Freak Wave Formation from Phase Coherence

Physical Review Letters, 2010

Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed conical scatterers. At high frequencies, the flow shows branching structures similar to those observed in stationary imaging of electron flow. Semiclassical simulations confirm that caustics in the ray dynamics are responsible for these structures. At lower frequencies, large deviations from Rayleigh's law for the wave height distribution are observed, which can only partially be described by existing multiple-scattering theories. In particular there are "hot spots" with intensities far beyond those expected in a random wave field. The results are analogous to flow patterns observed in the ocean in the presence of spatially varying currents or depth variations in the sea floor, where branches and hot spots lead to an enhanced frequency of freak or rogue wave formation.

Physica D: Nonlinear Phenomena, 2000

The mechanism of the freak wave formation related to the spatial-temporal focusing is studied within the framework of the Korteweg-de Vries equation. A method to find the wave trains whose evolution leads to the freak wave formation is proposed. It is based on the solution of the Korteweg-de Vries equation with an initial condition corresponding to the expected freak wave. All solutions of this Cauchy problem by the reversal of abscissa represent the possible forms of wave trains which evolve into the freak wave. It is found that freak waves are almost linear waves, and their characteristic Ursell parameter is small. The freak wave formation is possible also from the random wave field and the numerical simulation describes the details of this phenomenon. It is shown that freak waves can be generated not only for specific conditions, but also for relative wide classes of the wave trains. This mechanism explains the rare and short-lived character of the freak wave.

European Journal of Mechanics - B/Fluids, 2006

The freak wave formation due to the dispersive focusing mechanism is investigated experimentally without wind and in presence of wind. An asymmetric behaviour between the focusing and defocusing stages is found when the wind is blowing over the mechanically generated gravity wave group. This feature corresponds physically to the sustain of the freak wave mechanism on longer periods of time. Furthermore, a weak amplification of the freak wave and a shift in the downstream direction of the point where the waves merge are observed. The experimental results suggest that the Jeffreys' sheltering mechanism could play a key role in the coherence of the group of the freak wave. Hence, the Jeffreys' sheltering theory is introduced in a fully nonlinear model. The results of the numerical simulations confirm that the duration of the freak wave event increases with the wind velocity.

Comptes Rendus Mécanique, 2002

We are concerned by a special mechanism that can explain the formation of freak waves. We study numerically the long time evolution of a surface gravity wave packet, comparing a fully nonlinear model with Schrödinger-like simplified equations. We observe that the interaction between envelope solitons generates large waves. This is predicted by both models. The fully nonlinear simulations show a qualitative behaviour that differs significantly from the ones preticted by Schrödinger models, however. Indeed, the occurence of freak waves is much more frequent with the fully nonlinear model. This is a consequence of the long-time interaction between envelope solitons, which, in the fully nonlinear model, is totally different from the Schrödinger scenario. The fundamental differences appear for times when the simplified equations cease to be valid. Possible statistical models, based on the latter, should hence under-estimate the probability of freak wave formation. To cite this article: D. Clamond, J. Grue, C. R. Mecanique 330 (2002) 575-580.  2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS waves / freak wave / soliton enveloppe / interaction

Coastal Engineering Proceedings, 2011

The issues of freak waves are more and more popular since the late 1980s. This study tries to use the wavelet scalogram of freak wave records to investigate the energy characteristics during the occurrence of the freak waves. Through the analysis of the wave energy and phase, it is found that as freak waves occur, the component waves will lead to constructive superposition due to similar phases. The wavelet scalogram provides the other idea to explain the feature of freak waves.

Journal of Geophysical Research, 2004

1] The results of laboratory measurements on limiting freak waves in the presence of currents are reported. Both dispersive spatial-temporal focusing and wave-current interaction are used to generate freak waves in a partial random wave field in the presence of currents. Wave group structure, for example, spectral slope and frequency bandwidth, is found to be critical to the formation and the geometric properties of freak waves. A nondimensional spectral bandwidth is shown to well represent wave group structure and proves to be a good indicator in determining limiting freak wave characteristics. The role of a co-existing current in the freak wave formation is recognized. Experimental results confirm that a random wave field does not prevent freak wave formation due to dispersive focusing. Strong opposing currents inducing partial wave blocking significantly elevate the limiting steepness and asymmetry of freak waves. At the location where a freak wave occurs, the Fourier spectrum exhibits local energy transfer to high-frequency waves. The Hilbert-Huang spectrum, a time-frequency-amplitude spectrum, depicts both the temporal and spectral evolution of freak waves. A strong correlation between the magnitude of interwave instantaneous frequency modulation and the freak wave nonlinearity (steepness) is observed. The experimental results provide an explanation to address the occurrence and characteristic of freak waves in consideration of the onset of wave breaking.

2022

The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection of side-bands, which translate into an amplitude modulation of the wave field. The nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear Schrödinger equation (NLSE). In that case, the amplitude modulation of such coherent extreme wave structures is connected to a particular phase-shift seed in the carrier wave. In this letter, we show that phase-shifts localization applied to the background, excluding any amplitude modulation excitation, can indeed trigger extreme events. Such rogue waves can be for instance generated by considering the parametrization of fundamental breathers and thus, by seeding only the local phase-shift information to the regular carrier wave. Our wave tank experiments show an excellent agreement with the expected NLSE hydrodynamics and confirm that even though delayed in their evolution, breather-type extreme waves can be generated from a purely regular wave train. Such novel focusing mechanism awaits experimental confirmation in other nonlinear media, such optics, plasma, and Bose-Einstein condensates.

Physical Review Letters, 2001

Freak waves are very large, rare events in a random ocean wave train. Here we study the numerical generation of freak waves in a random sea state characterized by the JONSWAP power spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schroedinger (NLS) equation. We identify two parameters in the power spectrum that control the nonlinear dynamics: the Phillips parameter $\alpha$ and the enhancement coefficient $\gamma$. We discuss how freak waves in a random sea state are more likely to occur for large values of $\alpha$ and $\gamma$. Our results are supported by extensive numerical simulations of the NLS equation with random initial conditions. Comparison with linear simulations are also reported.

2006

This report deals with extreme wave phenomena. Exploration of the classical wave theories are made, both on the theoratical approach and on the statistical one. The first one shows wave generation phenomenon using only Euler's equation for a perfect fluid and gravity. On the other one, the statistical approach provides us with more real observations. Both models fail to explain some rare (or not so rare ?) events: freak waves. Then we defined what is a freak wave and some of the explanations that are given. Exploration on the non linear Schrödinger equation, which is known to give birth to gigantic waves is then the path taken. This equation could be easily derived from Euler's equations. Numerical solution of this equation are provided in the last chapter. Finally, the third part deals with spectral methods and how they are used to compute very easily non linear interaction for waves. Last chapter provides also results on this. In fact, the last chapter is devoted to the results obtained, either on solving NLS, either on the computation of surface waves.