Miguel Onorato

Freak Waves in Random Oceanic Sea States

Freak waves are very large, rare events in a random ocean wave train. Here we study their generation in a random sea state characterized by the Joint North Sea Wave Project spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schrödinger (NLS) equation. We show from extensive numerical simulations of the NLS equation how freak waves in a random sea state are more likely to occur for large values of the Phillips parameter alpha and the enhancement coefficient gamma. Comparison with linear simulations is also reported.

The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains

Abstract Rogue waves are rare “giant”, “freak”, “monster” or “steep wave” events in nonlinear deep water gravity waves which occasionally rise up to surprising heights above the background wave field. Holes are deep troughs which occur before and/or after the largest rogue crests. The dynamical behavior of these giant waves is here addressed as solutions of the nonlinear Schrodinger equation in both 1+1 and 2+1 dimensions. We discuss analytical results for 1+1 dimensions and demonstrate numerically, for certain sets of initial conditions, the ubiquitous occurrence of rogue waves and holes in 2+1 spatial dimensions. A typical wave field evidently consists of a background of stable wave modes punctuated by the intermittent upthrusting of unstable rogue waves.

Extreme wave events in directional, random oceanic sea states

We discuss the effect of the directional spreading on the occurrence of extreme wave events. We numerically integrate the envelope equation recently proposed by Trulsen et al. [Phys. Fluids 12, 2432 (2000)] as a weakly nonlinear model for realistic oceanic gravity waves. Initial conditions for numerical simulations are characterized by the spatial JONSWAP power spectrum for several values of the significant wave height, steepness, and directional spreading. We show that by increasing the directionality of the initial spectrum the appearance of extreme events is reduced.

Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin

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.

Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime

We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics.

Modulational instability and non-Gaussian statistics in experimental random water-wave trains

We study random, long-crested surface gravity waves in the laboratory environment. Starting with wave spectra characterized by random phases we consider the development of the modulational instability and the consequent formation of large amplitude waves. We address both dynamical and statistical interpretations of the experimental data. While it is well known that the Stokes wave nonlinearity leads to non-Gaussian statistics, we also find that the presence of the modulational instability is responsible for the departure from a Gaussian behavior, indicating that, for particular parameters in the wave spectrum, coherent unstable modes are quite prevalent, leading to the occurrence of what might be called a “rogue sea.” Statistical results are also compared with ensemble numerical simulations of the Dysthe equation.

On the Estimation of the Kurtosis in Directional Sea States for Freak Wave Forecasting

Based on Monte Carlosimulationsof the nonlinear Schrodingerequationin two horizontal dimensions, the dependence of the kurtosis on the directional energy distribution of the initial conditions is examined. The parametric survey is carried out to obtain the behavior of the kurtosis as function of the Benjamin-Feir index and directional spread in directional sea states. As directional dispersion effect becomes significant, the kurtosis monotonically decreases in comparison with the unidirectional waves. A parameterization of the kurtosisestimatedfromdirectionalspectra isproposedhere;the erroroftheparameterization isat most10%. The parameterization is verified against laboratory data, and good agreement is obtained.

The Intermediate Water Depth Limit of the Zakharov Equation and Consequences for Wave Prediction

Finite-amplitude deep-water waves are subject to modulational instability, which eventually can lead to the formation of extreme waves. In shallow water, finite-amplitude surface gravity waves generate a current and deviations from the mean surface elevation. This stabilizes the modulational instability, and as a consequence the process of nonlinear focusing ceases to exist when kh 1.363. This is a well-known property of surface gravity waves. Here it is shown for the first time that the usual starting point, namely the Zakharov equation, for deriving the nonlinear source term in the energy balance equation in wave forecasting models, shares this property as well. Consequences for wave prediction are pointed out.

Triggering Rogue Waves in Opposing Currents

We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity U(0) and the wave group velocity c(g). We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing nonlinear Schrödinger equation with nonconstant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.