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Extreme run-up events on a vertical wall due to nonlinear evolution of incident wave groups

Published online by Cambridge University Press:  24 May 2016

Gal Akrish ,
Oded Rabinovitch  and
Yehuda Agnon
Gal Akrish
Affiliation:
Faculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Oded Rabinovitch
Affiliation:
Faculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Yehuda Agnon
Affiliation:
Faculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Abstract

Nonlinear evolution of long-crested wave groups can lead to extreme interactions with coastal and marine structures. In the present study the role of nonlinear evolution in the formation of extreme run-up events on a vertical wall is investigated. To this end, the fundamental problem of interaction between non-breaking water waves and a vertical wall over constant water depth is considered. In order to simulate nonlinear wave–wall interactions, the high-order spectral method is applied to a computational domain which aims to represent a two-dimensional wave flume. Wave generation is simulated at the flume entrance by means of the additional potential concept. Through this concept, the implementation of a numerical wavemaker is applicable. In addition to computational efficiency, the adopted numerical approach enables one to consider the evolution of nonlinear waves while preserving full dispersivity. Utilizing these properties, the influence of the nonlinear wave evolution on the wave run-up can be examined for a wide range of water depths. In shallow water, it is known that nonlinear evolution of incident waves may result in extreme run-up events due to the formation of an undular bore. The present study reveals the influence of the nonlinear evolution on the wave run-up in deep-water conditions. The results suggest that extreme run-up events in deep water may occur as a result of the disintegration of incident wave groups into envelope solitons.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 644 - 664
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Copyright
© 2016 Cambridge University Press 

