Hostname: page-component-669899f699-tzmfd Total loading time: 0 Render date: 2025-05-01T00:57:20.277Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave–bottom interaction and extreme wave statistics due to shoaling and de-shoaling of irregular long-crested wave trains over steep seabed changes

Published online by Cambridge University Press:  11 February 2021

Jie Zhang Open the ORCID record for Jie Zhang [Opens in a new window]  and
Michel Benoit Open the ORCID record for Michel Benoit [Opens in a new window]
Jie Zhang
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, Institut de Recherche sur les Phénomènes Hors-Equilibre (IRPHE, UMR 7342), 13013Marseille, France
Michel Benoit*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, Institut de Recherche sur les Phénomènes Hors-Equilibre (IRPHE, UMR 7342), 13013Marseille, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The formation of abnormal (extreme) waves in coastal areas can be triggered by wave–seabed interaction, in particular by steep bottom changes. As an incident equilibrium sea state passes over a submerged step or bar, non-equilibrium dynamics appears locally and forces the sea state to a new, finite-depth equilibrium along with strong non-Gaussian statistics and an intensified occurrence probability of large waves. In this study, the experimental case Run 3 reported by Trulsen et al. (J. Fluid Mech., vol. 882, 2020, R2) has been investigated numerically with a fully nonlinear model. Furthermore, as both shoaling and de-shoaling effects exist in the set-up with a bar-profile bottom, an additional simulation with a step-profile bottom is performed to isolate the de-shoaling effects. The model is proven excellent by the confrontation of the measurements and simulated results in both time and spectral domains. Strong non-Gaussian behaviour of the sea state is highlighted after the up-slope transition by combining spectral and bi-spectral analyses, and characteristic parameters. With a harmonic extraction approach, we show evidence that both second- and third-order effects triggered by the non-equilibrium dynamics significantly enhance the local kurtosis and occurrence of extreme waves. The statistics of kinematics shows the asymmetry of the wave field evolves somewhat independently in the horizontal and vertical directions. By comparing the simulations of bar- and step-profile cases, we find the de-shoaling process is responsible for the upstream modulation of nonlinear and dispersive parameters, and the enhancement of kurtosis of both horizontal and vertical velocities and horizontal acceleration over the down-slope area.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: Coastal engineering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A28
Copyright
© The Author(s), 2021. 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

REFERENCES

Baldock, T.E., Swan, C. & Taylor, P.H. 1996 A laboratory study of nonlinear surface waves on water. Phil. Trans. R. Soc. Lond. A 354, 649–676.Google Scholar
Beji, S. & Battjes, J.A. 1993 Experimental investigation of wave propagation over a bar. Coast. Engng 19, 151–162.CrossRefGoogle Scholar
Belibassakis, K.A. & Athanassoulis, G.A. 2011 A coupled-mode system with application to nonlinear water waves propagating in finite water depth and in variable bathymetry regions. Coast. Engng 58, 337–350.CrossRefGoogle Scholar
Benjamin, T.B. & Feir, J.E. 1967 The disintegration of wave trains on deep water Part 1. Theory. J.Fluid Mech. 27, 417–430.CrossRefGoogle Scholar
Bingham, H.B. & Agnon, Y. 2005 A Fourier–Boussinesq method for nonlinear water waves. Eur. J. Mech. B/Fluids 24, 255–274.CrossRefGoogle Scholar
Bingham, H.B., Madsen, P.A. & Fuhrman, D.R. 2009 Velocity potential formulations of highly accurate Boussinesq-type models. Coast. Engng 56, 467–478.CrossRefGoogle Scholar
Bitner, E.M. 1980 Non-linear effects of the statistical model of shallow-water wind waves. Appl. Ocean Res. 2, 63–73.CrossRefGoogle Scholar
Boccotti, P. 2000 Wave Mechanics for Ocean Engineering. Elsevier Science.Google Scholar
