Abstract
This study addresses the impact of nonlinear wave evolution on the resulting wave force values on a vertical wall. To this end, the problem of interaction between non-breaking water waves and a vertical wall over constant depth is investigated. The investigation is performed using a two-dimensional wave flume model which is based on the high-order spectral method. Wave generation is simulated at the flume entrance by means of the additional potential concept. This model enables to preserve full dispersivity. Therefore, the model enables to examine the role of nonlinear evolution in the formation of extreme wave force values on a vertical wall for a wide range of water depths. The results for the force exerted on a vertical wall are presented for shallow and deep water conditions. In shallow water, extreme wave force values occur due to the formation of an undular bore. In deep water, extreme wave forces have been obtained as a result of disintegration process of incident wave groups into envelope solitons. Multiple maximum force values have been detected for each of the highest run-up peaks. This phenomenon has been introduced in shallow water conditions and is extended here for deep water conditions.
Similar content being viewed by others
References
Agnon Y, Bingham HB (1999) A non-periodic spectral method with application to nonlinear water waves. Eur J Mech B Fluids 18:527–534. doi:10.1016/S0997-7546(99)80047-8
Akrish G, Rabinovitch O, Agnon Y (2016) Extreme run-up events on a vertical wall due to nonlinear evolution of incident wave groups. J Fluid Mech 797:644–664. doi:10.1017/jfm.2016.283
Benjamin TB, Feir J (1967) The disintegration of wave trains on deep water Part 1. Theory. J Fluid Mech 27:417–430. doi:10.1017/S002211206700045X
Brennan J, Viotti C, Dias F (2014) Pressure fluctuations on a vertical wall during extreme run-up cycles. ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering
Carbone F, Dutykh D, Dudley JM, Dias F (2013) Extreme wave runup on a vertical cliff. Geophys Res Lett 40:3138–3143. doi:10.1002/grl.50637
Chambarel J, Kharif C, Touboul J (2009) Head-on collision of two solitary waves and residual falling jet formation. Nonlinear Process Geophys 16:111–122
Chen YY, Kharif C, Yang JH, Hsu HC, Touboul J, Chambarel J (2015) An experimental study of steep solitary wave reflection at a vertical wall. Eur J Mech B Fluids 49:20–28. doi:10.1016/j.euromechflu.2014.07.003
Clamond D, Francius M, Grue J, Kharif C (2006) Long time interaction of envelope solitons and freak wave formations. Eur J Mech B Fluids 25:536–553. doi:10.1016/j.euromechflu.2006.02.007
Cooker M, Weidman P, Bale D (1997) Reflection of a high-amplitude solitary wave at a vertical wall. J Fluid Mech 342:141–158. doi:10.1017/S002211209700551X
Craig W, Guyenne P, Hammack J, Henderson D, Sulem C (2006) Solitary water wave interactions. Phys Fluids 18:057106. doi:10.1063/1.2205916
Dean R, Darlymple R (1991) Water wave mechanics for engineers and scientists. World Scientific, Advanced Series on Ocean Engineering 2
Dommermuth DG, Yue DK (1987) A high-order spectral method for the study of nonlinear gravity waves. J Fluid Mech 184:267–288. doi:10.1017/S002211208700288X
Ducrozet G, Bonnefoy F, Le Touze D, Ferrant P (2012) A modified high-order spectral method for wavemaker modeling in a numerical wave tank. Eur J Mech B Fluids 34:19–34. doi:10.1016/j.euromechflu.2012.01.017
Dutykh D, Clamond D (2014) Efficient computation of steady solitary gravity waves. Wave Motion 51(1):86–99. doi:10.1016/j.wavemoti.2013.06.007
Dysthe K, Krogstad HE, Muller P (2008) Oceanic rogue waves. Annu Rev Fluid Mech 40:287–310. doi:10.1146/annurev.fluid.40.111406.102203
