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The sinking of the El Faro: predicting real world rogue waves during Hurricane Joaquin
TL;DR: In this paper, the authors present a study on the prediction of rogue waves during the 1-hour sea state of Hurricane Joaquin when the Merchant vessel El Faro sank east of the Bahamas on October 1, 2015.
Abstract: We present a study on the prediction of rogue waves during the 1-hour sea state of Hurricane Joaquin when the Merchant Vessel El Faro sank east of the Bahamas on October 1, 2015. High-resolution hindcast of hurricane-generated sea states and wave simulations are combined with novel probabilistic models to quantify the likelihood of rogue wave conditions. The data suggests that the El Faro vessel was drifting at an average speed of approximately~$2.5$~m/s prior to its sinking. As a result, we estimated that the probability that El Faro encounters a rogue wave whose crest height exceeds 14 meters while drifting over a time interval of 10~(50) minutes is $\sim1/400$~$(1/130)$. The largest simulated rogue wave has similar generating mechanism and characteristics of the Andrea, Draupner and Killard rogue waves as the constructive interference of elementary waves enhanced by bound nonlinearities.
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TL;DR: Research shows that soliton can partially swallow or spit out lump waves, and number of lump wave peaks will change with time.
Abstract: A (3+1)-dimensional Boiti–Boiti–Leon–Manna– Pempinelli equation is investigated, which describes nonlinear wave propagations in incompressible fluid. A condition proposition is obtained for polynomial function in bilinear form. New lump solution is constructed by applying the bilinear method and choosing proper polynomial function. Under different parameter settings, this lump solution possesses three types of multiple-lump waves, namely, two-, four- and eight-lump waves. Mixed solutions involving lump waves and solitons are also constructed. Interaction behaviors are observed between lump soliton and soliton. Research shows that soliton can partially swallow or spit out lump waves. Furthermore, number of lump wave peaks will change with time.
82 citations
TL;DR: In this paper, the authors review the state-of-the-art of rogue wave studies in optical and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields.
Abstract: We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whilst in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. Although significant progress in understanding rogue waves has been made based on an analogy between wave dynamics in optics and hydrodynamics, these comparisons have predominantly focused on one-dimensional nonlinear propagation scenarios. As a result, there remains significant debate about the dominant physical mechanisms driving the generation of ocean rogue waves in the complex environment of the open sea. Here, we review state-of-the-art of rogue wave studies in optics and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields. In hydrodynamics, we take care to review results that support both nonlinear and linear interpretations of ocean rogue wave formation, and in optics, we also summarise results from an emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We conclude with a discussion of important future research directions.
75 citations
TL;DR: A catalogue of anomalously large waves (rogue or freak waves) occurred in the World Ocean during 2011-2018 reported in mass media sources and scientific literature has been compiled and analyzed.
43 citations
TL;DR: Based on Hirota's bilinear structure, the authors evolute a new protuberance type arrangement of the (3+1)-dimensional Boiti-Boiti-Leon-Manna-Pempinelli equation, which depicts nonlinear wave spreads in incompressible fluid.
Abstract: Based on Hirota’s bilinear structure, we evolute a new protuberance type arrangement of the (3+1)-dimensional Boiti-Boiti-Leon-Manna-Pempinelli equation, which depicts nonlinear wave spreads in incompressible fluid. New lump arrangement is built by applying the bilinear strategy and picking appropriate polynomial. Under various parameter settings, this lump arrangement has three sorts of numerous irregularity waves, blended arrangements including lump waves and solitons are additionally developed. Association practices are seen between lump soliton and soliton. Research demonstrates that soliton can somewhat swallow or release lump waves. The shape and highlights for these subsequent arrangements are portrayed by exploiting the three-dimensional plots and comparing shape plots by picking suitable parameters. The physical significance of these charts is given.
29 citations
TL;DR: In this paper, the authors used reanalysis datasets to provide a long-term and global statistical assessment of the maximum wave parameters, namely crest, crest-to-trough and envelope heights.
23 citations
References
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TL;DR: The radiation stresses in water waves play an important role in a variety of oceanographic phenomena, for example in the change in mean sea level due to storm waves (wave set-up), the generation of "surf-beats", the interaction of waves with steady currents, and the steepening of short gravity waves on the crests of longer waves as discussed by the authors.
1,567 citations
1,552 citations
Book•
12 Jun 2007TL;DR: Random Fields and Geometry as discussed by the authors is a comprehensive survey of the general theory of Gaussian random fields with a focus on geometric problems arising in the study of random fields, including continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities.
Abstract: * Recasts topics in random fields by following a completely new way of handling both geometry and probability
* Significant exposition of the work of others in the field
* Presentation is clear and pedagogical
* Excellent reference work as well as excellent work for self study
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined.
The three parts to the monograph are quite distinct. Part I presents a user-friendly yet comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities. Part II gives a quick review of geometry, both integral and Riemannian, to provide the reader with the material needed for Part III, and to give some new results and new proofs of known results along the way. Topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory, and tube formulae are covered. In fact, this is the only concise, self-contained treatment of all of the above topics, which are necessary for the study of random fields. The new approach in Part III is devoted to the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities.
"Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory. These applications, to appear in a forthcoming volume, will cover areas as widespread as brain imaging, physical oceanography, and astrophysics.
1,465 citations
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TL;DR: In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory as mentioned in this paper, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model.
Abstract: Oceanic rogue waves are surface gravity waves whose wave heights are much larger than expected for the sea state. The common operational definition requires them to be at least twice as large as the significant wave height. In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory. There are exceptions, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model. A clear deviation from second-order theory occurs in numerical simulations and wave-tank experiments, in which a higher frequency of occurrence of rogue waves is found in long-crested waves owing to a nonlinear instability.
777 citations