Borthwick, A.G., Hunt, A.C., Feng, T., Taylor, P.H. & Stansby, P.K. 2006 Flow kinematics of focused wave groups on a plane beach in the U.K. coastal research facility. Coast. Engng 53, 1033–1044.CrossRefGoogle Scholar
Chapalain, G., Cointe, R. & Temperville, A. 1992 Observed and modeled resonantly interacting progressive water-waves. Coast. Engng 16, 267–300.CrossRefGoogle Scholar
Chen, H., Tang, X., Zhang, R. & Gao, J. 2018 Effect of bottom slope on the nonlinear triad interactions in shallow water. Ocean Dyn. 68, 469–483.CrossRefGoogle Scholar
Dommermuth, D. 2000 The initialization of nonlinear waves using an adjustment scheme. Wave Motion 32, 307–317.CrossRefGoogle Scholar
Ducrozet, G. & Gouin, M. 2017 Influence of varying bathymetry in rogue wave occurrence within unidirectional and directional sea-states. J.Ocean Engng 3, 309–324.Google Scholar
Dysthe, K., Krogstad, H.E. & Müller, P. 2008 Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310.CrossRefGoogle Scholar
Elgar, S. & Guza, R.T. 1985 Observations of bispectra of shoaling surface gravity waves. J.Fluid Mech. 161, 425–448.CrossRefGoogle Scholar
Fitzgerald, C.J., Taylor, P.H., Taylor, R.E., 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, 20130847.Google Scholar
Forristall, G.Z. 1978 On the statistical distribution of wave heights in a storm. J.Geophys. Res. 83 (C5), 2353–2358.CrossRefGoogle Scholar
Goda, Y. 2010 Random Seas and Design of Maritime Structures, 3rd edn. World Scientific Publishing Company.CrossRefGoogle Scholar
Gottlieb, S. 2005 On high order strong stability preserving Runge–Kutta and multi step time discretizations. J.Sci. Comput. 25, 105–128.Google Scholar
Gouin, M., Ducrozet, G. & Ferrant, P. 2016 Development and validation of a non-linear spectral model for water waves over variable depth. Eur. J. Mech. B/Fluids 57, 115–128.CrossRefGoogle Scholar
Gramstad, O., Zeng, H., Trulsen, K. & Pedersen, G.K. 2013 Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water. Phys. Fluids 25, 122103.CrossRefGoogle Scholar
Hasimoto, H. & Ono, H. 1972 Nonlinear modulation of gravity waves. J.Phys. Soc. Japan 33, 805–811.CrossRefGoogle Scholar
Hasselmann, K., Munk, W. & MacDonald, G. 1963 Bispectra of ocean waves. In M. Rosenblatt Time Series Analysis. John Wiley.Google Scholar
Janssen, P.A.E.M. 2003 Nonlinear four-wave interactions and freak waves. J.Phys. Oceanogr. 33, 863–884.2.0.CO;2>CrossRefGoogle Scholar
Janssen, P.A.E.M. & Onorato, M. 2007 The intermediate water depth limit of the Zakharov equation and consequences for wave prediction. J.Phys. Oceanogr. 37, 2389–2400.CrossRefGoogle Scholar
Kashima, H., Hirayama, K. & Mori, N. 2014 Estimation of freak wave occurrence from deep to shallow water regions. Coast. Engng Proc. 1 (34), waves 36.CrossRefGoogle Scholar
Kashima, H. & Mori, N. 2019 Aftereffect of high-order nonlinearity on extreme wave occurrence from deep to intermediate water. Coast. Engng 153, 103559.CrossRefGoogle Scholar
Katsardi, V., de Lutio, L. & Swan, C. 2013 An experimental study of large waves in intermediate and shallow water depths. Part I: wave height and crest height statistics. Coast. Engng 73, 43–57.CrossRefGoogle Scholar
Kharif, C. & Pelinovsky, E. 2003 Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B/Fluids 22, 603–634.CrossRefGoogle Scholar
Kim, Y.C. & Powers, E.J. 1979 Digital bispectral analysis and its applications to nonlinear wave interactions. IEEE T. Plasma Sci. 7, 120–131.CrossRefGoogle Scholar
Le Méhauté, B. 1976 An Introduction to Hydrodynamics and Water Waves. Springer.CrossRefGoogle Scholar
Longuet-Higgins, M.S. 1952 On the statistical distribution of the height of sea waves. J.Mar. Res. 11, 245–265.Google Scholar
Ma, Y., Ma, X. & Dong, G. 2015 Variations of statistics for random waves propagating over a bar. J.Mar. Sci. Technol. 23, 864–869.Google Scholar
Madsen, P.A., Fuhrman, D.R. & Wang, B. 2006 A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Engng 53, 487–504.CrossRefGoogle Scholar
Mansard, E.P.D. & Funke, E.R. 1980 The measurement of incident and reflected spectra using a least squares method. Coast. Engng Proc. 1 (17), 8.CrossRefGoogle Scholar
Massel, S.R. 1983 Harmonic generation by waves propagating over a submerged step. Coast. Engng 7, 357–380.CrossRefGoogle Scholar