Favre H (1935) Etude theorique et experimentale des ondes de translation dans les canaux decouverts. Dunod
Fenton JD, Rienecker MM (1982) A Fourier method for solving nonlinear water-wave problems: application to solitary–wave interactions. J Fluid Mech 118:411–443. doi:10.1017/S0022112082001141
Goda Y (1967) The fourth order approximation to the pressure of standing waves. Coast Eng Jpn 10:1–11
Grilli S, Svendsen IA (1990) Computation of nonlinear wave kinematics during propagation and runup on a slope. Water Wave Kinemat 178:387–412. doi:10.1007/978-94-009-0531-3_24
Gurevich AV, Pitaevskii LP (1974) Nonstationary structure of a collisionless shock wave. Sov Phys JETP 38:291–297
Kharif C, Pelinovsky E (2003) Physical mechanisms of the rogue wave phenomenon. Eur J Mech B Fluids 22:603–634. doi:10.1016/j.euromechflu.2003.09.002
Longuet-Higgins MS, Drazen DA (2002) On steep gravity waves meeting a vertical wall: a triple instability. J Fluid Mech 466:305–318. doi:10.1017/S0022112002001246
Madsen PA, Bingham HB, Liu H (2002) A new Boussinesq method for fully nonlinear waves from shallow to deep water. J Fluid Mech 462:1–30. doi:10.1017/S0022112002008467
Madsen PA, Fuhrman DR, Schaffer HA (2008) On the solitary wave paradigm for tsunamis. J Geophys Res Oceans 113. doi:10.1029/2008JC004932
Nikolkina I, Didenkulova I (2011) Rogue waves in 2006-2010. Nat Hazards Earth Syst Sci 11:2913–2924. doi:10.5194/nhess-11-2913-2011
O’Brien L, Dudley JM, Dias F (2013) Extreme wave events in Ireland: 14 680 BP-2012. Nat Hazards Earth Syst Sci 13:625–648. doi:10.5194/nhess-13-625-2013
Onorato M, Residori S, Bortolozzo U, Montina A, Arecchi F (2013) Rogue waves and their generating mechanisms in different physical contexts. Phys Rep 528:47–89. doi:10.1016/j.physrep.2013.03.001
Penney WG, Price AT (1952) Part 2. Finite periodic stationary gravity waves in a perfect liquid. Philos Trans R Soc A Math Phys Eng Sci 244:254–284
Peregrine D (1966) Calculations of the development of an undular bore. J Fluid Mech 25:321–330. doi:10.1017/S0022112066001678X
Shao S (2005) SPH simulation of solitary wave interaction with a curtain-type breakwater. J Hydraul Res 43:366–375. doi:10.1080/00221680509500132
Stoker JJ (1957) Water waves: the mathematical theory with applications. Interscience Publishers, New York
Su C, Mirie RM (1980) On head-on collisions between two solitary waves. J Fluid Mech 98:509–525. doi:10.1017/S0022112080000262
Tadjbakhsh I, Keller JB (1960) Standing surface waves of finite amplitude. J Fluid Mech 3:442–451. doi:10.1017/jfm.2015.382
Touboul J, Pelinovsky E (2014) Bottom pressure distribution under a solitonic wave reflecting on a vertical wall. Eur J Mech B Fluids 48:13–18. doi:10.1016/j.euromechflu.2014.03.011
Viotti C, Carbone F, Dias F (2014) Conditions for extreme wave runup on a vertical barrier by nonlinear dispersion. J Fluid Mech 748:768–788. doi:10.1017/jfm.2014.217
West BJ, Brueckner KA, Janda RS, Milder DM, Milton RL (1987) A new numerical method for surface hydrodynamics. J Geophys Res Oceans 92:11803–11824. doi:10.1029/JC092iC11p11803
Zakharov VE (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J Appl Mech Tech Phys 9:190–194. doi:10.1007/BF00913182
Acknowledgments
This study was supported by the Israel Ministry of Science, Space and Technology, Contract No. 605404541.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Akrish, G., Schwartz, R., Rabinovitch, O. et al. Impact of extreme waves on a vertical wall. Nat Hazards 84 (Suppl 2), 637–653 (2016). https://doi.org/10.1007/s11069-016-2367-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11069-016-2367-0