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Amplification of random wave run-up on the front face of a box driven by tertiary wave interactions

Published online by Cambridge University Press:  02 May 2019

W. Zhao*
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
P. H. Taylor
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
H. A. Wolgamot
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
R. Eatock Taylor
Affiliation:
Department of Engineering Science, University of Oxford, OxfordOX1 3PJ, UK
*
Email address for correspondence: wenhua.zhao@uwa.edu.au

Abstract

Wave run-up phenomena driven by nonlinear wave interactions with a fixed rectangular box are investigated. Experiments are carried out in different types of uni-directional waves with normal incidence. Significant wave run-ups featuring tertiary interaction effects, similar to those reported by Molin et al. (J. Fluid Mech., vol. 528, 2005, pp. 323–354) for a fixed vertical plate, are observed in regular wave tests. Transient wave group tests are conducted for comparison, to facilitate the analysis of the tertiary interactions in irregular waves. The most striking observation is that the wave surface elevations at the centre of the front face of the fixed box can reach $4\times$ the incident waves even in irregular waves, much larger than the ${\sim}2\times$ predicted from linear theory and observed for the transient groups. The extra amplification builds up slowly and is localized on the weather side of the box. It is believed to result from tertiary interactions between the incident and reflected wave fields upstream, which induce a local lensing effect and thus wave focusing on the weather side. These interactions, though a nonlinear process, occur at the first harmonic quantities rather than high harmonics. Supporting evidence is extracted from random wave runs using NewWave analysis, where surface amplifications and phase lag – both key characteristics of tertiary wave interactions – are identified. The identification of these tertiary interactions in irregular waves is new, and may be of practical importance.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Bingham, H. B., Fuhrman, D. R., Jamois, E. & Kimmoun, O. 2004 Nonlinear wave interaction with bottom-mounted structures by a high-order Boussinesq method. In Proceedings of the 18th International Workshop on Water Waves and Floating Bodies, March 28–31, Cortona, Italy, http://www.iwwwfb.org/Abstracts/iwwwfb19/iwwwfb19_03.pdf.Google Scholar
Boccotti, P. 1983 Some new results on statistical properties of wind waves. Appl. Ocean Res. 5 (3), 134140.CrossRefGoogle Scholar
Faltinsen, O. M., Newman, J. N. & Vinje, T. 1995 Nonlinear wave loads on a slender vertical cylinder. J. Fluid Mech. 289, 179198.CrossRefGoogle Scholar
Fitzgerald, C. J., Taylor, P. H., Eatock Taylor, R., Grice, J. & Zang, J. 2014 Phase manipulation and the harmonic components of ringing forces on a surface-piercing column. Proc. R. Soc. Lond. A 470 (2168), 20130847.CrossRefGoogle Scholar
Grice, J. R., Taylor, P. H. & Eatock Taylor, R. 2013 Near-trapping effects for multi-column structures in deterministic and random waves. Ocean Engng 58, 6077.CrossRefGoogle Scholar
Jamois, E., Fuhrman, D. R., Bingham, H. B. & Molin, B. 2006 A numerical study of nonlinear wave run-up on a vertical plate. Coast. Engng 53 (11), 929945.CrossRefGoogle Scholar
Jonathan, P. & Taylor, P. H. 1997 On irregular, nonlinear waves in a spread sea. J. Offshore Mech. Arctic Engng 119 (1), 3741.CrossRefGoogle Scholar
Lindgren, G. 1970 Some properties of a normal process near a local maximum. Ann. Math. Statist. 41, 18701883.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Phillips, O. M. 1962 Phase velocity effects in tertiary wave interactions. J. Fluid Mech. 12 (3), 333336.CrossRefGoogle Scholar
Malenica, S. & Molin, B. 1995 Third-harmonic wave diffraction by a vertical cylinder. J. Fluid Mech. 302, 203229.CrossRefGoogle Scholar
Molin, B., Kimmoun, O., Liu, Y., Remy, F. & Bingham, H. B. 2010 Experimental and numerical study of the wave run-up along a vertical plate. J. Fluid Mech. 654, 363386.CrossRefGoogle Scholar
Molin, B., Kimmoun, O., Remy, F. & Chatjigeorgiou, I. K. 2014 Third-order effects in wave–body interaction. Eur. J. Mech. (B/Fluids) 47, 132144.CrossRefGoogle Scholar
Molin, B., Remy, F. & Kimmoun, O. 2007 Second-order wave interaction with a vertical plate. J. Engng Maths 58 (1–4), 109119.CrossRefGoogle Scholar
Molin, B., Remy, F., Kimmoun, O. & Ferrant, P. 2003 Third-order interactions and wave run-up. In Proceedings of the 18th International Workshop on Water Waves and Floating Bodies, April 6–9, Le Croisic, France, http://www.iwwwfb.org/Abstracts/iwwwfb18/iwwwfb18_36.pdf.Google Scholar
Molin, B., Remy, F., Kimmoun, O. & Jamois, E. 2005 The role of tertiary wave interactions in wave-body problems. J. Fluid Mech. 528, 323354.CrossRefGoogle Scholar
Ohl, C. O. G., Eatock Taylor, R., Taylor, P. H. & Borthwick, A. G. L. 2001 Water wave diffraction by a cylinder array. Part 1. Regular waves. J. Fluid Mech. 442, 132.CrossRefGoogle Scholar
Phillips, O. M. 1981 Wave interactions – the evolution of an idea. J. Fluid Mech. 106, 215227.CrossRefGoogle Scholar
Santo, H., Taylor, P. H., Moreno, E. C., Stansby, P., Eatock Taylor, R., Sun, L. & Zang, J. 2017 Extreme motion and response statistics for survival of the three-float wave energy converter M4 in intermediate water depth. J. Fluid Mech. 813, 175204.CrossRefGoogle Scholar
Sun, L., Eatock Taylor, R. & Taylor, P. H. 2015 Wave driven free surface motion in the gap between a tanker and an FLNG barge. Appl. Ocean Res. 51, 331349.CrossRefGoogle Scholar
Zhao, W., Taylor, P. H., Wolgamot, H. A. & Eatock Taylor, R. 2018a Identifying linear and nonlinear coupling between fluid sloshing in tanks, roll of a barge and external free-surface waves. J. Fluid Mech. 844, 403434.CrossRefGoogle Scholar
Zhao, W., Taylor, P. H., Wolgamot, H. A. & Eatock Taylor, R. 2018b Linear viscous damping in random wave exrefd gap resonance at laboratory scale – NewWave analysis and reciprocity. J. Fluids Struct. 80, 5976.CrossRefGoogle Scholar
Zhao, W., Wolgamot, H. A., Taylor, P. H. & Eatock Taylor, R. 2017 Gap resonance and higher harmonics driven by focused transient wave groups. J. Fluid Mech. 812, 905939.CrossRefGoogle Scholar
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