Mei, C.C. 1992 The Applied Dynamics of Ocean Surface Waves. World Scientific Publishing Company.Google Scholar
Mori, N. & Janssen, P.A.E.M. 2006 On kurtosis and occurrence probability of freak waves. J.Phys. Oceanogr. 36, 1471–1483.CrossRefGoogle Scholar
Naess, A. 1985 On the distribution of crest to trough wave heights. Ocean Engng 12, 221–234.CrossRefGoogle Scholar
Olagnon, M. & Magnusson, A.K. 2004 Sensitivity study of sea state parameters in correlation to extreme wave occurrences. In Proc. 14th International Offshore and Polar Engineering Conf. (ISOPE), 23–28 May, Toulon, France.Google Scholar
Onorato, M., Osborne, A.R. & Serio, M. 2005 Modulational instability and non-Gaussian statistics in experimental random water-wave trains. Phys. Fluids 17, 078101.CrossRefGoogle Scholar
Papoutsellis, C.E., Charalampopoulos, A.G. & Athanassoulis, G.A. 2018 Implementation of a fully nonlinear Hamiltonian coupled-mode theory, and application to solitary wave problems over bathymetry. Eur. J. Mech. B/Fluids 72, 199–224.CrossRefGoogle Scholar
Raoult, C., Benoit, M. & Yates, M.L. 2016 Validation of a fully nonlinear and dispersive wave model with laboratory non-breaking experiments. Coast. Engng 114, 194–207.CrossRefGoogle Scholar
Sergeeva, A., Pelinovsky, E. & Talipova, T. 2011 Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework. Nat. Hazards Earth Syst. Sci. 11, 323–330.CrossRefGoogle Scholar
Serio, M., Onorato, M., Osborne, A.R. & Janssen, P.A.E.M. 2006 On the computation of the Benjamin–Feir index. Il Nuovo Cimento 28, 893–903.Google Scholar
Simon, B., Papoutsellis, C.E., Benoit, M. & Yates, M.L. 2019 Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach. J.Ocean Engng 5, 365–383.Google Scholar
Tian, Y. & Sato, S. 2008 A numerical model on the interaction between nearshore nonlinear waves and strong currents. Coast. Engng J. 50, 369–395.CrossRefGoogle Scholar
Toffoli, A., et al. . 2013 Experimental evidence of the modulation of a plane wave to oblique perturbations and generation of rogue waves in finite water depth. Phys. Fluids 25, 091701.CrossRefGoogle Scholar
Trulsen, K., Raustøl, A., Jorde, S. & Rye, L.B. 2020 Extreme wave statistics of long-crested irregular waves over a shoal. J.Fluid Mech. 882, R2.CrossRefGoogle Scholar
Trulsen, K., Zeng, H. & Gramstad, O. 2012 Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys. Fluids 24, 097101.CrossRefGoogle Scholar
Viotti, C. & Dias, F. 2014 Extreme waves induced by strong depth transitions: fully nonlinear results. Phys. Fluids 26, 051705.CrossRefGoogle Scholar
Yates, M.L. & Benoit, M. 2015 Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves. Intl J. Numer. Meth. Fluids 77, 616–640.CrossRefGoogle Scholar
Young, I.R. 1995 The determination of confidence limits associated with estimates of the spectral peak frequency. Ocean Engng 22, 669–686.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.CrossRefGoogle Scholar
Zang, J., Gibson, R., Taylor, P.H., Taylor, R.E. & Swan, C. 2006 Second order wave diffraction around a fixed ship-shaped body in unidirectional steep waves. J.Offshore Mech. Arctic Engng 128, 89–99.CrossRefGoogle Scholar
Zang, J., Taylor, P.H., Morgan, G., Tello, M., Grice, J. & Orszaghova, J. 2010 Experimental study of non-linear wave impact on offshore wind turbine flundations. In Coastlab10: 3rd International Conference on the Application of Physical Modelling to Port and Coastal Protection, 28th Sep.–1st Oct., Barcelona, Spain.Google Scholar
Zeng, H. & Trulsen, K. 2012 Evolution of skewness and kurtosis of weakly nonlinear unidirectional waves over a sloping bottom. Nat. Hazards Earth Syst. Sci. 12, 631–638.CrossRefGoogle Scholar
Zhang, J., Benoit, M., Kimmoun, O., Chabchoub, A. & Hsu, H.-C. 2019 Statistics of extreme waves in coastal waters: large scale experiments and advanced numerical simulations. Fluids 4, 99.CrossRefGoogle Scholar
Zheng, Y., Lin, Z., Li, Y., Adcock, T.A.A., Li, Y. & van den Bremer, T.S. 2020 Fully nonlinear simulations of unidirectional extreme waves provoked by strong depth transitions: the effect of slope. Phys. Rev. Fluids 5, 064804.CrossRefGoogle Scholar