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References

Agnon, Y. & Bingham, H. B. 1999 A non-periodic spectral method with application to nonlinear water waves. Eur. J. Mech. (B/Fluids) 18, 527–534.CrossRefGoogle Scholar
Bai, W. & Taylor, R. E. 2007 Numerical simulation of fully nonlinear regular and focused wave diffraction around a vertical cylinder using domain decomposition. Appl. Ocean Res. 29, 55–71.CrossRefGoogle Scholar
Benjamin, T. B. & Feir, J. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 417–430.Google Scholar
Bonnefoy, F., Le Touzé, D. & Ferrant, P. 2006 A fully-spectral 3D time-domain model for second-order simulation of wavetank experiments. Part A: formulation, implementation and numerical properties. Appl. Ocean Res. 28, 33–43.CrossRefGoogle Scholar
Byatt-Smith, J. G. 1971 An integral equation for unsteady surface waves and a comment on the Boussinesq equation. J. Fluid Mech. 49, 625–633.Google Scholar
Carbone, F., Dutykh, D., Dudley, J. M. & Dias, F. 2013 Extreme wave runup on a vertical cliff. Geophys. Res. Lett. 40, 3138–3143.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Chen, Y., Kharif, C., Yang, J., Hsu, H., 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.CrossRefGoogle Scholar
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.Google Scholar
Cooker, M., Weidman, P. & Bale, D. 1997 Reflection of a high-amplitude solitary wave at a vertical wall. J. Fluid Mech. 342, 141–158.Google Scholar
Craig, W., Guyenne, P., Hammack, J., Henderson, D. & Sulem, C. 2006 Solitary water wave interactions. Phys. Fluids 18, 057106.Google Scholar
Dean, R. & Dalrymple, R. 1991 Water Wave Mechanics for Engineers and Scientists. (Advanced Series on Ocean Engineering) , vol. 2. World Scientific.Google Scholar
Dommermuth, D. G. & Yue, D. K. 1987 A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288.CrossRefGoogle Scholar
Dommermuth, D. G., Yue, D. K., Lin, W., Rapp, R., Chan, E. & Melville, W. 1988 Deep-water plunging breakers: a comparison between potential theory and experiments. J. Fluid Mech. 189, 423–442.Google Scholar
Dysthe, K., Krogstad, H. E. & Müller, P. 2008 Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310.CrossRefGoogle Scholar
El, G., Grimshaw, R. H. & Smyth, N. F. 2006 Unsteady undular bores in fully nonlinear shallow-water theory. Phys. Fluids 18, 027104.Google Scholar
Favre, H. 1935 Etude Théorique et Expérimentale des Ondes de Translation dans les Canaux Découverts. Dunod.Google Scholar
Ji, X., Liu, S., Li, J. & Jia, W. 2015 Experimental investigation of the interaction of multidirectional irregular waves with a large cylinder. Ocean Engng 93, 64–73.Google Scholar
Kharif, C. & Pelinovsky, E. 2003 Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. (B/Fluids) 22, 603–634.CrossRefGoogle Scholar
Li, J., Wang, Z. & Liu, S. 2012 Experimental study of interactions between multi-directional focused wave and vertical circular cylinder, part I: wave run-up. Coast. Engng 64, 151–160.Google Scholar
Li, J., Wang, Z. & Liu, S. 2014 Experimental study of interactions between multi-directional focused wave and vertical circular cylinder, part II: wave force. Coast. Engng 83, 233–242.CrossRefGoogle Scholar
Madsen, P. A., Fuhrman, D. R. & Schäffer, H. A. 2008 On the solitary wave paradigm for tsunamis. J. Geophys. Res. 113, C12012.Google Scholar
Maxworthy, T. 1976 Experiments on collisions between solitary waves. J. Fluid Mech. 76, 177–186.CrossRefGoogle Scholar
Mirchina, N. & Pelinovsky, E. 1984 Increase in the amplitude of a long wave near a vertical wall. Izv. Atmos. Ocean. Phys. 20, 252–253.Google Scholar
Nikolkina, I. & Didenkulova, I. 2011 Rogue waves in 2006–2010. Nat. Hazards Earth Syst. Sci. 11, 2913–2924.CrossRefGoogle Scholar
O’Brien, L., Dudley, J. M. & Dias, F. 2013 Extreme wave events in Ireland: 14,680 BP–2012. Nat. Hazards Earth Syst. Sci. 13, 625–648.CrossRefGoogle Scholar
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.Google Scholar
Pelinovsky, E., Kharif, C. & Talipova, T. 2008 Large-amplitude long wave interaction with a vertical wall. Eur. J. Mech. (B/Fluids) 27, 409–418.Google Scholar
Pelinovsky, E. N. & Shurgalina, E. G. 2010 Anomalous wave amplification near a vertical barrier. Fund. Appl. Hydrophys. 4 (10), 28–37.Google Scholar
Pelinovsky, E. N., Shurgalina, E. G. & Rodin, A. A. 2015 Criteria for the transition from a breaking bore to an undular bore. Izv. Atmos. Ocean. Phys. 51, 530–533.Google Scholar
Peregrine, D. 1966 Calculations of the development of an undular bore. J. Fluid Mech. 25, 321–330.Google Scholar
Power, H. & Chwang, A. T. 1984 On reflection of a planar solitary wave at a vertical wall. Wave Motion 6, 183–195.Google Scholar
Soares-Frazao, S. & Guinot, V. 2008 A second-order semi-implicit hybrid scheme for one-dimensional Boussinesq-type waves in rectangular channels. Intl J. Numer. Meth. Fluids 58, 237–261.Google Scholar
Soares Frazao, S. & Zech, Y. 2002 Undular bores and secondary waves – experiments and hybrid finite-volume modelling. J. Hydraul. Res. 40, 33–43.Google Scholar
Stoker, J. 1957 Water Waves: The Mathematical Theory with Applications. Interscience.Google Scholar
Su, C. & Mirie, R. M. 1980 On head-on collisions between two solitary waves. J. Fluid Mech. 98, 509–525.Google Scholar
Su, M. Y. 1982 Evolution of groups of gravity waves with moderate to high steepness. Phys. Fluids 25, 2167–2174.CrossRefGoogle Scholar
Tissier, M., Bonneton, P., Marche, F., Chazel, F. & Lannes, D. 2011 Nearshore dynamics of tsunami-like undular bores using a fully nonlinear Boussinesq model. J. Coast. Res. 64, 603–607.Google Scholar
Trefethen, L. N. 2000 Spectral Methods in MATLAB. SIAM.Google Scholar
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.Google Scholar
West, B. J., Brueckner, K. A., Janda, R. S., Milder, D. M. & Milton, R. L. 1987 A new numerical method for surface hydrodynamics. J. Geophys. Res. 92, 11803–11824.Google Scholar
Yuen, H. C. & Lake, B. M. 1975 Nonlinear deep water waves: theory and experiment. Phys. Fluids 18, 956–960.CrossRefGoogle Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190–194.Google Scholar
Zakharov, V. & Shabat, A. 1972 Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62–69.Google Scholar