Modulational instability and non-Gaussian statistics in experimental random water-wave trains

2005 ◽  
Vol 17 (7) ◽  
pp. 078101 ◽  
Author(s):  
M. Onorato ◽  
A. R. Osborne ◽  
M. Serio ◽  
L. Cavaleri
Keyword(s):  
Water Wave ◽  
Modulational Instability ◽  
Wave Trains ◽  
Gaussian Statistics ◽  
Non Gaussian

Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution

2013 ◽  
Vol 720 ◽  
pp. 357-392 ◽  
Author(s):  
Wenting Xiao ◽  
Yuming Liu ◽  
Guangyu Wu ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Linear Theory ◽  
Nonlinear Wave ◽  
Rogue Wave ◽  
Modulational Instability ◽  
Rogue Waves ◽  
Single Wave ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Nonlinear Wave Field

AbstractWe study the occurrence and dynamics of rogue waves in three-dimensional deep water using phase-resolved numerical simulations based on a high-order spectral (HOS) method. We obtain a large ensemble of nonlinear wave-field simulations ($M= 3$ in HOS method), initialized by spectral parameters over a broad range, from which nonlinear wave statistics and rogue wave occurrence are investigated. The HOS results are compared to those from the broad-band modified nonlinear Schrödinger (BMNLS) equations. Our results show that for (initially) narrow-band and narrow directional spreading wave fields, modulational instability develops, resulting in non-Gaussian statistics and a probability of rogue wave occurrence that is an order of magnitude higher than linear theory prediction. For longer times, the evolution becomes quasi-stationary with non-Gaussian statistics, a result not predicted by the BMNLS equations (without consideration of dissipation). When waves spread broadly in frequency and direction, the modulational instability effect is reduced, and the statistics and rogue wave probability are qualitatively similar to those from linear theory. To account for the effects of directional spreading on modulational instability, we propose a new modified Benjamin–Feir index for effectively predicting rogue wave occurrence in directional seas. For short-crested seas, the probability of rogue waves based on number frequency is imprecise and problematic. We introduce an area-based probability, which is well defined and convergent for all directional spreading. Based on a large catalogue of simulated rogue wave events, we analyse their geometry using proper orthogonal decomposition (POD). We find that rogue wave profiles containing a single wave can generally be described by a small number of POD modes.

Experimental study of the stability of deep-water wave trains including wind effects

1999 ◽  
Vol 401 ◽  
pp. 55-84 ◽  
Author(s):  
TAKUJI WASEDA ◽  
MARSHALL P. TULIN
Keyword(s):  
Deep Water ◽  
Growth Rates ◽  
Water Wave ◽  
Modulational Instability ◽  
Wave System ◽  
Strong Wind ◽  
Wind Effects ◽  
Ocean Engineering ◽  
Wave Trains ◽  
Deep Water Wave

An experimental investigation on the initial instability of nonlinear deep-water wave trains including wind effects is reported. The experiment was conducted at the Ocean Engineering Laboratory wind-wave facility (50 m long, 4.2 m wide, 2.1 m deep), with a fully computer-controlled mechanical wave generator to explore the parameter space: steepness; sideband frequency; wind speed. The estimated growth rates of the Benjamin–Feir instability from seeded wind-free experiments agreed well with the theoretical prediction derived from Krasitskii's four-wave reduced equation as computed here. Wind was added to the same wave system; the growth rates of the sidebands were reduced for weak, and enhanced for strong wind forcing. Experiments with naturally selected sidebands, i.e. unseeded, were conducted as well; measurements showed that wind did not inhibit the growth of sidebands in the case of either two-dimensional or three-dimensional instabilities. A comparison of the results with earlier work suggests that there are two independent effects of wind: first, the alteration of the inviscid growth for a given modulational frequency as shown by comparison with the seeded experiments without wind; second, a change in the natural modulational frequency appearing in the presence of wind which is a function of the wave age, as observed in unseeded experiments. Both effects combined will determine whether the modulational instability is enhanced or suppressed; comparison of experimental results with theoretical predictions suggests that the effect of wind on the natural selection of the modulational frequency is the dominant effect. It was shown that for moderate to old waves, the net effect of wind on the modulational instability is small. For all the experiments except a few unseeded cases with weak breakers, the modulation was small and no breaking was observed within the tank.

scholarly journals Occurrence of extreme waves in three-dimensional mechanically generated wave fields propagating over an oblique current

