223 research outputs found
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Time-reversal (TR) refocusing of waves is one of fundamental principles in
wave physics. Using the TR approach, "Time-reversal mirrors" can physically
create a time-reversed wave that exactly refocus back, in space and time, to
its original source regardless of the complexity of the medium as if time were
going backwards. Lately, laboratory experiments proved that this approach can
be applied not only in acoustics and electromagnetism but also in the field of
linear and nonlinear water waves. Studying the range of validity and
limitations of the TR approach may determine and quantify its range of
applicability in hydrodynamics. In this context, we report a numerical study of
hydrodynamic TR using a uni-directional numerical wave tank, implemented by the
nonlinear high-order spectral method, known to accurately model the physical
processes at play, beyond physical laboratory restrictions. The applicability
of the TR approach is assessed over a variety of hydrodynamic localized and
pulsating structures' configurations, pointing out the importance of high-order
dispersive and particularly nonlinear effects in the refocusing of hydrodynamic
stationary envelope solitons and breathers. We expect that the results may
motivate similar experiments in other nonlinear dispersive media and encourage
several applications with particular emphasis on the field of ocean
engineering.Comment: 14 pages, 17 figures ; accepted for publication in Phys. Rev. Fluid
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 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
Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations
The rogue wave solutions (rational multi-breathers) of the nonlinear
Schrodinger equation (NLS) are tested in numerical simulations of weakly
nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order
solutions from 1 to 5 are considered. A higher accuracy of wave propagation in
space is reached using the modified NLS equation (MNLS) also known as the
Dysthe equation. This numerical modelling allowed us to directly compare
simulations with recent results of laboratory measurements in
\cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we
employed fully nonlinear simulations of potential Euler equations. These
simulations provided us with basic characteristics of long time evolution of
rational solutions of the NLS equation in the case of near breaking conditions.
The analytic NLS solutions are found to describe the actual wave dynamics of
steep waves reasonably well.Comment: under revision in Physical Review
Superregular breathers in optics and hydrodynamics: Omnipresent modulation instability beyond simple periodicity
Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales
Experiments on wind-perturbed rogue wave hydrodynamics using the Peregrine breather model
Being considered as a prototype for description of oceanic rogue waves, the Peregrine breather solution of the nonlinear Schrödinger equation has been recently observed and intensely investigated experimentally in particular within the context of water
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
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