Hostname: page-component-5f745c7db-xx4dx Total loading time: 0 Render date: 2025-01-07T05:12:28.740Z Has data issue: true hasContentIssue false
  • English
  • Français

Why rogue waves occur atop abrupt depth transitions

Published online by Cambridge University Press:  26 May 2021

Yan Li Open the ORCID record for Yan Li [Opens in a new window] ,
Samuel Draycott Open the ORCID record for Samuel Draycott [Opens in a new window] ,
Yaokun Zheng ,
Zhiliang Lin ,
Thomas A.A. Adcock Open the ORCID record for Thomas A.A. Adcock [Opens in a new window]  and
Ton S. van den Bremer Open the ORCID record for Ton S. van den Bremer [Opens in a new window]
Yan Li*
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, OxfordOX1 3PJ, UK Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491Trondheim, Norway
Samuel Draycott
Affiliation:
Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, ManchesterM13 9PL, UK
Yaokun Zheng
Affiliation:
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai200240, PR China
Zhiliang Lin
Affiliation:
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai200240, PR China
Thomas A.A. Adcock
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, OxfordOX1 3PJ, UK
Ton S. van den Bremer
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, OxfordOX1 3PJ, UK Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CDDelft, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Abrupt depth transitions (ADTs) have recently been identified as potential causes of ‘rogue’ ocean waves. When stationary and (close-to-) normally distributed waves travel into shallower water over an ADT, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show, by comparing to new experiments and numerical simulations, that the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the ADT, and new second-order free waves generated due to the ADT.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , R5
Check for updates
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.)

References

REFERENCES

Adcock, T.A.A. & Taylor, P.H. 2014 The physics of anomalous (‘rogue’) ocean waves. Rep. Prog. Phys. 77 (10), 105901.CrossRefGoogle Scholar
Benjamin, T.B. & Feir, J.E. 1967 The disintegration of wave trains on deep water Part 1. Theory. J. Fluid Mech. 27 (3), 417–430.CrossRefGoogle Scholar
Bolles, C.T., Speer, K & Moore, M.N.J. 2019 Anomalous wave statistics induced by abrupt depth change. Phys. Rev. Fluids 4 (1), 011801.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 (4), 309–324.Google Scholar
Dudley, J.M., Genty, G., Mussot, A., Chabchoub, A. & Dias, F. 2019 Rogue waves and analogies in optics and oceanography. Nat. Rev. Phys. 1 (11), 675–689.CrossRefGoogle Scholar
Dysthe, K.B., Krogstad, H.E. & Müller, P. 2008 Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310.CrossRefGoogle Scholar
Fedele, F., Brennan, J., De León, S.P., Dudley, J. & Dias, F. 2016 Real world ocean rogue waves explained without the modulational instability. Sci. Rep. 6, 27715.CrossRefGoogle ScholarPubMed
Forristall, G.Z. 2000 Wave crest distributions: observations and second-order theory. J. Phys. Oceanogr. 30 (8), 1931–1943.2.0.CO;2>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 (12), 122103.CrossRefGoogle 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
Kashima, H., Hirayama, K. & Mori, N. 2014 Estimation of freak wave occurrence from deep to shallow water regions. Coast. Engng 1 (34), 36.CrossRefGoogle Scholar
Kharif, C., Pelinovsky, E. & Slunyaev, A. 2008 Rogue Waves in the Ocean. Springer Science & Business Media.Google Scholar
Lawrence, C., Trulsen, K. & Gramstad, O. 2021 Statistical properties of wave kinematics in long-crested irregular waves propagating over non-uniform bathymetry. Phys. Fluids 33 (4), 046601.CrossRefGoogle Scholar
Li, Y., Draycott, S., Adcock, T.A.A. & van den Bremer, T.S. 2021 a Surface wavepackets subject to an abrupt depth change. Part II: experimental analysis. J. Fluid Mech. 915, A72.CrossRefGoogle Scholar
Li, Y., Zheng, Y.K., Lin, Z.L., Adcock, T.A.A. & van den Bremer, T.S. 2021 b Surface wavepackets subject to an abrupt depth change. Part I: second-order theory. J. Fluid Mech. 915, A71.CrossRefGoogle Scholar
Ma, Y.X., Dong, G. & Ma, X. 2014 Experimental study of statistics of random waves propagating over a bar. Coast. Engng 1 (34), 30.CrossRefGoogle Scholar
Majda, A.J., Moore, M.N.J. & Qi, D. 2019 Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change. Proc. Natl Acad. Sci. USA 116 (10), 3982–3987.CrossRefGoogle ScholarPubMed
Massel, S.R. 1983 Harmonic generation by waves propagating over a submerged step. Coast. Engng 7 (4), 357–380.CrossRefGoogle Scholar
Mei, C.C., Stiassnie, M. & Yue, D.K.P. 1989 Theory and Applications of Ocean Surface Waves: Part 1: Linear Aspects Part 2: Nonlinear Aspects. World Scientific.Google Scholar
Mori, N. & Janssen, P.A.E.M. 2006 On kurtosis and occurrence probability of freak waves. J. Phys. Oceanogr. 36 (7), 1471–1483.CrossRefGoogle Scholar
Onorato, M., Residori, S., Bortolozzo, U., Montina, A. & Arecchi, F.T. 2013 Rogue waves and their generating mechanisms in different physical contexts. Phys. Rep. 528, 47–89.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 (2), 323–330.CrossRefGoogle Scholar
Tayfun, M.A. 1980 Narrow-band nonlinear sea waves. J. Geophys. Res.: Oceans 85 (C3), 1548–1552.CrossRefGoogle Scholar
Tayfun, M.A. 1986 On narrow-band representation of ocean waves: 1. Theory. J. Geophys. Res.: Oceans 91 (C6), 7743–7752.CrossRefGoogle Scholar
Toffoli, A., Monbaliu, J., Onorato, M., Osborne, A.R., Babanin, A.V. & Bitner-Gregersen, E. 2007 Second-order theory and setup in surface gravity waves: a comparison with experimental data. J. Phys. Oceanogr. 37 (11), 2726–2739.CrossRefGoogle Scholar
Trulsen, K. 2018 Rogue waves in the ocean, the role of modulational instability, and abrupt changes of environmental conditions that can provoke non equilibrium wave dynamics. In The Ocean in Motion (ed. M. G. Velarde et al. .), pp. 239–247. Springer.CrossRefGoogle Scholar
Trulsen, K., Raustøl, A., Jorde, S. & Bæverfjord Rye, L. 2020 Extreme wave statistics of long-crested irregular waves over a shoal. J. Fluid Mech. 882, R2.CrossRefGoogle Scholar
Trulsen, K., Zeng, H.M. & Gramstad, O. 2012 Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys. Fluids 24 (9), 097101.CrossRefGoogle Scholar
Viotti, C. & Dias, F. 2014 Extreme waves induced by strong depth transitions: fully nonlinear results. Phys. Fluids 26 (5), 051705.CrossRefGoogle 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 (3), 631–638.CrossRefGoogle Scholar
Zhang, J. & Benoit, M. 2021 Wave–bottom interaction and extreme wave statistics due to shoaling and de-shoaling of irregular long-crested wave trains over steep seabed changes. J. Fluid Mech. 912, A28.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.K., Lin, Z.L., Li, Y., Adcock, T.A.A., Li, Y. & van den Bremer, T.S. 2020 Fully nonlinear simulations of extreme waves provoked by strong depth transitions: the effect of slope. Phys. Rev. Fluids 5, 064804.CrossRefGoogle Scholar