impact pressures in aerated water entry of a symmetrical wedge. J. Fluid Mech. 1010, A4.10.1017/jfm.2025.280CrossRefGoogle Scholar
Yamamoto, Y., Ohtsubo, H. & Kohno, Y. 1984 Water impact of wedge model. J. Soc. Naval Arch. Japan 1984 (155), 236–245.10.2534/jjasnaoe1968.1984.236CrossRefGoogle Scholar
Yettou, E.M., Desrochers, A. & Champoux, Y. 2006 Experimental study on the water impact of a symmetrical wedge. Fluid Dyn. Res. 38 (1), 47.10.1016/j.fluiddyn.2005.09.003CrossRefGoogle Scholar
Yettou, E.M., Desrochers, A. & Champoux, Y. 2007 A new analytical model for pressure estimation of symmetrical water impact of a rigid wedge at variable velocities. J. Fluid. Struct. 23 (3), 501–522.10.1016/j.jfluidstructs.2006.10.001CrossRefGoogle Scholar
Zhang, N., Xiao, L., Cheng, Z., Wei, H. & Chen, G. 2024 Classification of breaking wave impact loads on a fixed surface-piercing square column with an overhanging deck. Coast. Engng 193, 104570.10.1016/j.coastaleng.2024.104570CrossRefGoogle Scholar
Zhao, R. & Faltinsen, O. 1993 Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612.10.1017/S002211209300028XCrossRefGoogle Scholar