The evolution of rogue wave triplets and super rogue waves in superthermal polarized space dusty plasma

2019 ◽  
Vol 26 (11) ◽  
pp. 113702 ◽  
Author(s):  
Kuldeep Singh ◽  
N. S. Saini
Keyword(s):  
Dusty Plasma ◽  
Rogue Wave ◽  
Rogue Waves

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

scholarly journals ROGUE WAVE ASYMMETRY IN THE DIRECT NUMERICAL SIMULATIONS OF DIRECTIONAL JONSWAP WAVES

2020 ◽  
pp. 48
Author(s):  
Alexey Slunyaev ◽  
Anna Kokorina
Keyword(s):  
Water Wave ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Hydrodynamic Equations ◽  
Laboratory Measurements ◽  
Term Evolution ◽  
Typical Picture ◽  
High Order Spectral Method

The asymmetry between the troughs from the rear and front sides of rogue waves is the particular object of the present study. In our previous simulations of unidirectional waves the typical picture of a rogue waves possesses the trend that most of the rogue waves where characterized by deeper rear troughs. In the present work we broaden the discussion of the rogue wave front-to-crest asymmetry to the directional case. The direct numerical simulation of primitive water equations is an affordable alternative to the in-situ or laboratory measurements, in particularly when the interest is focused on the long-term evolution or on the detailed consideration of the water wave movement in space and time. In this work we simulate irregular surface waves in the hydrodynamic equations using the High-Order Spectral Method, and focus on the so-called rogue waves.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/plseXdjpE6c

scholarly journals On the physical constraints for the exceeding probability of deep water rogue waves

2021 ◽  
Author(s):  
Saulo Mendes ◽  
Alberto Scotti ◽  
Paul Stansell
Keyword(s):  
Sample Size ◽  
Rogue Wave ◽  
Probability Distributions ◽  
Rogue Waves ◽  
Uneven Distribution ◽  
Large Set ◽  
Sea State ◽  
Sampling Variability ◽  
The North ◽  
Wave Heights

<p><strong>(manuscript accepted into Applied Ocean Research https://www.researchgate.net/publication/344786014)</strong></p><p><strong>Abstract</strong></p><p>Nearly four decades have elapsed since the first efforts to obtain a realistic narrow-banded model for extreme wave crests and heights were made, resulting in a couple of dozen different exceeding probability distributions. These models reflect results of numerical simulations and storm records measured from oil platforms, buoys, and more recently, satellite data. Nevertheless, no consensus has been achieved in either deterministic or operational approaches. Typically, distributions found in the literature analyze a very large set of waves with large variations in sea-state parameters while neglecting homogeneous smaller samples, such that we lack a suitable definition for the sample size and homogeneity of sea variables, also known as sampling variability (Bitner-Gregersen et al., 2020). Naturally, a possible consequence of such sample size inconsistency is the apparent disagreement between several studies regarding the prediction of rogue wave occurrence, as some studies can report less rogue wave heights while others report more rogue waves or the same statistics predicted by Longuet-Higgins (1952), sometimes a combination of the three in the very same study (Stansell, 2004; Cherneva et al., 2005). In this direction, we have obtained a dimensionless parameter capable of measuring how large the deviations in sea state variables can be so that accuracy in wave statistics is preserved.  In particular, we have defined which samples are too heterogeneous to create an accurate description of the uneven distribution of rogue wave likelihood among different storms (Stansell, 2004). Though the literature is rich in physical bounds for single waves, here we describe empirical physical limits for the ensemble of waves (such as the significant steepness) devised to bound these variables within established and prospective wave distributions. Furthermore, this work supplies a combination of sea state parameters that provide guidance on the influence of sea states influence on rogue wave occurrence. Based on these empirical limits, we conjecture a mathematical model for the dependence of the expected maximum of normalized wave heights and crests on the sea state parameters, thus explaining the uneven distribution of rogue wave likelihood among different storms collected by infrared laser altimeters of the North Alwyn oil platform discussed in Stansell (2004). Finally, we demonstrate that for heights and crests beyond 90% of their thresholds (H>2H<sub>1/3</sub> for heights), the exceeding probability becomes stratified, i.e. they resemble layers of probability curves according to each sea state, suggesting the existence of a dynamical definition for rogue waves rather than purely statistical.</p><p> </p><p><strong>References</strong></p><p>Bitner-Gregersen, E. M., Gramstad, O., Magnusson, A., Malila, M., 2020. Challenges in description of nonlinear waves due to sampling variability. J. Mar. Sci. Eng. 8, 279.</p><p>Longuet-Higgins, M., 1952. On the statistical distribution of the heights of sea waves. Journal of Marine Research 11, 245–265.</p><p>Stansell, P., 2004. Distribution of freak wave heights measured in the north sea. Appl. Ocean Res. 26, 35–48.</p><p>Cherneva, Z., Petrova, P., Andreeva, N., Guedes Soares, C., 2005. Probability distributions of peaks, troughs and heights of wind waves measured in the black sea coastal zone. Coastal Engineering 52, 599–615.</p>

