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.

scholarly journals The general coupled Hirota equations: modulational instability and higher-order vector rogue wave and multi-dark soliton structures

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180625 ◽  
Author(s):  
Guoqiang Zhang ◽  
Zhenya Yan ◽  
Li Wang
Keyword(s):  
Nonlinear Wave ◽  
Rogue Wave ◽  
Modulational Instability ◽  
Distribution Patterns ◽  
Rogue Waves ◽  
Dark Soliton ◽  
Scalar Model ◽  
Optical Fields ◽  
Dark Solitons ◽  
Hirota Equations

The general coupled Hirota equations are investigated, which describe the wave propagations of two ultrashort optical fields in a fibre. Firstly, we study the modulational instability for the focusing, defocusing and mixed cases. Secondly, we present a unified formula of high-order rational rogue waves (RWs) for the focusing, defocusing and mixed cases, and find that the distribution patterns for novel vector rational RWs of focusing case are more abundant than ones in the scalar model. Thirdly, the N th-order vector semirational RWs can demonstrate the coexistence of N th-order vector rational RWs and N breathers. Fourthly, we derive the multi-dark-dark solitons for the defocsuing and mixed cases. Finally, we derive a formula for the coexistence of dark solitons and RWs. These results further enrich and deepen the understanding of localized wave excitations and applications in vector nonlinear wave systems.

Prediction of Oceanic Rogue Waves Through Tracking Energy Fluxes

2017 ◽  
Author(s):  
Qiuchen Guo ◽  
Mohammad-Reza Alam
Keyword(s):  
Spatial Distribution ◽  
Wave Field ◽  
Spectral Method ◽  
Nonlinear Wave ◽  
Statistical Approach ◽  
Preventive Measures ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Wave Fields ◽  
Weakly Nonlinear

Here, we show that location of an upcoming rogue wave can be inferred, well in advance, from spatial distribution of energy flux across the ocean surface. We use a statistical approach, and by investigating hundreds of numerical rogue wave realizations in weakly nonlinear wave fields establish a quantitative metric via which predictions can be made. Direct simulations are performed by a higher-order spectral method (HOS), and JONSWAP distribution is used to initialize the wave field. The presented metric may establish a readily achievable measure to identify turbulent locations within a sea, through which timely preventive measures can be taken to minimize damages to lives and properties.

Evolution of a nonlinear wave field along a tank: experiments and numerical simulations based on the spatial Zakharov equation

2001 ◽  
Vol 427 ◽  
pp. 107-129 ◽  
Author(s):  
L. SHEMER ◽  
HAIYING JIAO ◽  
E. KIT ◽  
Y. AGNON
Keyword(s):  
Theoretical Model ◽  
Wave Field ◽  
Nonlinear Wave ◽  
Numerical Study ◽  
Spectral Width ◽  
Spatial Evolution ◽  
Zakharov Equation ◽  
Free Wave ◽  
Laboratory Tank ◽  
Nonlinear Wave Field

Evolution of a nonlinear wave field along a laboratory tank is studied experimentally and numerically. The numerical study is based on the Zakharov nonlinear equation, which is modified to describe slow spatial evolution of unidirectional waves as they move along the tank. Groups with various initial shapes, amplitudes and spectral contents are studied. It is demonstrated that the applied theoretical model, which does not impose any constraints on the spectral width, is capable of describing accurately, both qualitatively and quantitatively, the slow spatial variation of the group envelopes. The theoretical model also describes accurately the variation along the tank of the spectral shapes, including free wave components and the bound waves.

scholarly journals Real-world rogue wave probabilities

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Dion Häfner ◽  
Johannes Gemmrich ◽  
Markus Jochum
Keyword(s):  
Real World ◽  
Rogue Wave ◽  
Ocean Waves ◽  
Rogue Waves ◽  
Order Theory ◽  
Linear Superposition ◽  
Sea State ◽  
Single Wave ◽  
The Common ◽  
A Minor

AbstractRogue waves are dangerous ocean waves at least twice as high as the surrounding waves. Despite an abundance of studies conducting simulations or wave tank experiments, there is so far no reliable forecast for them. In this study, we use data mining and interpretable machine learning to analyze large amounts of observational data instead (more than 1 billion waves). This reveals how rogue wave occurrence depends on the sea state. We find that traditionally favored parameters such as surface elevation kurtosis, steepness, and Benjamin–Feir index are weak predictors for real-world rogue wave risk. In the studied regime, kurtosis is only informative within a single wave group, and is not useful for forecasting. Instead, crest-trough correlation is the dominating parameter in all studied conditions, water depths, and locations, explaining about a factor of 10 in rogue wave risk variation. For rogue crests, where bandwidth effects are unimportant, we find that skewness, steepness, and Ursell number are the strongest predictors, in line with second-order theory. Our results suggest that linear superposition in bandwidth-limited seas is the main pathway to “everyday” rogue waves, with nonlinear contributions providing a minor correction. This casts some doubt whether the common rogue wave definition as any wave exceeding a certain height threshold is meaningful in practice.

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

scholarly journals Rogue Waves With Rational Profiles in Unstable Condensate and Its Solitonic Model

2021 ◽  
Vol 9 ◽  
Author(s):  
D. S. Agafontsev ◽  
A. A. Gelash
Keyword(s):  
Plane Wave ◽  
Stationary State ◽  
Rogue Wave ◽  
Modulational Instability ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Bound State ◽  
Wave Formation ◽  
Soliton Interaction ◽  
Long Time

In this brief report we study numerically the spontaneous emergence of rogue waves in 1) modulationally unstable plane wave at its long-time statistically stationary state and 2) bound-state multi-soliton solutions representing the solitonic model of this state. Focusing our analysis on the cohort of the largest rogue waves, we find their practically identical dynamical and statistical properties for both systems, that strongly suggests that the main mechanism of rogue wave formation for the modulational instability case is multi-soliton interaction. Additionally, we demonstrate that most of the largest rogue waves are very well approximated–simultaneously in space and in time–by the amplitude-scaled rational breather solution of the second order.

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