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.

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.

Characteristics of the breathers, rogue waves and soliton waves in a (2 + 1)-dimensional generalized Nizhnik–Novikov–Veselov equation

2019 ◽  
Vol 33 (03) ◽  
pp. 1950014 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Rogue Wave ◽  
Solitary Wave Solution ◽  
Dynamical Behavior ◽  
Rogue Waves ◽  
Bilinear Forms ◽  
Wave Fields ◽  
Rogue Wave Solution ◽  
Bell’S Polynomials

In this work, a (2 + 1)-dimensional generalized Nizhnik–Novikov–Veselov (GNNV) equation, which can be reduced to several integrable equations, is under investigation. By virtue of Bell’s polynomials, an effective and straightforward way is presented to succinctly construct its two bilinear forms. Furthermore, based on the bilinear formalism and the extended homoclinic test, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. The results can be used to enrich the dynamical behavior of the (2 + 1)-dimensional nonlinear wave fields.

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.

Local Analysis of Wave Fields Produced From Hindcasted Rogue Wave Sea States

2015 ◽  
Author(s):  
Frédéric Dias ◽  
Joseph Brennan ◽  
Sonia Ponce de León ◽  
Colm Clancy ◽  
John Dudley
Keyword(s):  
Wave Field ◽  
Climate Models ◽  
Rogue Wave ◽  
Coarse Grained ◽  
Local Analysis ◽  
Physical Factors ◽  
Sea State ◽  
Accurate Analysis ◽  
Wave Fields ◽  
Spectral Models

Global-scale wave climate models, such as WAVEWATCH III, are widely used in oceanography to hindcast the sea state that occurred in a particular geographic area at a particular time. These models are applied in rogue-wave science for characterizing the sea states associated with observations of rogue waves (e.g., the well known “Draupner” [1] or “Andrea” [2] waves). While spectral models are generally successful in providing realistic representations of the sea state and are able to handle a large number of physical factors, they are also based on a very coarse grained representation of the wave field and therefore unsuitable for a detailed resolution of the wave field and refined wave-height statistics. On the other hand, local wave models based on first-principle fluid dynamics equations (such as the Higher Order Spectral Method) are able to represent wave fields in detail, but in general they are hard to interface with the full complexity of real-world sea conditions. This paper displays our efforts in coupling these two types of models in order to enhance our understanding of past extreme events and provide scope for rogue wave risk evaluation. In particular, high resolution numerical simulations of a wave field similar to the “Andrea” wave one are performed, allowing for accurate analysis of the event.

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.

Large-time evolution of statistical moments of wind–wave fields

2013 ◽  
Vol 726 ◽  
pp. 517-546 ◽  
Author(s):  
Sergei Y. Annenkov ◽  
Victor I. Shrira
Keyword(s):  
Wave Field ◽  
Large Time ◽  
Random Wave ◽  
Wave Spectra ◽  
Large Time Asymptotics ◽  
Wave Fields ◽  
Weakly Nonlinear ◽  
Time Asymptotics ◽  
Random Wave Field ◽  
Skewness And Kurtosis

AbstractWe study the long-term evolution of weakly nonlinear random gravity water wave fields developing with and without wind forcing. The focus of the work is on deriving, from first principles, the evolution of the departure of the field statistics from Gaussianity. Higher-order statistical moments of elevation (skewness and kurtosis) are used as a measure of this departure. Non-Gaussianity of a weakly nonlinear random wave field has two components. The first is due to nonlinear wave–wave interactions. We refer to this component as ‘dynamic’, since it is linked to wave field evolution. The other component is due to bound harmonics. It is non-zero for every wave field with finite amplitude, contributes both to skewness and kurtosis of gravity water waves and can be determined entirely from the instantaneous spectrum of surface elevation. The key result of the work, supported both by direct numerical simulation (DNS) and by the analysis of simulated and experimental (JONSWAP) spectra, is that in generic situations of a broadband random wave field the dynamic contribution to kurtosis is small in absolute value, and negligibly small compared with the bound harmonics component. Therefore, the latter dominates, and both skewness and kurtosis can be obtained directly from the instantaneous wave spectra. Thus, the departure of evolving wave fields from Gaussianity can be obtained from evolving wave spectra, complementing the capability of forecasting spectra and capitalizing on the existing methodology. We find that both skewness and kurtosis are significant for typical oceanic waves; the non-zero positive kurtosis implies a tangible increase of freak wave probability. For random wave fields generated by steady or slowly varying wind and for swell the derived large-time asymptotics of skewness and kurtosis predict power law decay of the moments. The exponents of these laws are determined by the degree of homogeneity of the interaction coefficients. For all self-similar regimes the kurtosis decays twice as fast as the skewness. These formulae complement the known large-time asymptotics for spectral evolution prescribed by the Hasselmann equation. The results are verified by the DNS of random wave fields based on the Zakharov equation. The predicted asymptotic behaviour is shown to be very robust: it holds both for steady and gusty winds.