Meteotsunami of 29 August 1916 at Santo Domingo, Dominican Republic - analysis of the destruction of the USS Memphis

2019 ◽  
pp. 16-36
Author(s):  
Джордж Парарас-Караяннис
Keyword(s):  
Dominican Republic ◽  
Deep Water ◽  
Rogue Wave ◽  
Meteorological Data ◽  
Barometric Pressure ◽  
Rogue Waves ◽  
Rayleigh Distribution ◽  
Careful Examination ◽  
Santo Domingo ◽  
Storm Waves

Пересмотренные официальные записи Следственного суда ВМС США содержат выводы о том, что разрушение бронированного крейсера USS Memphis 29 августа 1916 года на якоре у гавани Санто-Доминго (Сьюдад-Трухильо) Доминиканской Республики, остров Эспаньола, вероятно, было вызвано «тропическим волнением» «сейсмической бурей» или «цунами». Тем не менее, современный анализ этой морской катастрофы свидетельствует о том, что гибель корабля произошла не по какой-либо из этих причин, а из-за волн-убийц метеоцунами, вызванных быстрым, значительным и прогрессирующим падением атмосферного давления, которое началось в районе около 22 августа и было связано с проходящим ураганом, который в его самой близкой точке был около 250 морских миль на юг. Кроме того, штормовые волны от этого урагана двигались в направлении Санто-Доминго, преломляясь в резонансе у берега, и усиливались и трансформировались низким барометрическим давлением, мелким континентальным шельфом и местными особенностями побережья и батиметрией залива. Настоящий анализ основан на тщательном изучении судового журнала и наблюдений за событиями со стороны экипажа и людей на берегу. Учитывая ограниченные метеорологические данные того периода времени, в настоящем анализе использовался эмпирический подход для грубой оценки функции распределения Рэлея, верхнего предела изменчивости высоты штормовой волны вдали от наиболее интенсивных потоков ветра, а также максимального периода, длины волны и амплитуды генерируемых штормовых волн в глубине . Основываясь на теориях кноидальных волн и волн Эйри, период и скорость наиболее значительных экстремальных внутренних волн имели метеорологическое происхождение, которое было преобразовано в мелкой воде в результате резонансного и наложенного прихода двух других волн, которые создали трехступенчатое плато, на переднем фронте огромная одиночная волна-убийца метеоцунами высотой около 70 футов, с тремя четкими ступенями, двумя плато на передней поверхности и предшествующей впадиной длиной около 300 футов. Основываясь на этом анализе, настоящее исследование пришло к выводу, что именно эта значительная волна метеоцунами / волна-убийца в сочетании с одновременно прибывающими штормовыми волнами охватила Мемфис USS в 16 ч. 40 м. 29 августа 1916 года, разорвав цепи якорей и разрушая его на скалах Санто-Доминго. Official revised records of a U.S. Navy Court of Inquiry concluded that the 29 August 1916 destruction of the armored cruiser USS Memphis anchored off Santo Domingo (Ciudad Trujillo) harbor of the Dominican Republic, Island of Hispaniola, was probably caused by a “tropical disturbance”, a “seismic storm”, or a “tsunami”. However, the present analysis of this naval disaster documents that the loss of the ship was not due to any of these causes, but to rogue waves of a meteotsunami generated from a rapid, significant and progressive drop in atmospheric pressure which begun in the area around August 22 and was associated with a passing hurricane which at its closest point was about 250 nautical miles to the south. Also, storm waves from this hurricane moved towards Santo Domingo refracting in resonance near shore and were further amplified and transformed by the low barometric pressure, the shallow continental shelf and the local coastal features and bathymetry of the bay. The present analysis is based on careful examination of the ship’s log, and on observations of events by the crew and people on the shore. Given the limited meteorological data of that time period, the present analysis used an empirical approach to roughly evaluate the Rayleigh distribution function, the upper limit of storm wave height variability away from the most intense wind fetches, as well as the maximum period, wavelength and deep-water heights of generated storm waves. Based on Airy and cnoidal wave theories, the deep water period and celerity of the most significant extreme wave was of meteorological origin which was transformed in shallower water by the resonant and superimposed arrival of two other waves which created a three step plateau on the face of a huge single rogue wave of the meteotsunami, estimated to be about 70 feet in height, with three distinct steps, two plateaus on its forward face, and a preceding trough estimated to be 300 ft. long. Based on this analysis, the present study concluded that it was this significant meteotsunami/rogue wave, in combination with concurrently arriving storm swells, that engulfed the USS Memphis at 1640 hour in the afternoon of 29 August 1916 - breaking the chains of its anchors and wrecking it on the rocks of Santo Domingo.

