Hunting for Rogue Waves in a Three-Dimensional Nonlinear Wavefield: A Direct Simulation-Based Approach

2009 ◽  
Author(s):  
Wenting Xiao ◽  
Yuming Liu ◽  
Dick K. P. Yue
Keyword(s):  
Nonlinear Wave ◽  
Rogue Wave ◽  
Wave Spectrum ◽  
Three Dimensional ◽  
Rogue Waves ◽  
High Order ◽  
Wave Steepness ◽  
Large Wave ◽  
Resonant Interactions ◽  
Wavefield Simulation

We describe an investigation of the occurrence, statistics, and generation mechanisms of rogue wave in the open sea using direct three-dimensional phase-resolved nonlinear wavefield simulations. To achieve this we develop an efficient nonlinear wavefield simulation capability based on the high-order spectrum method which solves the primitive phase-resolved Euler equations. The simulations account for nonlinear wave-wave interactions up to an arbitrary high order in the wave steepness and are capable of accounting for effects of bottom bathymetry, variable current, and direct physics-based models for wind input and wave breaking dissipation. We apply direct large-scale simulations to obtain a large number of phase-resolved nonlinear wavefields, initially specified by directional wave spectra. The typical spatial-temporal domain size of such numerical nonlinear wavefields is O(103 km2) over evolution time of O(hr). These spatial and temporal scales account for quartet resonant interactions and partially for quintet resonant interactions among wave components in the wavefield. From the simulated nonlinear wavefields, rogue wave events are identified and their occurrence statistics are studied. It is shown that the classic linear theory (i.e. Rayleigh distribution) significantly underestimates the rogue wave occurrence. Second-order theory improves the Rayleigh prediction, but still underestimates the rogue wave occurrence in wavefields with moderately large wave steepness and relatively narrow directional spreading and spectrum bandwidth. The influence of key wave spectrum parameters (such as significant wave height, directional spreading, effective steepness, and spectrum bandwidth) on the rogue wave occurrence is analyzed. The classification of rogue waves according to their configuration is also obtained. The key characteristics of a rogue wave or rogue wave group in terms of kinematics and surface structure are analyzed and quantified. The nonlinear wave simulations, which provide full three-dimensional kinematics and dynamics of rogue wave events, provide a powerful tool for understanding the underlying mechanisms of their generation. They are elucidated by specific examples.

Rogue Waves and Hybrid Solutions of the Boussinesq Equation

2017 ◽  
Vol 72 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Ji-Guang Rao ◽  
Yao-Bin Liu ◽  
Chao Qian ◽  
Jing-Song He
Keyword(s):  
Boussinesq Equation ◽  
Rogue Wave ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Hirota Bilinear

AbstractThe rational and semirational solutions in the Boussinesq equation are obtained by the Hirota bilinear method and long wave limit. It is shown that the rational solutions contain dark and bright rogue waves, and their typical dynamics are analysed and illustrated. The semirational solutions possess a range of hybrid solutions, and the hybrid of rogue wave and solitons are demonstrated in detail by the three-dimensional figures. Under certain parameter conditions, a new kind of semirational solutions consisted of rogue waves, breathers and solitons is discovered, which describes the dynamics of the rogue waves interacting with the breathers and solitons at the same time.

High-order rogue waves of the Benjamin–Ono equation and the nonlocal nonlinear Schrödinger equation

2017 ◽  
Vol 31 (29) ◽  
pp. 1750269 ◽  
Author(s):  
Wei Liu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
High Order ◽  
Wave Patterns ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

High-order rogue wave solutions of the Benjamin–Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin–Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

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.

Nonlinear phase-resolved reconstruction of irregular water waves

2018 ◽  
Vol 838 ◽  
pp. 544-572 ◽  
Author(s):  
Yusheng Qi ◽  
Guangyu Wu ◽  
Yuming Liu ◽  
Moo-Hyun Kim ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Reconstruction Error ◽  
High Order ◽  
Order Effects ◽  
Wave Fields ◽  
Wave Measurements ◽  
Wave Nonlinearity

We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\mathcal{P}}_{NL}$ matches the linear predictable zone ${\mathcal{P}}_{L}$, verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\mathcal{P}}_{NL}$ contains and is generally greater than ${\mathcal{P}}_{L}$. Thus ${\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\mathcal{P}}_{NL}$ when the underlying wave field is not known.

