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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 14, issue 4 | Copyright

Special issue: Extreme seas and ship operations

Nat. Hazards Earth Syst. Sci., 14, 959-968, 2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 24 Apr 2014

Research article | 24 Apr 2014

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

H. D. Zhang1, C. Guedes Soares1, Z. Cherneva1, and M. Onorato2 H. D. Zhang et al.
  • 1Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal
  • 2Dipartimento di Fisica, Universitá di Torino, Via P. Giuria 1, 10125 Torino, Italy

Abstract. Spatial variation of nonlinear wave groups with different initial envelope shapes is theoretically studied first, confirming that the simplest nonlinear theoretical model is capable of describing the evolution of propagating wave packets in deep water. Moreover, three groups of laboratory experiments run in the wave basin of CEHIPAR (Canal de Experiencias Hidrodinámicas de El Pardo, known also as El Pardo Model Basin) was founded in 1928 by the Spanish Navy. are systematically compared with the numerical simulations of the nonlinear Schrödinger equation. Although a little overestimation is detected, especially in the set of experiments characterized by higher initial wave steepness, the numerical simulation still displays a high degree of agreement with the laboratory experiments. Therefore, the nonlinear Schrödinger equation catches the essential characteristics of the extreme waves and provides an important physical insight into their generation. The modulation instability, resulting from the quasi-resonant four-wave interaction in a unidirectional sea state, can be indicated by the coefficient of kurtosis, which shows an appreciable correlation with the extreme wave height and hence is used in the modified Edgeworth–Rayleigh distribution. Finally, some statistical properties on the maximum wave heights in different sea states have been related with the initial Benjamin–Feir index.

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