152 research outputs found
Freak Waves in Random Oceanic Sea States
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 and the enhancement
coefficient . We discuss how freak waves in a random sea state are more
likely to occur for large values of and . Our results are
supported by extensive numerical simulations of the NLS equation with random
initial conditions. Comparison with linear simulations are also reported.Comment: 7 pages, 6 figures, to be published in Phys. Rev. Let
Extreme events in discrete nonlinear lattices
We perform statistical analysis on discrete nonlinear waves generated though
modulational instability in the context of the Salerno model that interpolates
between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable
discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in
the form of discrete rogue or freak waves that may arise as a result of rapid
coalescence of discrete breathers or other nonlinear interaction processes. We
find power law dependence in the wave amplitude distribution accompanied by an
enhanced probability for freak events close to the integrable limit of the
equation. A characteristic peak in the extreme event probability appears that
is attributed to the onset of interaction of the discrete solitons of the AL
equation and the accompanied transition from the local to the global
stochasticity monitored through the positive Lyapunov exponent of a nonlinear
map.Comment: 5 pages, 4 figures; reference added, figure 2 correcte
Role of friction-induced torque in stick-slip motion
We present a minimal quasistatic 1D model describing the kinematics of the
transition from static friction to stick-slip motion of a linear elastic block
on a rigid plane. We show how the kinematics of both the precursors to
frictional sliding and the periodic stick-slip motion are controlled by the
amount of friction-induced torque at the interface. Our model provides a
general framework to understand and relate a series of recent experimental
observations, in particular the nucleation location of micro-slip instabilities
and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure
Linear and Nonlinear Rogue Wave Statistics in the Presence of Random Currents
We review recent progress in modeling the probability distribution of wave
heights in the deep ocean as a function of a small number of parameters
describing the local sea state. Both linear and nonlinear mechanisms of rogue
wave formation are considered. First, we show that when the average wave
steepness is small and nonlinear wave effects are subleading, the wave height
distribution is well explained by a single "freak index" parameter, which
describes the strength of (linear) wave scattering by random currents relative
to the angular spread of the incoming random sea. When the average steepness is
large, the wave height distribution takes a very similar functional form, but
the key variables determining the probability distribution are the steepness,
and the angular and frequency spread of the incoming waves. Finally, even
greater probability of extreme wave formation is predicted when linear and
nonlinear effects are acting together.Comment: 25 pages, 12 figure
On the modulation instability development in optical fiber systems
Extensive numerical simulations were performed to investigate all stages of
modulation instability development from the initial pulse of pico-second
duration in photonic crystal fiber: quasi-solitons and dispersive waves
formation, their interaction stage and the further propagation. Comparison
between 4 different NLS-like systems was made: the classical NLS equation, NLS
system plus higher dispersion terms, NLS plus higher dispersion and
self-steepening and also fully generalized NLS equation with Raman scattering
taken into account. For the latter case a mechanism of energy transfer from
smaller quasi-solitons to the bigger ones is proposed to explain the dramatical
increase of rogue waves appearance frequency in comparison to the systems when
the Raman scattering is not taken into account.Comment: 9 pages, 54 figure
Solitary wave interaction in a compact equation for deep-water gravity waves
In this study we compute numerical traveling wave solutions to a compact
version of the Zakharov equation for unidirectional deep-water waves recently
derived by Dyachenko & Zakharov (2011) Furthermore, by means of an accurate
Fourier-type spectral scheme we find that solitary waves appear to collide
elastically, suggesting the integrability of the Zakharov equation.Comment: 8 pages, 5 figures, 23 references. Other author's papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh/ . arXiv admin note:
text overlap with arXiv:1204.288
Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves
We study the nonlinear energy transfer around the peak of the spectrum of
surface gravity waves by taking into account nonhomogeneous effects. In the
narrow-banded approximation the kinetic equation resulting from a
nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at
the same time the random version of the Benjamin-Feir instability and the
Landau damping phenomenon. We analytically derive the values of the Phillips'
constant and the enhancement factor for which the
narrow-banded approximation of the JONSWAP spectrum is unstable. By performing
numerical simulations of the nonlinear Schr\"{o}dinger equation we check the
validity of the prediction of the related kinetic equation. We find that the
effect of Landau damping is to suppress the formation of coherent structures.
The problem of predicting freak waves is briefly discussed.Comment: 4 pages, 3 figure
Observation of Kuznetsov-Ma soliton dynamics in optical fibre
The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation
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
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