Time-Domain Investigation of a Semisubmersible in Rogue Waves

2002 ◽  
Author(s):  
Gu¨nther F. Clauss ◽  
Christian Schmittner ◽  
Katja Stutz
Keyword(s):  
Time Domain ◽  
Rogue Wave ◽  
Limit State ◽  
Rogue Waves ◽  
Ultimate Limit State ◽  
Peak Period ◽  
Large Wave ◽  
Safety Standards ◽  
Design Wave Height ◽  
Present Design

Heave, pitch and roll motions as well as airgap are key characteristics of semisubmersibles in extreme seas which are defined by Ultimate Limit State design conditions (ULS) with a specified 100-year design wave height Hs and peak period Tp. The increasing number of reported rogue waves with unexpected large wave heights (Hmax/Hs > 2), crest heights (ζmax//Hmax > 0.6), wave steepness and group patterns (e.g. Three Sisters) may suggest a reconsideration of design codes by implementing an Accidental Limit State (ALS) with a return period of 104 years. For investigating the consequences of specific extreme sea conditions this paper analyses the seakeeping behaviour of a semisubmersible in a reported rogue wave, the Draupner New Year Wave embedded in irregular sea states. The numerical time-domain invegstigation using a panel method and potential theory is compared to frequency-domain results. In particular, the characteristics of the embedded rogue wave is varied to analyse the dynamic response of the semisubmersible in extreme wave sequences For validation, the selected sea condition is generated in a physical wave tank, and the sea-keeping behaviour of the semisubmersible is evaluated at model scale. In conclusion, the results deomstrate the consequences of rogue wave impacts, with respect to the relevance of present design methods and safety standards.

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.

Predicting Extreme Waves From Wave Spectral Properties Using Machine Learning

2019 ◽  
Author(s):  
Odin Gramstad ◽  
Elzbieta Bitner-Gregersen
Keyword(s):  
Machine Learning ◽  
Spectral Properties ◽  
Wave Spectrum ◽  
Wave Model ◽  
Rogue Waves ◽  
Wave Steepness ◽  
Extreme Waves ◽  
Learning Methods ◽  
Wave Statistics ◽  
Machine Learning Methods

Abstract An important question in the context of rogue waves is whether the statistical properties of individual waves, and in particular the probability of extreme and rogue waves, can be linked to the properties of the underlying wave spectrum of the relevant sea state. It has been suggested that a narrow wave spectrum (in frequency or direction) combined with a large wave steepness may lead to increased occurrence of extreme waves. Parameters based on the ratio of the wave steepness to the spectral band-widths have therefore been suggested as indicators of increased probability of extreme waves. However, for realistic ocean conditions the success of such parameters seems to be questionable. In this paper, we investigate relations between short-time wave statistics and wave spectral properties by using machine learning methods that can take a much wider range of spectral properties, or even the entire directional wave spectrum, into account. Numerical simulations with a nonlinear wave model that provides phase-resolved wave information are combined with wave spectra from a spectral wave model. Machine learning methods are then employed to investigate how well the wave statistics can be predicted from knowledge about the wave spectrum. The results are discussed in the context of existing parameters suggested as indicators of rogue waves, as well as with respect to potential warning against sea states in which extreme waves are expected to occur, based on wave-forecast from spectral wave models.

scholarly journals Fast Solar Flare Proton Acceleration by MHD Turbulence

1990 ◽  
Vol 142 ◽  
pp. 375-382
Author(s):  
Dean. F. Smith
Keyword(s):  
Nonlinear Wave ◽  
Wave Spectrum ◽  
Wave Interaction ◽  
Impulsive Behavior ◽  
Mhd Turbulence ◽  
Wave Interactions ◽  
Proton Acceleration ◽  
Large Wave ◽  
M Wave ◽  
Wave Distribution

Proton acceleration by short-wavelength Alfven (A) waves resonant at the first harmonic of the proton gyrofrequency is reconsidered, taking into account nonlinear wave-wave interactions, collisionless wave losses, and wave escape losses in the geometry of a model coronal loop. It is shown that for the A wave levels required for acceleration in the transrelativistic regime in the 1982 June 3 flare and for acceleration in the nonrelativistic regime in the 1980 June 7 flare, the nonlinear wave interaction of scattering on the polarization clouds of ions will be important. This interaction rapidly isotropizes the A waves which divide their energy with fast magnetosonic (M) waves with a negligible change in their frequency spectrum. Because of electron Landau damping and escape losses, the M waves are confined to two narrow cones about the magnetic field and the total (A+M) wave distribution is still highly anisotropic. The total (A+M) wave spectrum has the same acceleration efficiency as a pure A wave spectrum. There are two principal problems with models of this type. The first is that a large wave energy density is required in a fairly narrow range in k-space. The second is that the protons are effectively bottled up. This makes very impulsive behavior as in the 7 June 1980 flare difficult to explain because proton precipitation is relatively slow.

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.

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