The nonlinear evolution of deep-water wave groups, which are initiated by unstable three-wave systems, have been observed in a large wave tank (50 m long, 4.2 m wide, 2.1 m deep), equipped with a programmable, high-resolution wave generator. A large number of experiments were conducted (over 80 cases) for waves 1.0–4.0 m long, initial steepness ε=0.10–0.28, and normalized sideband frequency differences, δω=δω, 0.2–1.4. Using an array of eight high-resolution wave wires distributed in range (up to 43 m fetch), spectral evolution was studied in detail including the effect of background disturbances on the evolution. Minimizing those, new observations were made which extend the pioneering work of Lake et al. (1977) and of Melville (1982). Foremost, near recurrence without downshifting was observed without breaking, despite a significant but reversible energy transfer to the lower sideband at peak modulation; complete recurrence was prevented by the spreading of discretized energy to higher frequencies. Strong breaking was found to increase the transfer of energy from the higher to the lower sideband and to render that transfer irreversible. The end state of the evolution following strong breaking is an effective downshifting of the spectral energy, where the lower and the carrier wave amplitudes nearly coincide; the further evolution of this almost two-wave system was not studied here. Breaking during strong modulation was observed not only for the fastest growing initial condition, but over a wide parameter range. An explanation of the sideband behaviour in both the breaking and non-breaking case was given based on wave energy and momentum considerations, including the separate effects of energy and momentum loss due to breaking, and transfer to discretized higher frequencies throughout the spectra. Attention was drawn to the latter, which was almost universally observed.

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...

The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < ɛ < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect of directionality, and successfully parameterizes the observed occurrence of freak waves in the tank. Analysis of the high-resolution hindcast wave field of the northwest Pacific reveals that such a directionally confined wind sea with high extreme wave probability is rare and corresponds mostly to a swell–wind sea mixed condition. Therefore, extreme wave occurrence in the sea as a result of quasi-resonant wave–wave interaction is a rare event that occurs only when the wind sea directionality is extremely narrow.

Internal solitary waves in a system of two fluids, silicone oil and water, bounded above by a free surface are studied both experimentally and theoretically. By adjusting an extra volume of silicone oil released from a reservoir, a wide range of amplitude waves are generated in a wave tank. Wave profiles as well as wave speeds are measured using multiple wave probes and are then compared with both the weakly nonlinear Korteweg–de Vries (KdV) models and the strongly nonlinear Miyata–Choi–Camassa (MCC) models. As the density difference between the two fluids in the experiment is relatively small (approximately 14 %), but non-negligible, special attention is paid to the effect of the boundary condition at the top surface. The nonlinear models valid for rigid-lid (RL) and free-surface (FS) boundary conditions are considered separately. It is found that the solitary wave of the FS model for a given amplitude is consistently narrower than that of the RL model and it propagates at a slightly lower speed. Due to strong nonlinearity in the internal-wave motion, the weakly nonlinear KdV models fail to describe the measured internal solitary wave profiles of intermediate and large wave amplitudes. The strongly nonlinear MCC-FS model agrees better with the measurements than the MCC-RL model, which indicates that the free-surface boundary condition at the top surface is crucial in describing the internal solitary waves in the experiment correctly. Leaving the top surface free in the experiment allows us to observe small and relatively short wave packets on the top surface, particularly when the amplitude of the internal solitary wave is large. Once excited, the wave packet is located above the front half of the internal solitary wave and propagates with a speed close to that of the internal solitary wave underneath. A simple resonance mechanism between short surface waves and long internal waves without and with nonlinear effects is examined to estimate the characteristic wavelength of modulated short surface waves, which is found to be in good agreement with the observed wavelength when nonlinearity is taken into account. Using ray theory, the evolution of short surface waves in the presence of a background current induced by an internal solitary wave is also investigated to examine the location of the modulated surface wave packet.

The breaking of waves is an important mechanism for a number of physical, chemical and biological processes in the ocean. Intuitively, waves break when they become too steep. Unfortunately, a general consensus on the ultimate shape of waves has not been achieved yet due to the complexity of the breaking mechanism which still remains the least understood of all processes affecting waves. To estimate the limiting shape of ocean waves, here we present a statistical analysis of a large sample of individual wave steepness. Data were collected from measurements of the surface elevation in laboratory facilities and the open sea under a variety of sea state conditions. Observations reveal that waves are able to reach steeper profiles than the Stokes' limit for stationary waves. Due to the large number of records this finding is statistically robust.

[1] On 23 June 2008, a fishing boat with 20 crewmembers onboard sank in reportedly moderate sea-state conditions in the Kuroshio Extension region east of Japan. To determine the sea state at the time of the incident, we conducted a hindcast wave simulation, as realistically as possible, using an improved third-generation wave model driven by wind and current reanalysis products. Our results indicated that at the time of the accident, the wave steepness increased and the spectral peakedness narrowed, creating a sea state favorable for freak wave occurrence due to quasi-resonance. Detailed analyses of the spectral evolution revealed that nonlinear coupling of swell and windsea waves was the key to generating the narrow spectrum. Under the influence of rising wind speed, the swell system grew exponentially at the expense of the windsea energy, and the bimodal crossing sea state transformed into a freakish unimodal sea.

We analyze a concurrent simulation result of the ocean circulation and tidal currents using a data‐assimilative ocean general circulation model covering the Western North Pacific with horizontal resolution of 1/36° to investigate possible interactions between them. Four sites of active M2 internal tide variability in open ocean (hot spots), such as Tokara Strait, Izu Ridge, Luzon Strait, and Ogasawara Ridge, are detected from both the satellite observation and the simulation. Energy cycle analysis of the simulated M2 baroclinic tide indicates two types of the hot spots: dissipation (Tokara Strait and Izu Ridge) and radiation (Luzon Strait and Ogasawara Ridge) dominant sites. Energy conversion from barotropic to baroclinic M2 tides at the hot spots is modulated considerably by the lower‐frequency changes in the density field. Modulation at the two spots (Tokara Strait and Izu Ridge) is affected by the Kuroshio path variation together with the seasonal variation of the shallow thermocline. At the other two sites, influence from changes in the relatively deep stratification through the Kuroshio intrusion into South China Sea (Luzon Strat) and mesoscale eddy activity (Ogasawara Ridge) is dominant in the modulation.

We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified nonlinear Schrödinger equation which establishes that rogue waves can be triggered by a nonhomogeneous current characterized by a negative horizontal velocity gradient.