We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.

Stereo video techniques are effective for estimating the space-time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. To prove this, we consider an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea. In particular, we deployed WASS at the oceanographic platform Acqua Alta, off the Venice coast, Italy. Three experimental studies were performed, and the overlapping field of view of the acquired stereo images covered an area of approximately 1100 m2. Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directional spectra and wave statistics that agree well with theoretical models. From the observed wavenumber-frequency spectrum one can also predict the vertical profile of the current flow underneath the wave surface. Finally, future improvements of WASS and applications are discussed

We present a second-order stochastic model of weakly nonlinear waves and develop theoretical expressions for the expected shape of large surface displacements. The model also leads to an exact theoretical expression for the statistical distribution of large wave crests in a form that generalizes the Tayfun distribution (Tayfun, J. Geophys. Res., vol. 85, 1980, p. 1548). The generalized distribution depends on a steepness parameter given by μ = λ₃/3, where λ₃ represents the skewness coefficient of surface displacements. It converges to the Tayfun distribution in narrowband waves, where both distributions describe the crests of all waves well. In broadband waves, the generalized distribution represents the crests of large waves just as well whereas the Tayfun distribution appears as an upper bound and tends to overestimate them. However, the theoretical nature of the generalized distribution presents practical difficulties in oceanic applications. We circumvent these by adopting an appropriate approximation for the steepness parameter. Comparisons with wind-wave measurements from the North Sea suggest that this approximation allows both distributions to assume an identical form with which we can describe the distribution of large wave crests fairly accurately. The same comparisons also show that third-order nonlinear effects do not appear to have any discernable effect on the statistics of large surface displacements or wave crests.

Linear defect modes in one-dimensional photonic lattices are studied theoretically. For negative (repulsive) defects, various localized defect modes are found. The strongest confinement of the defect modes appears when the lattice intensity at the defect site is nonzero rather than zero. When launched at small angles into such a defect site of the lattice, a Gaussian beam can be trapped and undergo snake oscillations under appropriate conditions.

Observed crest speeds of maximally steep, breaking water waves are much slower than expected. Our fully nonlinear computations of unsteadily propagating deep water wave groups show that each wave crest approaching its maximum height slows down significantly and either breaks at this reduced speed, or accelerates forward unbroken. This previously noted crest slowdown behavior was validated as generic in our extensive laboratory and field observations. It is likely to occur in unsteady dispersive nonlinear wave groups in other natural systems.