36 research outputs found
Extreme dynamics of wave groups on jet currents
Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in Shrira and Slunyaev [“Nonlinear dynamics of trapped waves on jet currents and rogue waves,” Phys. Rev. E 89, 041002(R) (2014)] for the waves trapped on current robust long-lived envelope solitary waves localized in both horizontal directions become possible, such wave patterns cannot exist in the absence of the current. In this work, we investigate interactions between envelope solitons of essentially nonlinear trapped waves by means of the direct numerical simulation of the Euler equations. The solitary waves remain localized in both horizontal directions for hundreds of wave periods. We also demonstrate a high efficiency of the developed analytic nonlinear mode theory for description of the long-lived solitary patterns up to remarkably steep waves. We show robustness of the solitons in the course of interactions and the possibility of extreme wave generation as a result of solitons' collisions. Their collisions are shown to be nearly elastic. These robust solitary waves obtained from the Euler equations without weak nonlinearity assumptions are viewed as a plausible model of rogue waves on jet currents
Self-similarity of rogue wave generation in gyrotrons: Beyond the Peregrine breather
Within the framework of numerical simulations, we study the gyrotron dynamics
under conditions of a significant excess of the operating current over the
starting value, when the generation of electromagnetic pulses with anomalously
large amplitudes ("rogue waves") are realized. We demonstrate that the relation
between peak power and duration of rogue waves is self-similar, but does not
reproduce the one characteristic for Peregrine breathers. Remarkably, the
discovered self-similar relation corresponds to the exponential nonlinearity of
an equivalent Schr\"odinger-like evolution equation. This interpretation can be
used as a theoretical basis for explaining the giant amplitudes of gyrotron
rogue waves
Freak waves in 2005
International audienceInformation about freak wave events in the ocean reported by mass media and derived from personal observations in 2005 is collected and analysed. Nine cases are selected as true freak wave events from a total number of 27 mentioned. Besides rogue waves in the open sea, the problem of freak wave events on the shore is emphasized. These accidents are related to unexpected wave impact upon the coast and shore constructions or to sudden intensive flooding of the coast. Of the nine events considered reliable here, three events correspond to open-sea cases, while the six others occurred nearshore
Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry
Experimental results describing random, uni-directional, long crested, water
waves over non-uniform bathymetry confirm the formation of stable coherent wave
packages traveling with almost uniform group velocity. The waves are generated
with JONSWAP spectrum for various steepness, height and constant period. A set
of statistical procedures were applied to the experimental data, including the
space and time variation of kurtosis, skewness, BFI, Fourier and moving Fourier
spectra, and probability distribution of wave heights. Stable wave packages
formed out of the random field and traveling over shoals, valleys and slopes
were compared with exact solutions of the NLS equation resulting in good
matches and demonstrating that these packages are very similar to deep water
breathers solutions, surviving over the non-uniform bathymetry. We also present
events of formation of rogue waves over those regions where the BFI, kurtosis
and skewness coefficients have maximal values.Comment: 41 pages, 21 figure
Rogue waters
In this essay we give an overview on the problem of rogue or freak wave
formation in the ocean. The matter of the phenomenon is a sporadic occurrence
of unexpectedly high waves on the sea surface. These waves cause serious danger
for sailing and sea use. A number of huge wave accidents resulted in damages,
ship losses and people injuries and deaths are known. Now marine researchers do
believe that these waves belong to a specific kind of sea waves, not taken into
account by conventional models for sea wind waves. This paper addresses to the
nature of the rogue wave problem from the general viewpoint based on the wave
process ideas. We start introducing some primitive elements of sea wave physics
with the purpose to pave the way for the further discussion. We discuss linear
physical mechanisms which are responsible for high wave formation, at first.
Then, we proceed with description of different sea conditions, starting from
the open deep sea, and approaching the sea cost. Nonlinear effects which are
able to cause rogue waves are emphasised. In conclusion we briefly discuss the
generality of the physical mechanisms suggested for the rogue wave explanation;
they are valid for rogue wave phenomena in other media such as solid matters,
superconductors, plasmas and nonlinear opticsComment: will be published in Contemporary Physic
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
Modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet
We study the nonlinear modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet of given thickness and density in a basin of a constant depth. For weakly nonlinear perturbations, we derive the nonlinear Schrodinger equation and investigate the conditions when a quasi-sinusoidal wave becomes unstable with respect to amplitude modulation. The domains of instability are presented in the planes of governing physical parameters; the shapes of the domains exhibit fairly complicated patterns. It is shown that, under certain conditions, the modulational instability can develop from shorter groups and for fewer wave periods than in the situation of deep-water gravity waves on a free water surface. The modulational instability can occur at the conditions shallower than that known for the free water surface kh = 1.363, where k is the wavenumber and h is the water depth. Estimates of parameters of modulated waves are given for the typical physical conditions of an ice-covered sea