Some breather type solutions of the NLS equation have been suggested by Henderson et al (to appear in Wave Motion) as models for a class 'freak' wave events seen 2D-simulations on surface gravity waves. In this paper we first take closer look these simple and compare them with some simulation data (Henderson to Motion). Our findings tend strengthen idea al. Especially Ma so called Peregrine solution may provide useful analytical events.

Simulations have been performed with a fairly narrow band numerical gravity wave model (higher-order nls type) and computational domain of dimensions fourier modes corresponding to truncated jonswap spectra different angular distributions giving both short- long-crested waves. A development the on so-called benjamin–feir timescale is seen, similar one reported by dysthe et al. (J. Fluid Mech. vol. 478, 2003, p.1). The probability surface elevation crest height are found fit theoretical...

We discuss two independent, large scale experiments performed in wave basins of different dimensions which the statistics surface elevation are addressed. Both facilities equipped with a maker capable generating waves prescribed frequency and directional properties. The experimental results show that probability formation amplitude strongly depends on properties waves. Sea states characterized by long-crested steep more likely to be populated freak respect those spreading.

A wave basin experiment has been performed in the MARINTEK laboratories, one of largest existing three-dimensional tanks world. The aim is to investigate effects directional energy distribution on statistical properties surface gravity waves. Different degrees directionality have considered, starting from long-crested waves up distributions with a spread ±30° at spectral peak. Particular attention given tails function elevation, heights and crests. Comparison simplified model based...

Nonlinear modulational instability of wavepackets is one the mechanisms responsible for formation large-amplitude water waves. Here, mechanically generated waves in a three-dimensional basin and numerical simulations nonlinear have been compared order to assess ability models describe evolution weakly predict probability occurrence extreme within variety random directional wave fields. Numerical performed following two different approaches: integration modified Schrödinger equation potential...

We show experimental evidence that as relatively long unidirectional waves propagate over a sloping bottom, from deeper to shallower domain, there can be local maximum of kurtosis and skewness close the side slope. also probability large wave envelope has near therefore anticipate freak have slope for waves.

We propose a new approach for modeling weakly nonlinear waves, based on enhancing truncated amplitude equations with exact linear dispersion. Our example is the Schrödinger (NLS) equation deep-water waves. The enhanced NLS reproduces exactly conditions four-wave resonance (the “figure 8” of Phillips) even bandwidths greater than unity. Sideband instability uniform Stokes waves limited to finite only, and agrees well results McLean; therefore, sideband cannot produce energy leakage...

Numerical simulations of the evolution gravity wave spectra fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using nonlinear Schrödinger (NLS) equation approximately verify stability criteria Alber (1978) in two-dimensional but not three-dimensional case. Using a modified NLS (Trulsen et al. 2000) ‘relax’ towards quasi-stationary state on timescale (ε 2 ω 0 ) −1 . In this low-frequency face is steepened spectral peak downshifted. The show power-law...

A large number of simulations have been performed to reveal how the occurrence freak waves on deep water depends group and crest lengths for fixed steepness. It is found that there a sharp qualitative transition between short- long-crested sea, length approximately ten wavelengths. For short statistics deviates little from Gaussian their independent (or Benjamin–Feir index, BFI). long strongly non-Gaussian BFI) good indicator increased wave activity.

Abstract. We consider the effect of slowly varying depth on values skewness and kurtosis weakly nonlinear irregular waves propagating from deeper to shallower water. It is known that equilibrium value decreases with decreasing for constant depth. Waves over a sloping bottom must continually adjust toward new state. demonstrate may need considerable horizontal propagation distance in order environment, therefore can be notably different each corresponding both top beyond slope. A change...

This paper presents the effects of two-dimensional bathymetry on evolution skewness and kurtosis surface elevation velocity field in long-crested irregular waves propagating over a circular shoal submerged bar with semicircular step. For shoal, we show that has local maximum top shoal. We find horizontal similar behaviour to elevation, but two maxima at different locations lee side step, which acts converging lens, refraction contributes statistical properties deviate from Gaussian statistics.

