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In this study, the relation between rogue wave occurrence statistics and properties of the directional wind-wave spectrum is investigated. The study is conducted by means of the fully nonlinear phase-resolving numerical model and the high-order spectral model. Benjamin-Feir Index (BFI ), Π numbers and Modulation Index, which are designed to represent instabilities in nonlinear wave systems, are used as indicators for the occurrence of rogue waves. Rogue wave statistics and indicator parameters' performance are assessed based on numerical simulations and compared against in situ measurements. Directional Π 2 is found to be the best performing indicator. It is also observed that probability of rogue wave occurrence further peaks up at high directionality where modulational instability should be suppressed. It is argued that this condition is associated with the linear superposition of waves coming from different directions. Therefore, both directionality and instability, i.e. both linear and nonlinear effects, appear to be important physical mechanisms contributing to the extreme wave statistics. However, it is also argued that rogue wave occurrence is a transient (fast) event and cannot be accurately represented with conventional probability distribution functions. [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]

The observation-based source terms available in the third-generation wave model WAVEWATCH III (i.e., the ST6 package for parameterizations of wind input, wave breaking, and swell dissipation terms) are recalibrated and verified against a series of academic and realistic simulations, including the fetch/duration-limited test, a Lake Michigan hindcast, and a 1-yr global hindcast. The updated ST6 not only performs well in predicting commonly used bulk wave parameters (e.g., significant wave height and wave period) but also yields a clearly improved estimation of high-frequency energy level (in terms of saturation spectrum and mean square slope). In the duration-limited test, we investigate the modeled wave spectrum in a detailed way by introducing spectral metrics for the tail and the peak of the omnidirectional wave spectrum and for the directionality of the two-dimensional frequency–direction spectrum. The omnidirectional frequency spectrum E(f) from the recalibrated ST6 shows a clear transition behavior from a power law of approximately f−4 to a power law of about f−5, comparable to previous field studies. Different solvers for nonlinear wave interactions are applied with ST6, including the Discrete Interaction Approximation (DIA), the more expensive Generalized Multiple DIA (GMD), and the very expensive exact solutions [using the Webb–Resio–Tracy method (WRT)]. The GMD-simulated E(f) is in excellent agreement with that from WRT. Nonetheless, we find the peak of E(f) modeled by the GMD and WRT appears too narrow. It is also shown that in the 1-yr global hindcast, the DIA-based model overestimates the low-frequency wave energy (wave period T > 16 s) by 90%. Such model errors are reduced significantly by the GMD to ~20%. [ABSTRACT FROM AUTHOR]

The concept of a constant-flux layer is usually employed for vertical profiling of the wind measured at some elevation near the ocean surface. The surface waves, however, modify the balance of turbulent stresses very near the surface, and therefore such extrapolations can introduce significant biases. This is particularly true for buoy measurements in extreme conditions, when the anemometer mast is within the wave boundary layer (WBL) or even below the wave crests. In this paper, field data and aWBL model are used to investigate such biases. It is shown that near the surface the turbulent stresses are less than those obtained by extrapolation using the logarithmic-layer assumption, and the mean wind speeds very near the surface, based on Lake George field observations, are up to 5% larger. The behavior is then simulated by means of a WBL model coupled with nonlinear waves, which confirmed the observations and revealed further details of complex behaviors at the wind-wave boundary layer. [ABSTRACT FROM AUTHOR]

Evolution of nonlinear wave groups to breaking under wind forcing was studied by means of a fully nonlinear numerical model and in a laboratory experiment. Dependence of distance to breaking and modulation depth (height ratio of the highest and the lowest waves in a group) on wind forcing was described. It was shown that in the presence of a certain wind forcing both distance to breaking and modulation depth decrease; the latter signifies slowing down of the instability growth. It was also shown that wind forcing significantly reduces the energy loss in a single breaking event. [ABSTRACT FROM AUTHOR]

Progression of nonlinear wave groups to breaking was studied numerically and experimentally. Evolution of such wave group parameters as a function of distance to breaking and modulation depth-the height ratio of the highest and the lowest waves in the group-was described. Numerical model results demonstrated good agreement with experimental results in describing the behavior of the distance to breaking and modulation depth as functions of initial wave steepness. It was shown that energy loss appears to be a function of the modulation depth at the breaking onset. Energy loss grows with modulation depth up to a certain threshold of the latter. It was also shown that breaking probability for wave groups with modulation depth below 2.2 is very low. [ABSTRACT FROM AUTHOR]

The paper extends a pilot study into a detailed investigation of properties of breaking waves and processes responsible for breaking. Simulations of evolution of steep to very steep waves to the point of breaking are undertaken by means of the fully nonlinear Chalikov-Sheinin model. Particular attention is paid to evolution of nonlinear wave properties, such as steepness, skewness and asymmetry, in the physical, rather than Fourier space, and to their interplay leading to the onset of breaking. The role of superimposed wind is also investigated. The capacity of the wind to affect the breaking onset is minimal unless the wind forcing is very strong. Wind is, however, important as a source of energy for amplification of the wave steepness and ultimately altering the breaking statistics. A detailed laboratory study is subsequently described. The theoretical predictions are verified and quantified. In addition, some features of the nonlinear development not revealed by the model (i.e. reduction of the wave period which further promotes an increase in steepness prior to breaking) are investigated. Physical properties of the incipient breaker are measured and examined, as well as characteristics of waves both preceding and following the breaker. The experiments were performed both with and without a superimposed wind, the role of which is also investigated. Since these idealized two-dimensional results are ultimately intended for field applications, tentative comparisons with known field data are considered. Limitations which the modulational instability mechanism can encounter in real broadband three-dimensional environments are highlighted. Also, substantial examination of existing methods of breaking onset detection are discussed and inconsistencies of existing measurements of breaking rates are pointed out. [ABSTRACT FROM AUTHOR]

To withstand the local wave climate, coastal structure design relies on our understanding of the wave characteristics at the structure wall and the forces they impose onto the wall. However, despite the vast number of protective structures along our coasts, detailed field observations of waves measured directly at the structure wall are virtually absent. In this study, rare observations of wave characteristics at a vertical wall are presented. Contrary to linear wave theory, results suggest that the standing waves are highly nonlinear. Waves at the wall have considerably larger kurtosis and skewness compared to the incoming wave field and the wave steepness at the wall is observed to exceed the theoretical wave steepness limit of standing waves. • Rare field observations of standing waves are presented. • Waves at the wall have high kurtosis and skewness than in the undisturbed field. • Waves at the wall can exceed the steepness limit of standing waves. [ABSTRACT FROM AUTHOR]

We have investigated the dispersion of tracer particles by numerically simulating ensemble nonlinear gravity waves on the surface of an infinitely deep fluid. Using the concepts of passive Lagrangian markers and insights from weak wave turbulence theory, we validated fundamental predictions for particle kinematics associated with scaling laws and probability density functions. These results improve the understanding of wave-driven transport phenomena that depart far from equilibrium and the development of the high-fidelity models of transport processes in geophysical systems. • Dispersion of particles by nonlinear water waves has been investigated numerically. • Predictions of the Weak Wave Turbulence Theory have been confirmed. • The self-similarity form for Probability Density Function has been validated. [ABSTRACT FROM AUTHOR]