Nonlinear modulational instability of wavepackets is one of the mechanisms responsible for the formation of large-amplitude water waves. Here, mechanically generated waves in a three-dimensional basin and numerical simulations of nonlinear waves have been compared in order to assess the ability of numerical models to describe the evolution of weakly nonlinear waves and predict the probability of occurrence of extreme waves within a variety of random directional wave fields. Numerical simulations have been performed following two different approaches: numerical integration of a modified nonlinear Schrödinger equation and numerical integration of the potential Euler equations based on a higher-order spectral method. Whereas the first makes a narrow-banded approximation (both in frequency and direction), the latter is free from bandwidth constraints. Both models assume weakly nonlinear waves. On the whole, it has been found that the statistical properties of numerically simulated wave fields are in good quantitative agreement with laboratory observations. Moreover, this study shows that the modified nonlinear Schrödinger equation can also provide consistent results outside its narrow-banded domain of validity.

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[1] We analyze the sea state conditions during which the accident of the cruise ship Louis Majesty took place. The ship was hit by a large wave that destroyed some windows at deck number five and caused two fatalities. Using the wave model (WAM), driven by the Consortium for Small-Scale Modelling (COSMO-ME) winds, we perform a detailed hindcast of the local wave conditions. The results reveal the presence of two comparable wave systems characterized almost by the same frequency. We discuss such sea state conditions in the framework of a system of two coupled Nonlinear Schrödinger (CNLS) equations, each of which describe the dynamics of a single spectral peak. For some specific parameters, we discuss the breather solutions of the CNLS equations and estimate the maximum wave amplitude. Even though, due to the lack of measurements, it is impossible to establish the nature of the wave that caused the accident, we show that the angle between the two wave systems during the accident was close to the condition for which the maximum amplitude of the breather solution is observed.

[1] We present an experimental and numerical investigation on the statistical properties of the surface elevation in crossing sea conditions. Experiments are performed in a very large wave basin (70 m × 50 m × 3 m) and numerical results are obtained using a higher order method for solving the Euler equations. Both experimental and numerical results indicate that the number of extreme events depends on the angle between the two interacting systems. This outcome is supported by recent theoretical investigations which have highlighted that the instability of wave packets may be triggered by the nonlinear interactions between coexisting, non-collinear wave systems. Citation: Toffoli, A., E. M.Bitner-Gregersen, A. R. Osborne, M. Serio, J. Monbaliu, and M. Onorato (2011), Extreme waves in random crossing seas: Laboratory experiments and numerical simulations, Geophys.

Wind field ensembles from six CMIP5 models force wave model time slices of the northeast Atlantic over the last three decades of the 20th and the 21st centuries. The future wave climate is investigated by considering the RCP4.5 and RCP8.5 emission scenarios. The CMIP5 model selection is based on their ability to reconstruct the present (1971–2000) extratropical cyclone activity, but increased spatial resolution has also been emphasized. In total, the study comprises 35 wave model integrations, each about 30 years long, in total more than 1000 years. Here annual statistics of significant wave height are analyzed, including mean parameters and upper percentiles. There is general agreement among all models considered that the mean significant wave height is expected to decrease by the end of the 21st century. This signal is statistically significant also for higher percentiles, but less evident for annual maxima. The RCP8.5 scenario yields the strongest reduction in wave height. The exception to this is the north western part of the Norwegian Sea and the Barents Sea, where receding ice cover gives longer fetch and higher waves. The upper percentiles are reduced less than the mean wave height, suggesting that the future wave climate has higher variance than the historical period.

The overall oscillatory motion on the ocean surface is a combination of a large variety of different types of waves. All these waves are primarily classified according to the generation and restoring mechanisms, which induce oscillations within a wide band of periods and associated wavelengths. The resulting waves and induced motion through the water column affect a large number of marine processes and engineering activities that take place on the surface and in the most superficial sublayers of ocean. These include the exchange of heat and gases, ocean mixing, transport of sediment, coastal morphology, seakeeping, offshore engineering, and renewable energy among many others. A description of the different types of ocean surface waves and their concurrent classification is presented.

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