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Accurate estimation of extreme wave condition is desired for the rational design of offshore structures, but the estimation results are known to have uncertainty from various sources. The quality and quantity of the available extreme wave data differ among ocean regions since the atmospheric causes of extreme waves are not identical. This paper provides insight into how the different extreme wave behaviors influence the uncertainty of extreme wave estimation at each location. A review of extreme waves in four regions, namely the Gulf of Mexico, North West Pacific, Adriatic Sea, and the North Sea, revealed the difference in data uncertainty, shape parameter, and frequency of occurrence. The likelihood-weighted method was introduced to quantitatively assess the impact of each parameter on the uncertainty of extreme wave analysis. Case study based on representative parameters of the Gulf of Mexico and the North Sea revealed the large epistemic uncertainty for a region dominated by tropical cyclones. The assessment conducted in this paper is unique as it evaluates the epistemic uncertainty inherited in the extreme sample data. When the epistemic uncertainty is large, such as the case illustrated for the Gulf of Mexico, the variance from different approaches may not be significant against the epistemic uncertainty inherited in the sample data. [ABSTRACT FROM AUTHOR]

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schro¨ dinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite; consequently, beam dynamics form. Spatiotemporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D + 1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large-amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, solids, plasma, hydrodynamics, and optics. [ABSTRACT FROM AUTHOR]

We examine and discuss the spatial evolution of the statistical properties of mechanically generated surface gravity wave fields, initialized with unidirectional spectral energy distributions, uniformly distributed phases, and Rayleigh distributed amplitudes. We demonstrate that nonlinear interactions produce an energy cascade towards high frequency modes with a directional spread and trigger localized intermittent bursts. By analyzing the probability density function of Fourier mode amplitudes in the high frequency range of the wave energy spectrum, we show that a heavy-tailed distribution emerges with distance from the wave generator as a result of these intermittent bursts, departing from the originally imposed Rayleigh distribution, even under relatively weak nonlinear conditions. [ABSTRACT FROM AUTHOR]