A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30• at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests.Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

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.

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, non-linear interactions in deep water; 4, white-capping dissipation; 5, non-linear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. Keywords

We discuss two independent, large scale experiments performed in two wave basins of different dimensions in which the statistics of the surface wave elevation are addressed. Both facilities are equipped with a wave maker capable of generating waves with prescribed frequency and directional properties. The experimental results show that the probability of the formation of large amplitude waves strongly depends on the directional properties of the waves. Sea states characterized by long-crested and steep waves are more likely to be populated by freak waves with respect to those characterized by a large directional spreading. DOI: 10.1103/PhysRevLett.102.114502 PACS numbers: 47.35.Bb, 47.55.NÀ An important task in the study of surface gravity waves is the determination of the probability density function of the surface wave elevation. The knowledge of the probability of the occurrence of large amplitude waves is essential for different engineering purposes such as the prediction of wave forces and structural responses or the design of offshore structures. A deep comprehension of the physical mechanisms of the generation of such waves is also a first step towards the development of an operational methodology for the probabilistic forecast of freak waves. It is well known that surface gravity waves obey nonlinear equations and, to date, a universal tool suitable for deriving the probability distribution function of a nonlinear system has not yet been developed. Fortunately, water waves are on average weakly nonlinear [1,2] and solutions can be generally written as power series, where the small parameter, in the case of deep water waves, is the wave steepness ". Strong departure from Gaussian statistics of the surface elevation can be observed if third order nonlinearities are considered. At such order it has been shown numerically [3] and theoretically [4] that, for long-crested waves, a generalization of the Benjamin-Feir instability [5] (or modulational instability [2]) for random spectra can take place [6]. This instability, that corresponds to a quasiresonant four-wave interaction in Fourier space, results in the formation of large amplitude waves (or rogue waves) [7] which affect the statistical properties of the surface elevation (see, for example, [8]). This is particularly true if the ratio between the wave steepness and the spectral bandwidth, known as the Benjamin-Feir Index (BFI), is large [4]. We mention that rogue waves have also been recently observed in optical systems [9] and in acoustic turbulence in He II [10] where giant waves are observed during an inverse cascade process.We emphasize that in many different fields of physics (plasmas [11,12], nonlinear optics [13,14], chargedparticle beam dynamics [15,16]) the modulational instability plays an important role; under suitable physical conditions a nonlinear Schrödinger equation can be derived and the modulational instability can be analyzed directly with this equation [2]. A major question which has to be addressed (and is the subject of the pre...

In this paper, different partitioning techniques and methods to identify wind sea and swell are investigated, addressing both 1D and 2D schemes. Current partitioning techniques depend largely on arbitrary parameterizations to assess if wave systems are significant or spurious. This makes the implementation of automated procedures difficult, if not impossible, to calibrate. To avoid this limitation, for the 2D spectrum, the use of a digital filter is proposed to help the algorithm keep the important features of the spectrum and disregard the noise. For the 1D spectrum, a mechanism oriented to neglect the most likely spurious partitions was found sufficient for detecting relevant spectral features. Regarding the identification of wind sea and swell, it was found that customarily used methods sometimes largely differ from one another. Evidently, methods using 2D spectra and wind information are the most consistent. In reference to 1D identification methods, attention is given to two widely used methods, namely, the steepness method used operationally at the National Data Buoy Center (NDBC) and the Pierson–Moskowitz (PM) spectrum peak method. It was found that the steepness method systematically overestimates swell, while the PM method is more consistent, although it tends to underestimate swell. Consistent results were obtained looking at the ratio between the energy at the spectral peak of a partition and the energy at the peak of a PM spectrum with the same peak frequency. It is found that the use of partitioning gives more consistent identification results using both 1D and 2D spectra.

Abstract. Two-way feedback occurs between offshore wind and waves. However, the influence of the waves on the wind profile remains understudied, in particular the momentum transfer between the sea surface and the atmosphere. Previous studies showed that for swell waves it is possible to have increasing wind speeds in case of aligned wind–wave directions. However, the opposite is valid for opposed wind–wave directions, where a decrease in wind velocity is observed. Up to now, this behavior has not been included in most numerical models due to the lack of an appropriate parameterization of the resulting effective roughness length. Using an extensive data set of offshore measurements in the North Sea and the Atlantic Ocean, we show that the wave roughness length affecting the wind is indeed dependent on the alignment between the wind and wave directions. Moreover, we propose a new roughness length parameterization, taking into account the dependence on alignment, consisting of an enhanced roughness length for increasing misalignment. Using this new roughness length parameterization in numerical models might facilitate a better representation of offshore wind, which is relevant to many applications including offshore wind energy and climate modeling.

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