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Research Papers: Ocean Engineering

# Comparison of Distributions of Wave Heights From Nonlinear Schröedinger Equation Simulations and Laboratory Experiments

[+] Author and Article Information
Huidong Zhang, Zhivelina Cherneva, Carlos Guedes Soares

Centre for Marine Technology
and Ocean Engineering (CENTEC),
Instituto Superior Técnico,
Lisbon 1049-001, Portugal

Miguel Onorato

Dipartimento di Fisica,
Universitá di Torino,
Via P. Giuria 1,
Torino 10125, Italy

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received April 17, 2013; final manuscript received July 30, 2015; published online August 20, 2015. Assoc. Editor: Celso P. Pesce.

J. Offshore Mech. Arct. Eng 137(5), 051102 (Aug 20, 2015) (7 pages) Paper No: OMAE-13-1038; doi: 10.1115/1.4031218 History: Received April 17, 2013; Revised July 30, 2015

## Abstract

Numerical simulations of the nonlinear Schrödinger (NLS) equation are performed by imposing randomly synthesized free surface displacement at the wave maker characterized by the Joint North Sea Wave Project (JONSWAP) spectrum and compared with four different sea states generated in the deepwater wave basin of Marintek. The comparisons show that the numerical simulations have a high degree of agreement with the laboratory experiments although a little overestimation can be observed, especially in the severe sea state. Thus, the simulations still catch the main characteristics of extreme waves and provide an important physical insight into their generation. The coefficient of kurtosis $λ40$ presents a similar spatial evolution trend with the abnormal wave density, and the nonlinear Gram–Charlier (GC) model is used to predict the wave height distribution. It is demonstrated again that the theoretical approximation based on the GC expansion can describe large wave heights reasonably well in most cases. However, if the sea state is severe, wave breaking can significantly decrease the actual tail of wave height distribution, and discrepancy occurs when comparing with the numerical simulation. Moreover, the number of waves also plays an important role on the prediction of extreme wave height.

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Topics: Simulation , Waves , Seas

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## Figures

Fig. 1

Layout of the Marintek wave basin and gauge locations

Fig. 2

Relationship between the coefficient of kurtosis and the BFI. The full and empty marks represent the experimental and simulated results, respectively.

Fig. 3

Relationship between the scaled maximum wave height and the coefficient of kurtosis. The full and empty marks still have the same meaning as in Fig. 2.

Fig. 4

Relationship between Λ and Λapp. The full and empty marks still have the same meaning as in Fig. 2.

Fig. 5

Spatial variation of the coefficient of kurtosis in case 8241. The full and empty marks still have the same meaning as in Fig. 2.

Fig. 6

Spatial variation of the rogue wave density in case 8241. The full and empty marks still have the same meaning as in Fig. 2.

Fig. 7

Exceedance distributions of scaled wave heights. The four rows correspond to four different sea states listed in Table 1. The three columns present the results obtained in the locations of gauges 1, 5, and 8, respectively. The solid line, dash line, and thick dotted-dashed line mean Rayleigh distribution, GC models in experiment, and in simulation in sequence. The full and empty marks still have the same meaning as in Fig. 2.

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