Hostname: page-component-f554764f5-44mx8 Total loading time: 0 Render date: 2025-04-10T05:51:19.642Z Has data issue: false hasContentIssue false
  • English
  • Français

Enhanced extreme wave statistics of irregular waves due to accelerating following current over a submerged bar

Published online by Cambridge University Press:  09 January 2023

Jie Zhang Open the ORCID record for Jie Zhang [Opens in a new window] ,
Yuxiang Ma Open the ORCID record for Yuxiang Ma [Opens in a new window] ,
Ting Tan ,
Guohai Dong  and
Michel Benoit Open the ORCID record for Michel Benoit [Opens in a new window]
Jie Zhang
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, PR China
Yuxiang Ma*
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, PR China
Ting Tan
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, PR China
Guohai Dong
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, PR China
Michel Benoit
Affiliation:
EDF R&D, Laboratoire National d'Hydraulique et Environnement (LNHE), Chatou 78400, France LHSV, Ecole des Ponts, EDF R&D, Chatou 78400, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence of a background current in a wave flume. We investigate the non-equilibrium phenomenon (NEP) induced by significant changes of water depth and mean horizontal flow velocity as wave trains pass over the bar. Using skewness and kurtosis as proxies, we show evidence that an accelerating following current could increase the sea-state non-Gaussianity and enhance both the magnitude and spatial extent of the NEP. We also find that below a ‘saturation relative water depth’ $k_p h_2 \approx 0.5$ ($k_p$ being the peak wavenumber in the shallow area of depth $h_2$), although the NEP manifests, the decrease of the relative water depth does not further enhance the maximum skewness and kurtosis over the bar crest. This work highlights the nonlinear physics according to which a following current could provoke higher freak wave risk in coastal areas where modulation instability plays an insignificant role.

JFM classification

Geophysical and Geological Flows: Topographic effects Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A50
Check for updates
Copyright
© The Author(s), 2023. 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