Analytic rogue wave-type solutions for the generalized (2+1)-dimensional Boussinesq Equation

2021 ◽  
pp. 2150380
Author(s):  
Xiu-Rong Guo
Keyword(s):  
Boussinesq Equation ◽  
Rogue Wave ◽  
Wave Interaction ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Wave Type ◽  
Hirota Bilinear Form ◽  
Basic Facts ◽  
2D And 3D ◽  
Solitary Wave Interaction

Based on the Hirota bilinear form of the generalized (2+1)-dimensional Boussinesq equation, which can be expressed as the shallow water wave mechanism appearing in fluid mechanics, we applied the new polynomial functions to construct the rational solutions and rogue wave-type solutions. Next, the system parameters control on the rational solutions and rogue wave-type solutions were also shown. As a result, we found the following basic facts: (i) these parameters may affect the wave shapes, amplitude, and bright/dark for this considered equation, (ii) the solitary wave interaction rogue waves and triplet rogue wave-type solutions can be viewed on [Formula: see text], [Formula: see text], and [Formula: see text] planes, respectively. Their nonlinear dynamic behaviors were presented by numerical simulation of the 2D- and 3D-plots.

Rogue Wave and Breather Structures with “High Frequency” and “Low Frequency” in 𝒫𝒯-Symmetric Nonlinear Couplers with Gain and Loss

2016 ◽  
Vol 71 (10) ◽  
pp. 961-969 ◽  
Author(s):  
Dang-Jun Yu ◽  
Jie-Fang Zhang
Keyword(s):  
High Frequency ◽  
Rogue Wave ◽  
Low Frequency ◽  
Zero Solution ◽  
Rogue Waves ◽  
Transformation Method ◽  
Rational Solutions ◽  
Plane Wave Solution ◽  
Gain And Loss ◽  
Basic Characteristics

AbstractBased on the modified Darboux transformation method, starting from zero solution and the plane wave solution, the hierarchies of rational solutions and breather solutions with “high frequency” and “low frequency” of the coupled nonlinear Schrödinger equation in parity-time symmetric nonlinear couplers with gain and loss are constructed, respectively. From these results, some basic characteristics of multi-rogue waves and multi-breathers are studied. Based on the property of rogue wave as the “quantum” of pattern structure in rogue wave hierarchy, we further study the novel structures of the superposed Akhmediev breathers, Kuznetsov-Ma solitons and their combined structures. It is expected that these results may give new insight into the context of the optical communications and Bose-Einstein condensations.

Are There Different Kinds of Rogue Waves?

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Paul C. Liu ◽  
Keith R. MacHutchon
Keyword(s):  
Rogue Wave ◽  
Rogue Waves ◽  
Rayleigh Distribution ◽  
The Other ◽  
South Indian Ocean ◽  
Gas Drilling ◽  
Wave Measurements ◽  
South Indian ◽  
Theoretical Considerations

There is clearly no immediate answer to the question posted by the title of this paper. Inasmuch as that there are not much definitively known about rogue waves and that there is still no universally accepted definition for rogue waves in the ocean, we think there might just be even more than one kind of rogue waves to contend with. While the conventional approach has generally designated waves with Hmax∕Hs greater than 2.2 as possible rogue waves, based on Rayleigh distribution considerations, there is conspicuously no provision as to how high the ratio of Hmax∕Hs can be and thus not known how high can a rogue wave be. In our analysis of wave measurements made from a gas-drilling platform in South Indian Ocean, offshore from Mossel Bay, South Africa, we found a number of cases that indicated Hmax∕Hs could be valued in the range between 4 and 10. If this were to be the case, then these records could be considered to be “uncommon” rogue waves, whereas a record of Hmax∕Hs in the range between 2 and 4 could be considered to comprise “typical” rogue waves. On the other hand, the spikes in the Hmax data could have been caused by equipment malfunction or some other phenomenon. Clearly, the question of whether or not there are different kinds of rogue waves cannot be readily answered by theoretical considerations alone and there is a crucial need for long-term wave time-series measurements for studying rogue waves.

Breather wave, rogue wave and lump wave solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid

2018 ◽  
Vol 32 (20) ◽  
pp. 1850223 ◽  
Author(s):  
Ming-Zhen Li ◽  
Bo Tian ◽  
Yan Sun ◽  
Xiao-Yu Wu ◽  
Chen-Rong Zhang
Keyword(s):  
Wave Velocity ◽  
Water Waves ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Dispersion Effect ◽  
Wave Solutions ◽  
Weak Perturbation ◽  
Petviashvili Equation ◽  
Nonlinearity Effect ◽  
Lump Wave

Under investigation in this paper is a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili equation, which describes the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in a fluid. Via the Hirota method and symbolic computation, the lump wave, breather wave and rogue wave solutions are obtained. We graphically present the lump waves under the influence of the dispersion effect, nonlinearity effect, disturbed wave velocity effects and perturbed effects: Decreasing value of the dispersion effect can lead to the range of the lump wave decreases, but has no effect on the amplitude. When the value of the nonlinearity effect or disturbed wave velocity effects increases respectively, lump wave’s amplitude decreases but lump wave’s location keeps unchanged. Amplitudes of the lump waves are independent of the perturbed effects. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity. When the value of the dispersion effect decreases, range of the rogue wave increases. When the value of the nonlinearity effect or disturbed wave velocity effects decreases respectively, rogue wave’s amplitude decreases. Value changes of the perturbed effects cannot influence the rogue wave.

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