The commonly used forms of the modified nonlinear Schrödinger equations for deep water (Dysthe, Proc. R. Soc. Lond. A, vol. 369, 1979, p. 105) and arbitrary depth (Brinch–Nielsen & Jonsson, Wave Motion , 8, 1986, 455) do not conserve momentum are Hamiltonian. We show how these can be brought into Hamiltonian form, with action, being conserved. derive new fourth-order equation depth, starting from Zakharov enhanced kernel Krasitskii ( J. Fluid Mech. 272, 1994, 1).

Linear refraction of waves on inhomogeneous current is known to provoke extreme waves. We investigate the effect nonlinearity this phenomenon, with respect variation significant wave height, kurtosis and occurrence freak Monte Carlo simulations are performed employing a modified nonlinear Schrödinger equation that includes effects prescribed non-potential current. recommend should be defined by local criterion according distribution at each location constant current, not global either...

Using a Boussinesq model with improved linear dispersion, we show numerical evidence that bottom non-uniformity can provoke significantly increased probability of freak waves as wave field propagates into shallower water, in agreement recent experimental results [K. Trulsen, H. Zeng, and O. Gramstad, “Laboratory provoked by non-uniform bathymetry,” Phys. Fluids 24, 097101 (2012)]. Increased values skewness, kurtosis, be found on the side slope, maximum close to end slope. The is typically...

Abstract We discuss the crossing sea state and probability of rogue waves during accident tanker Prestige on 13 November 2002. present newly computed hindcast spectra for every hour that day at nearby locations, showing development a bimodal with two wave systems nearly right angle. employ four different nonlinear models capable computing phase‐resolved surface from spectra, allowing us to estimate statistics occurrence waves. At location moment accident, give expected values kurtosis κ =...

Experimental and numerical evidence have shown that nonuniform bathymetry may alter significantly the statistical properties of surface elevation in irregular wave fields. The probability “rogue” waves is increased near edge upslope as long-crested propagate into shallower water. present paper studies statistics kinematics propagating over a shoal with Monte Carlo approach. High order spectral method employed propagation model, variational Boussinesq model to calculate kinematics. horizontal...

We report laboratory experiments of long-crested irregular water surface waves propagating over a shoal, with attention to the region down-slope behind shoal. measure elevation field, horizontal velocity field in water, and resulting forces on submerged cylinder placed In addition, we calculate acceleration field. From this, find that presence shoal can modify wave such be enhanced thicker extreme tails increased values skewness kurtosis depending location cylinder. The spatial dependence...

Abstract Wave statistical properties and occurrence of extreme rogue waves in crossing sea states are investigated. Compared to previous studies a more extensive set investigated, both with respect spectral shape the individual wave systems angle separation peak frequency two systems. It is shown that, because effects described by Piterbarg, for linear state expected maximum crest elevation over given surface area depends on so that largest when propagate close 90°. further nonlinear...

The conservative evolution of weakly nonlinear narrow-banded gravity waves in deep water is investigated numerically with a modified Schrödinger equation, for application to wide wave tanks. When the constrained two dimensions, no permanent shift peak spectrum observed. In three allowing oblique sideband perturbations, permanently downshifted. Dissipation or breaking may therefore not be necessary produce downshift. emergence standing across tank also predicted.

Analysis of moored current measurements in the Strait Gibraltar is provided here. The vertical internal displacements (double amplitudes) with a semidiurnal frequency are extremely large and sometimes exceed 200 m. It found that these associated forced tidal waves over Camarinal Sill, which crosses strait. separation components showed amplitude tide M2 69 m, while amplitudes other (S2, K1, O1) 3–5 times smaller. decrease distance from sill and, at 50 km sill, 3 smaller than sill. energy...

The authors discuss the spatio-temporal domain, here referred to as predictable zone, in which waves can be predicted deterministically based on an observation a limited spatial or temporal domain. A key issue is whether group phase speed of observed governs extent zone. have addressed this again using linear wave theory both computer-generated synthetic fields and laboratory experimental observations. find that adequately indicates zone for forecasting horizons relevant offshore maritime...