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

Abstract

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.

Modelling of the spatial evolution of extreme laboratory wave crest and trough heights with the NLS-type equations

“…Once the nonlinearity increases,  will become a little smaller than  app which is obviously opposite to the second-order theoretical conclusion obtained by Tayfun and Fedele [13]. According to the previous research [19] [24], it is found that the modulational instability does not contribute too much to the discrepancy between these two parameters in the absence of bound wave effects. Therefore, it seems that the difference is caused by the combined effects of modulational instability and bound wave effects.…”

“…A modification of the NLS equation was derived by Dysthe [20] on the basis of a systematic asymptotic procedure. The Dysthe equation or MNLS equation takes into account the fourth order in wave steepness and bandwidth, being capable of representing the asymmetric features of propagating wave packets with narrow spectral bandwidth in deep water [21]- [24]. Further modifications of NLS-type equations have continued such as the spatial form proposed by Lo and Mei [25] for the purpose of performing a convenient comparison with experimental observations, and the one called BMNLS equation appropriate for wider wave spectra, given by Trulsen and Dysthe [26] and Trulsen et al [27] by adding the higher-order dispersive terms.…”

Hindcast of extreme sea states in North Atlantic extratropical storms

“…He extended the standard theory of four-wave interactions by including effects of nonresonant interactions and derived an expression for the kurtosis in terms of the action density function. Recently comparisons of the predictions of this equation with laboratory measurements showed good agreement (Zhang et al 2014). The nonlinear four-wave transfer is related with the generation of higher-order cumulants such as the kurtosis (C 4 ).…”

Modelling of the temporal and spatial evolutions of weakly nonlinear random directional waves with the modified nonlinear Schrödinger equations

“…represent an important source of information for the statistics of extreme waves which are rare in nature. Although various forms of NLS-type equations have been applied in the comparison with measurements in the wave basins and open seas [32]- [35], the research on the numerical difference of the spatial and temporal model is still not enough considering that only some discussions on unidirectional nonlinear wave group with an initial Gaussian envelope were presented by Shemer and Dorfman [36]. Therefore, the main aim in this study is to further check the applicability of spatial and temporal MNLS equations in simulating the more realistic sea states characterized by JONSWAP spectrum with different directionality xxx xyy…”