2011 ◽  
Vol 11 (3) ◽  
pp. 895-903 ◽  
Author(s):  
A. Toffoli ◽  
L. Cavaleri ◽  
A. V. Babanin ◽  
M. Benoit ◽  
E. M. Bitner-Gregersen ◽  
...  
Keyword(s):  
Modulational Instability ◽  
Three Dimensional ◽  
Wave Direction ◽  
Subsequent Increase ◽  
Wave Fields ◽  
Wave Trains ◽  
Directional Wave ◽  
The Mean ◽  
Wave Maker ◽  
Non Gaussian

Abstract. Laboratory experiments were performed to study the dynamics of three- dimensional mechanically generated waves propagating over an oblique current in partial opposition. The flow velocity varied along the mean wave direction of propagation with an increasing trend between the wave-maker and the centre of the tank. Tests with regular wave packets traversing the area of positive current gradient showed that the concurrent increase of wave steepness triggered modulational instability on otherwise stable wave trains and hence induced the development of very large amplitude waves. In random directional wave fields, the presence of the oblique current resulted in a weak reinforcement of wave instability with a subsequent increase of the probability of occurrence of extreme events. This seems to partially compensate the suppression of strongly non-Gaussian properties due to directional energy distribution.

Extreme vertical drafts in the polar summer mesosphere: A super mesospheric bore?

2021 ◽  
Author(s):  
Jorge Luis Chau ◽  
Raffaele Marino ◽  
Fabio Feraco ◽  
Juan M. Urco ◽  
Gerd Baumgarten ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Extreme Event ◽  
Ice Clouds ◽  
Wind Variability ◽  
Near Space ◽  
The Earth ◽  
Radar Echoes ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Impact Planning

<p>The polar summer mesosphere is the Earth’s coldest region, allowing the formation of mesospheric ice clouds, potentially linked to climate change. These clouds produce strong radar echoes that are used as tracers of mesospheric dynamics. Here we report the first observations of extreme vertical drafts in the mesosphere, characterized by velocities larger than 40 m/s, i.e., more than five standard deviations larger than the observed wind variability. The morphology seems to resemble mesospheric bores, however the scales observed are much larger. Powerful vertical drafts, intermittent in space and time, emerge also in direct numerical simulations of stratified flows, predicting non-Gaussian statistics of vertical velocities. This evidence suggests that mesospheric bores might result from the interplay of gravity waves and turbulent motions. Our extreme event is interpreted as a mesospheric "super-bore", impacting mesospheric mixing and ice-formation, and would potentially impact planning of sub-orbital flights, and the investigation of biological material in the near space.</p>

Non-Gaussian statistics of partially coherent light in atmospheric turbulence

2020 ◽  
Vol 29 (6) ◽  
pp. 064203 ◽  
Author(s):  
Hao Ni ◽  
Chunhao Liang ◽  
Fei Wang ◽  
Yahong Chen ◽  
Sergey A. Ponomarenko ◽  
...  
Keyword(s):  
Atmospheric Turbulence ◽  
Coherent Light ◽  
Partially Coherent ◽  
Partially Coherent Light ◽  
Gaussian Statistics ◽  
Non Gaussian

Experimental investigation on the evolution of the modulation instability with dissipation

2012 ◽  
Vol 711 ◽  
pp. 101-121 ◽  
Author(s):  
Y. Ma ◽  
G. Dong ◽  
M. Perlin ◽  
X. Ma ◽  
G. Wang
Keyword(s):  
Experimental Investigation ◽  
Modulational Instability ◽  
Experimental Results ◽  
Damping Term ◽  
Wave Flume ◽  
Perturbation Frequency ◽  
Linear Damping ◽  
Wave Trains ◽  
Momentum Integral ◽  
The Waves

AbstractAn experimental investigation focusing on the effect of dissipation on the evolution of the Benjamin–Feir instability is reported. A series of wave trains with added sidebands, and varying initial steepness, perturbed amplitudes and frequencies, are physically generated in a long wave flume. The experimental results directly confirm the stabilization theory of Segur et al. (J. Fluid Mech., vol. 539, 2005, pp. 229–271), i.e. dissipation can stabilize the Benjamin–Feir instability. Furthermore, the experiments reveal that the effect of dissipation on modulational instability depends strongly on the perturbation frequency. It is found that the effect of dissipation on the growth rates of the sidebands for the waves with higher perturbation frequencies is more evident than on those of waves with lower perturbation frequencies. In addition, numerical simulations based on Dysthe’s equation with a linear damping term included, which is estimated from the experimental data, can predict the experimental results well if the momentum integral of the wave trains is conserved during evolution.

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