Related papers: Evolution of extreme nonlinear wave fields over st…

Bathymetric changes have been experimentally shown to affect the occurrence of rogue waves. We recently derived a non-homogeneous correction to the spectral analysis, allowing to describe the evolution of the rogue wave probability over a…

The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…

Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…

The impact of shoaling on linear water waves is well-known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least…

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves.…

Nonlinear wave interactions affect the evolution of steep wave groups, their breaking and the associated kinematic field. Laboratory experiments are performed to investigate the effect of the underlying focussing mechanism on the shape of…

In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…

Rogue waves (RWs) can form on the ocean surface due to quasi-four wave resonant interaction or superposition principle. Both mechanisms have been acutely studied. The first of the two is known as the nonlinear focusing mechanism and leads…

Nonlinear wave run-up on the beach caused by harmonic wave maker located at some distance from the shore line is studied experimentally. It is revealed that under certain wave excitation frequencies a significant increase in run-up…

Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects…

We provide a justification with rigorous error estimates showing that the leading term in weakly nonlinear geometric optics expansions of highly oscillatory reflecting pulses is close to the uniquely determined exact solution for small…

We study the formation of extreme events in incoherent systems described by envelope equations, such as the Nonliner Schr\"odinger equation. We derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the…

The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…

We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation…

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…

We study the stabilization and the wellposedness of solutions of the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation. The novelty of this paper is that we deal with the difficulty that the main…

Wave impact and run-up onto vertical obstacles are among the most important phenomena which must be taken into account in the design of coastal structures. From linear wave theory, we know that the wave amplitude on a vertical wall is twice…

Different from statistical considerations on stochastic wave fields, this paper aims to contribute to the understanding of (some of) the underlying physical phenomena that may give rise to the occurrence of extreme, rogue, waves. To that…

We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growth rate is vastly surpassed for steeper waves by an…

We study experimentally, in a large-scale basin, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We observe the emergence of nonlinear localized structures that evolve on a stochastic wave…