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.

Efficient Fourier-collocation method for full scattering data of Zakharov-Shabat periodic problem

2021 ◽  
Author(s):  
Ilya Mullyadzhanov ◽  
Rustam Mullyadzhanov ◽  
Andrey Gelash
Keyword(s):  
Wave Field ◽  
Collocation Method ◽  
Nonlinear Wave ◽  
Periodic Problem ◽  
Physical Review ◽  
Scattering Data ◽  
Eigenvalue Spectrum ◽  
Plane Wave Solution ◽  
Wave Fields ◽  
Fourier Collocation

<p>The one-dimensional nonlinear Schrodinger equation (NLSE) serves as a universal model of nonlinear wave propagation appearing in different areas of physics. In particular it describes weakly nonlinear wave trains on the surface of deep water and captures up to certain extent the phenomenon of rogue waves formation. The NLSE can be completely integrated using the inverse scattering transform method that allows transformation of the wave field to the so-called scattering data representing a nonlinear analogue of conventional Fourier harmonics. The scattering data for the NLSE can be calculated by solving an auxiliary linear system with the wave field playing the role of potential – the so-called Zakharov-Shabat problem. Here we present a novel efficient approach for numerical computation of scattering data for spatially periodic nonlinear wave fields governed by focusing version of the NLSE. The developed algorithm is based on Fourier-collocation method and provides one an access to full scattering data, that is main eigenvalue spectrum (eigenvalue bands and gaps) and auxiliary spectrum (specific phase parameters of the nonlinear harmonics) of Zakharov-Shabat problem. We verify the developed algorithm using a simple analytic plane wave solution and then demonstrate its efficiency with various examples of large complex nonlinear wave fields exhibiting intricate structure of bands and gaps. Special attention is paid to the case when the wave field is strongly nonlinear and contains solitons which correspond to narrow gaps in the eigenvalue spectrum, see e.g. [1], when numerical computations may become unstable [2]. Finally we discuss applications of the developed approach for analysis of numerical and experimental nonlinear wave fields data.</p><p>The work was supported by Russian Science Foundation grant No. 20-71-00022.</p><p>[1] A. A. Gelash and D. S. Agafontsev, Physical Review E 98, 042210 (2018).</p><p>[2] A. Gelash and R. Mullyadzhanov, Physical Review E 101, 052206 (2020).</p>

scholarly journals On the influence of wind on extreme wave events

2007 ◽  
Vol 7 (1) ◽  
pp. 123-128 ◽  
Author(s):  
J. Touboul
Keyword(s):  
Numerical Analysis ◽  
Spectral Method ◽  
Modulational Instability ◽  
Rogue Waves ◽  
High Order ◽  
Instability Wave ◽  
Extreme Wave ◽  
Wave Fields ◽  
The Impact ◽  
High Order Spectral Method

Abstract. This work studies the impact of wind on extreme wave events, by means of numerical analysis. A High Order Spectral Method (HOSM) is used to generate freak, or rogue waves, on the basis of modulational instability. Wave fields considered here are chosen to be unstable to two kinds of perturbations. The evolution of components during the propagation of the wave fields is presented. Their evolution under the action of wind, modeled through Jeffreys' sheltering mechanism, is investigated and compared to the results without wind. It is found that wind sustains rogue waves. The perturbation most influenced by wind is not necessarily the most unstable.

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