Adcock, T.A.A. & Taylor, P.H. 2014 The physics of anomalous (‘rogue’) ocean waves. Rep. Prog. Phys. 77, 105901.CrossRefGoogle ScholarPubMed
Akhmediev, N. & Pelinovsky, E. 2010 Editorial – introductory remarks on ‘Discussion & debate: rogue waves – towards a unifying concept?’ Eur. Phys. J. 185, 1–4.Google Scholar
Akselsen, A.H. & Ellingsen, S.Å. 2019 Sheared free-surface flow over three-dimensional obstructions of finite amplitude. J. Fluid Mech. 878, 740–767.CrossRefGoogle Scholar
Benjamin, T.B. 1967 Instability of periodic wavetrains in nonlinear dispersive systems. Proc. R. Soc. A 299, 59–76.Google Scholar
Bretherton, F.P. & Garrett, C.J.R. 1969 Wavetrains in inhomogeneous moving media. Proc. Math. Phys. Engng Sci. 302, 529–554.Google Scholar
Buttle, N.R., Pethiyagoda, R., Moroney, T.J. & McCue, S.W. 2018 Three-dimensional free-surface flow over arbitrary bottom topography. J. Fluid Mech. 846, 166–189.CrossRefGoogle Scholar
Chawla, A. & Kirby, J.T. 2002 Monochromatic and random wave breaking at blocking points. J. Geophys. Res. 107, 3067.CrossRefGoogle Scholar
Curtis, C.W. & Murphy, M. 2020 Evolution of spectral distributions in deep-water constant vorticity flows. Water Waves 2, 361–380.CrossRefGoogle Scholar
Dematteis, G., Grafke, T., Onorato, M. & Vanden-Eijnden, E. 2019 Experimental evidence of hydrodynamic instantons: the universal route to rogue waves. Phys. Rev. X 9, 041057.Google Scholar
Ducrozet, G., Abdolahpour, M., Nelli, F. & Toffoli, A. 2021 Predicting the occurrence of rogue waves in the presence of opposing currents with a high-order spectral method. Phys. Rev. Fluids 6, 064803.CrossRefGoogle Scholar
Ducrozet, G. & Gouin, M. 2017 Influence of varying bathymetry in rogue wave occurrence within unidirectional and directional sea-states. J. Ocean Engng Mar. Energy 3, 309–324.CrossRefGoogle Scholar
Dysthe, K., Krogstad, H.E. & Müller, P. 2008 Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310.CrossRefGoogle Scholar
Fedele, F., Brennan, J., Ponce de León, S., Dudley, J. & Dias, F. 2016 Real world ocean rogue waves explained without the modulational instability. Sci. Rep. 6, 27715.CrossRefGoogle ScholarPubMed
Gerber, M. 1987 The Benjamin–Feir instability of a deep-water Stokes wavepacket in the presence of a non-uniform medium. J. Fluid Mech. 176, 311–332.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
Hjelmervik, K.B. & Trulsen, K. 2009 Freak wave statistics on collinear currents. J. Fluid Mech. 637, 267–284.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
Kharif, C., Kraenkel, R.A., Manna, M.A. & Thomas, R. 2010 The modulational instability in deep water under the action of wind and dissipation. J. Fluid Mech. 664, 138–149.CrossRefGoogle Scholar
Kharif, C. & Pelinovsky, E. 2003 Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. (B/Fluids) 22, 603–634.CrossRefGoogle Scholar
Lavrenov, I.V. & Porubov, A.V. 2006 Three reasons for freak wave generation in the non-uniform current. Eur. J. Mech. (B/Fluids) 25, 574–585.CrossRefGoogle 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, 046601.CrossRefGoogle Scholar
Lawrence, C., Trulsen, K. & Gramstad, O. 2022 Extreme wave statistics of surface elevation and velocity field of gravity waves over a two-dimensional bathymetry. J. Fluid Mech. 939, A41.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 2. experimental analysis. J. Fluid Mech. 915, A72.CrossRefGoogle Scholar
Li, Y., Draycott, S., Zheng, Y., Lin, Z., Adcock, T.A.A. & van den Bremer, T.S. 2021 b Why rogue waves occur atop abrupt depth transitions. J. Fluid Mech. 919, R5.CrossRefGoogle Scholar
Li, Y., Zheng, Y., Lin, Z., Adcock, T.A.A. & van den Bremer, T.S. 2021 c Surface wavepackets subject to an abrupt depth change. Part 1. second-order theory. J. Fluid Mech. 915, A71.CrossRefGoogle Scholar
Liao, B., Dong, G., Ma, Y. & Gao, J.L. 2017 Linear-shear-current modified Schrödinger equation for gravity waves in finite water depth. Phys. Rev. E 96, 043111.CrossRefGoogle ScholarPubMed
Longuet-Higgins, M.S. & Stewart, R.W. 1961 The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10, 529–549.CrossRefGoogle Scholar
Ma, Y., Chen, H., Ma, X. & Dong, G. 2017 A numerical investigation on nonlinear transformation of obliquely incident random waves on plane sloping bottoms. Coast. Engng 130, 65–84.CrossRefGoogle Scholar
Ma, Y., Dong, G., Perlin, M., Ma, X., Wang, G. & Xu, J. 2010 Laboratory observations of wave evolution, modulation and blocking due to spatially varying opposing currents. J. Fluid Mech. 661, 108–129.CrossRefGoogle 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
Mendes, S., Scotti, A., Brunetti, M. & Kasparian, J. 2022 Non-homogeneous analysis of rogue wave probability evolution over a shoal. J. Fluid Mech. 939, A25.CrossRefGoogle Scholar
Onorato, M., Proment, D. & Toffoli, A. 2011 Triggering rogue waves in opposing currents. Phys. Rev. Lett. 107, 184502.CrossRefGoogle ScholarPubMed
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
Onorato, M. & Suret, P. 2016 Twenty years of progresses in oceanic rogue waves: the role played by weakly nonlinear models. Nat. Hazards 84, 541–548.CrossRefGoogle Scholar
Peregrine, D.H. 1976 Interaction of water waves and currents. In Advances in Applied Mechanics (ed. C.-S. Yih), pp. 9–117. Elsevier.CrossRefGoogle Scholar
Stocker, J.R. & Peregrine, D.H. 1999 The current-modified nonlinear Schrödinger equation. J. Fluid Mech. 399, 335–353.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
Toffoli, A., Cavaleri, L., Babanin, A.V., Benoit, M., Bitner-Gregersen, E.M., Monbaliu, J., Onorato, M., Osborne, A.R. & Stansberg, C.T. 2011 Occurrence of extreme waves in three-dimensional mechanically generated wave fields propagating over an oblique current. Nat. Hazards Earth Syst. Sci. 11, 895–903.CrossRefGoogle Scholar
Toffoli, A., Waseda, T., Houtani, H., Cavaleri, L., Greaves, D. & Onorato, M. 2015 Rogue waves in opposing currents: an experimental study on deterministic and stochastic wave trains. J. Fluid Mech. 769, 277–297.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, R.Y. Tarakanov & A.V. Marchenko), pp. 239–247. Springer International Publishing.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
Voronovich, V.V., Shrira, V.I. & Thomas, G. 2008 Can bottom friction suppress ‘freak wave’ formation? J. Fluid Mech. 604, 263–296.CrossRefGoogle Scholar
White, B.S. & Fornberg, B. 1998 On the chance of freak waves at sea. J. Fluid Mech. 355, 113–138.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, 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
Zhang, J., Benoit, M. & Ma, Y. 2022 Equilibration process of out-of-equilibrium sea-states induced by strong depth variation: evolution of coastal wave spectrum and representative parameters. Coast. Engng 174, 104099.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