Persistence of Peregrine Breather in Random Sea States

Rogue waves are widely recognized as great threats to human oceanic activities. The effectiveness of using the Peregrine breather to model rogue waves has been successfully demonstrated in both numerical and physical wave tank. Additionally, its persistence in random seas has been confirmed in some cases, so that it can also be employed to model rogue waves in random seas. However, based on the results obtained by using the fully nonlinear numerical simulations in this paper, it is reported that the persistence of the Peregrine breather will be affected by the nonlinearities of the random seas, i.e., the spectral bandwidth and the background wave steepness. The investigation on the effects of the two parameters indicates that the Peregrine breather cannot persist thus may not be employed to model rogue waves in random seas in some cases. This paper provides knowledge about how to select background wave parameters, in order to model rogue waves by using the Peregrine breather, which can help saving significant time for designing the experiments

Spectral properties of the Peregrine soliton observed in a water wave tank

The Peregrine soliton, which is commonly considered to be a prototype of a rogue wave in deep water, is observed and measured in a wave tank. Using the measured data of water elevation, we calculated the spectra of the Peregrine soliton and confirmed that they have triangular shapes, in accordance with the theory

Directional Soliton and Breather Beams

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite, consequently, a beam dynamics forms. Spatio-temporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D+1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, plasma, hydrodynamics and optics

Spectral up- and downshifting of Akhmediev breathers under wind forcing

We experimentally and numerically investigate the effect of wind forcing on the spectral dynamics of Akhmediev breathers, a wave-type known to model the modulation instability. We develop the wind model to the same order in steepness as the higher order modifcation of the nonlinear Schroedinger equation, also referred to as the Dysthe equation. This results in an asymmetric wind term in the higher order, in addition to the leading order wind forcing term. The derived model is in good agreement with laboratory experiments within the range of the facility's length. We show that the leading order forcing term amplifies all frequencies equally and therefore induces only a broadening of the spectrum while the asymmetric higher order term in the model enhances higher frequencies more than lower ones. Thus, the latter term induces a permanent upshift of the spectral mean. On the other hand, in contrast to the direct effect of wind forcing, wind can indirectly lead to frequency downshifts, due to dissipative effects such as wave breaking, or through amplification of the intrinsic spectral asymmetry of the Dysthe equation. Furthermore, the definitions of the up- and downshift in terms of peak- and mean frequencies, that are critical to relate our work to previous results, are highlighted and discussed.Comment: 30 pages, 11 figure

Enquête séroépidémiologique de la rhinopneumonie des équidés en Tunisie

Une enquête séroépidémiologique, réalisée sur 789 équidés (400 élevés au Nord-Est de la Tunisie, 389 dans la région du Sahel et du Centre), a permis de détecter, par le test de fixation du complément, des anticorps spécifiques contre le virus de la rhinopneumonie équine. Les résultats ont montré que 15 équidés (1,9 %) étaient séropositifs, avec des taux variables d'anticorps fixant le complément. Ces résultats sont discutés en relation avec ceux obtenus par d'autres auteurs en Tunisie et dans les pays voisins

Experimental Study of Dispersion and Modulational Instability of Surface Gravity Waves on Constant Vorticity Currents

This paper examines experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional (1D + 1) constant vorticity nonlinear Schrödinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from 0 to −0.87 s−1. For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the 95 % confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between 0 and −0.48 s−1. Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE

Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves

In this paper, we model Rogue Waves as localized instabilities emerging from homogeneous and stationary background wavefields, under NLS dynamics. This is achieved in two steps: given any background Fourier spectrum P(k), we use the Wigner transform and Penrose’s method to recover spatially periodic unstable modes, which we call unstable Penrose modes. These can be seen as generalized Benjamin–Feir modes, and their parameters are obtained by resolving the Penrose condition, a system of nonlinear equations involving P(k). Moreover, we show how the superposition of unstable Penrose modes can result in the appearance of localized unstable modes. By interpreting the appearance of an unstable mode localized in an area not larger than a reference wavelength λ0 as the emergence of a Rogue Wave, a criterion for the emergence of Rogue Waves is formulated. Our methodology is applied to δ spectra, where the standard Benjamin–Feir instability is recovered, and to more general spectra. In that context, we present a scheme for the numerical resolution of the Penrose condition and estimate the sharpest possible localization of unstable modes. Keywords: Rogue Waves; Wigner equation; Nonlinear Schrodinger equation; Penrose modes; Penrose conditio

Hydrodynamic X Waves

Stationary wave groups exist in a range of nonlinear dispersive media, including optics, Bose-Einstein condensates, plasma, and hydrodynamics. We report experimental observations of nonlinear surface gravity X waves, i.e., X -shaped wave envelopes that propagate over long distances with constant form. These can be described by the 2 D + 1 nonlinear Schrödinger equation, which predicts a balance between dispersion and diffraction when the envelope (the arms of the X ) travel at ± arctan ( 1 / √ 2 ) ≈ ± 35.2 6 ° to the carrier wave. Our findings may help improve understanding the lifetime of extremes in directional seas and motivate further studies in other nonlinear dispersive media

Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction

We investigate the matter rogue wave in Bose-Einstein Condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; Rogue wave is unstable and the decay rate of the atomic number can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein Condensates