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Occurrence of Extreme Waves in Finite Water Depth

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Abstract

For random unidirectional wave fields propagating on water of infinite depths, high-order nonlinearity such as modulational instability is responsible for strong departures from Gaussian-and second-order-based statistics. For finite water depth, on the contrary, wave instability attenuates and eventually vanishes for relative water depths as low as \(kh = 1.36\) (where k is the wavenumber of the dominant waves and h the water depth). Experimental results, nonetheless, indicates that oblique (directional) perturbations are capable of triggering and sustaining modulational instability and possibly lead to a wave amplitude growth even if \(kh < 1.36\). Here a comparative analysis of the statistical properties of surface gravity waves in water of finite depth is discussed by analyzing laboratory experiments, field measurements, and numerical simulations to assess the role of modulational instability on wave statistics and particularly on the occurrence of extremes. Despite evidence of modulational instability in regular wave fields, results presented herein seems to indicates that wave instability has a negligible effect on wave statistics, which remains primarily affected by second-order contributions.

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Acknowledgments

This work has been supported by the European Communitys Sixth Framework Programme through the grant to the budget of the Integrated Infrastructure Initiative HYDRALAB IV within the Transnational Access Activities, Contract No. 022441. F.W.O. project G.0333.09 and E.U. project EXTREME SEAS (contract SCP8-GA-2009-234175) are acknowledged. The authors also acknowledge the Hercules Foundation and the Flemish Government department EWI for providing access to the Flemish Supercomputer Center.

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Authors and Affiliations

  1. Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40 Box 2448, 3001, Heverlee, Belgium

    Leandro Fernandez & Jaak Monbaliu

  2. Department of General Physics, University of Torino, Via Pietro Giuria 1, 10125, Torino, Italy

    Miguel Onorato

  3. Center for Ocean Engineering, Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, Swinburne, VIC, 3122, Australia

    Alessandro Toffoli

Authors
  1. Leandro Fernandez
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  2. Miguel Onorato
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  3. Jaak Monbaliu
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  4. Alessandro Toffoli
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Correspondence to Leandro Fernandez .

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Editors and Affiliations

  1. Institute of Applied Physics and Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia

    Efim Pelinovsky

  2. Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), Marseille, France

    Christian Kharif

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Fernandez, L., Onorato, M., Monbaliu, J., Toffoli, A. (2016). Occurrence of Extreme Waves in Finite Water Depth. In: Pelinovsky, E., Kharif, C. (eds) Extreme Ocean Waves. Springer, Cham. https://doi.org/10.1007/978-3-319-21575-4_3

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