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Interaction with an opposing current amplifies wave modulation and accelerates nonlinear wave focusing in regular wavepackets. This results in large-amplitude waves, usually known as rogue waves, even if the wave conditions are less prone to extremes. Laboratory experiments in three independent facilities are presented here to assess the role of opposing currents in changing the statistical properties of unidirectional and directional mechanically generated random wavefields. The results demonstrate in a consistent and robust manner that opposing currents induce a sharp and rapid transition from weakly to strongly non-Gaussian properties. This is associated with a substantial increase in the probability of occurrence of rogue waves for unidirectional and directional sea states, for which the occurrence of extreme and rogue waves is normally the least expected.

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.

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.

A series of experiments were conducted in a wave basin (50 m long, 10 m wide and 5 m deep) generating two waves propagating at an angle by a directional wavemaker. When the two waves were selected from a resonant triplet, an initially non-existing wave grew as the waves propagated down the tank. The linear growth rate of the resonating wave agreed well with third-order resonance theory based on Zakharov’s reduced gravity equation. Additional experiments with opposing and coflowing mean current with large temporal and spatial variations were conducted. As the flow rate increased, the linear growth was suppressed. As reproduced numerically with Zakharov’s equation, the resonant interaction saturated at time scales inversely proportional to the magnitude of the forced random resonance detuning. It is conjectured that the resonance is detuned by the variation and not by the mean of the current field due to wavelength-dependent Doppler shift and to the refraction of wave rays. Further analysis of the spectral evolution revealed that while discrete peaks appear at high frequencies as a result of dynamical cascading, a continuously saturated spectrum develops in the background as the current speed increases. Additional experiments were conducted studying the evolution of the random directional wave on a dynamical time scale under the influence of current. Due to random resonance detuning by the current, the spectral tail tended to be suppressed.

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. Key Points Occurrence of extreme waves depends on the angle between crossing wave fronts Crossing seas triggers the formation of extreme waves Experimental and numerical verification of wave instability in crossing seas

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.

Field observations of water temperature on the Australian North‐West Shelf (Eastern Indian Ocean) with the support of numerical simulations are used to demonstrate that the injection of turbulence generated by the wave orbital motion substantially contributes to the mixing of the upper ocean. Measurements also show that a considerable deepening of the mixed layer occurs during tropical cyclones, when the production of wave‐induced turbulent kinetic energy overcomes the contribution of the current‐generated shear turbulence. Despite a significant contribution to the deepening of the mixed layer, the effect of a background current and atmospheric forcing are not on their own capable of justifying the observed deepening of the mixed layer through most of the water column. Furthermore, variations of a normally shallow mixed layer depth are observed within a relatively short timescale of approximately 10 hours after the intensification of wave activity and vanish soon after the decay of storm surface waves. This rapid development tends also to exclude any significant contribution by wave breaking, as small rates of vertical diffusivity for wave breaking‐induced turbulence would require longer timescales to influence the depth of the mixed layer. Key Points Effect of non‐breaking wave induced turbulence on ocean mixing Contribution of wave motion in deepening the mixed layer depth Empirical verification of non‐breaking wave induced turbulence process

A theoretical model of water wave overwash of a thin floating plate is proposed. The nonlinear shallow-water equations are used to model the overwash, and the linear potential-flow/thin-plate model to force it. Model predictions are compared with overwash depths measured during a series of laboratory wave basin experiments. The model is shown to be accurate for incident waves of low steepness or short length.

Linear instability of two-dimensional wave fields and its concurrent evolution in time is here investigated by means of the Alber equation for narrow-banded random surface waves in deep water subject to inhomogeneous disturbances. The probability of freak waves in the context of these simulations is also discussed. The instability is first studied for the symmetric Lorentz spectrum, and continued for the realistic asymmetric Joint North Sea Wave Project (JONSWAP) spectrum of ocean waves with variable directional spreading and steepness. It is found that instability depends on the directional spreading and parameters $\\alpha $ and $\\gamma $ of the JONSWAP spectrum, where $\\alpha $ and $\\gamma $ are the energy scale and the peak enhancement factor, respectively. Both influence the mean steepness of waves with such a spectrum, although in different ways. Specifically, if the instability stops as a result of the directional spreading, increase of the steepness by increasing $\\alpha $ or $\\gamma $ can reactivate it. A criterion for the instability is suggested as a dimensionless ‘width parameter’, $\\Pi $ . For the unstable conditions, long-time evolution is simulated by integrating the Alber equation numerically. Recurrent evolution is obtained, which is a stochastic counterpart of the Fermi–Pasta–Ulam recurrence obtained for the cubic Schrödinger equation. This recurrence enables us to study the probability of freak waves, and the results are compared to the values given by the Rayleigh distribution. Moreover, it is found that stability–instability transition, the most unstable mode, recurrence duration and freak wave probability depend solely on the dimensionless ‘width parameter’, $\\Pi $ .

Traditionally, the directional distribution of ocean waves has been regarded as unimodal, with energy concentrated mainly on the wind direction. However, numerical experiments and field measurements have already demonstrated that the energy of short waves tends to be accumulated along two off‐wind directions, generating a bimodal directional distribution. Here, numerical simulations of the potential Euler equations are used to investigate the temporal evolution of initially unimodal directional wave spectra. Because this approach does not include external forcing such as wind and breaking dissipation, spectral changes are only driven by nonlinear interactions. The simulations show that the wave energy spreads outward from the spectral peak, following two characteristic directions. As a result, the directional distribution develops a bimodal form as the wavefield evolves. Although bimodal properties are more pronounced in the high wave number part of the spectrum, in agreement with previous field measurements, the simulations also show that directional bimodality characterizes the spectral peak.