Cyril Mokrani, Stephane Abadie


Impulsive loads are difficult to predict due to the extremely non linear response to incident wave conditions. This behavior is related to air dynamics and local wave shape. The present study focuses on the latter.We propose a new method to predict pressure peaks generated during breaking wave impacts. In this method, the plunging jet is assimilated to two equivalent triangular jets (wedge impact) with variable inclination in time. The basic case of wedge impact is first studied in the paper. Semi empirical laws relating pressure peak and incident angle are derived based on numerical results obtained with a Navier-Stokes model . The more general case of a breaking wave is then investigated. By making an analogy with the wedge impact case and inverting the relation obtained before, we computed the location where the equivalent angles have to be taken on the free surface. We show that these points correspond to the minimum curvature section on the free surface. In another simulation of a breaking wave, we finally show how the relation can be applied to give a first approximation of the pressure peak only based on the free surface local shape.


vertical break-water; pressure peak; breaking wave; wedge; impact


S. Abadie and C. Mokrani. On the influence of breaking wave local geometry on impulsive loads. Proceeding of the International Offshore and Polar Engineering Conference, 2012.

S. Abadie, J.P. Caltagirone, and P. Watremez. Splash-up generation in a plunging breaker. Computational fluid mechanics, S´erie II.b:553–559, 1998.

M.J. Cooker and D.H. Peregrine. Pressure-impulse theory for liquid impact problems. J. Fluid Mech., 297: 193–214, 1995.http://dx.doi.org/10.1017/S0022112095003053

E. Cumberbatch. The impact of a water wedge of a wall. J. Fluid Mech, 7:353–374, 1960.http://dx.doi.org/10.1017/S002211206000013X

Z.N. Dobrovol'skaya. On some problems of similarity flow of fluid with a free surface. J. Fluid Mech, 36:805–529, 1969.http://dx.doi.org/10.1017/S0022112069001996

M. Greco. A Two Dimensional Study of Green-Water Loading. PhD thesis, Faculty of Marine Technology, Trondheim, 2001.

S.T. Grilli, I.A. Svendsen, and R. Subramanya. Breaking criterion and characteristics for solitary waves on slopes. Journal Of Waterway, Port, Coastal and Ocean Engineering, 123(3):102–112, 1997.http://dx.doi.org/10.1061/(ASCE)0733-950X(1997)123:3(102)

P. Hull and G. Muller. An investigation of breaker heights, shapes and pressures. Ocean Engineering, 29:59–79, 2002.http://dx.doi.org/10.1016/S0029-8018(00)00075-5

P. Lubin, S. Vincent, S. Abadie, and J.P. Caltagirone. Three dimensional large eddy simulation of air entrainment under plunging breaking waves. Coastal engineering, 53:631–655, 2006.http://dx.doi.org/10.1016/j.coastaleng.2006.01.001

C. Lugni, M. Brocchini, and O.M. Faltinsen. Wave impact loads : The role of the flip-through. Physics of Fluids, 18:122101–122118, 2006.http://dx.doi.org/10.1063/1.2399077

C. Mokrani. Impact de vagues d’eferlantes sur un obstacle vertical. Mod`ele th’eorique et calcul num’erique des pics de pression. PhD thesis, Universit’e de Pau et des Pays de l'Adour, 2012.

S. Nagai. Wave forces on structures, academic press, new york. Advances in Hydroscience, 9:253–324, 1973.

G. Pianet, S. Vincent, J. Leboi, J.P. Caltagirone, and M. Anderhuber. Simulating compressible gas bubbles with a smooth volume tracking. International Journal of Multiphase Flow, 36:273–283, 2010.http://dx.doi.org/10.1016/j.ijmultiphaseflow.2009.12.002

A.F. Whillock. Measurements of forces resulting from normal and oblique wave approaches to small scale sea walls. Coastal Engineering, 11:297–308, 1987.http://dx.doi.org/10.1016/0378-3839(87)90030-5

G.X. Wu. Fluid impact on a solid boundary. Journal of Fluids ans Structures, 23:755–765, 2007.

D.L. Yougs, K.W. Morton, and M.J. Baines. Time-dependent multimaterial flow with large fluid distorsion. Numerical methods for fluids dynamics, Academic Press, New York, 1982.

S. Zhang, D.K.P. Yue, and K. Tanizawa. Simulation of plunging wave impact on a vertical wall. J. Fluid Mech, 327:221–254, 1996.http://dx.doi.org/10.1017/S002211209600852X

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.