Solitary wave dynamics in shallow water over periodic topography

Nakoulima, Ousseynou; Zahibo, Narcisse; Pelinovsky, Efim; Talipova, Tatiana; Kurkin, A. A.

doi:10.1063/1.1984492

Cited by 23 publications

(26 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This dynamics is known to depend on the ratio of nonlinearity length with respect to the width of the transition zone (Tappert and Zabusky, 1971;Pelinovsky, 1971;Nakoulima et al, 2005). If the solitary wave amplitude is large, the soliton quickly adapts to the local depth, so that its new length coincides with the local conditions.…”

Section: The Korteweg-de Vries Modelmentioning

confidence: 99%

“…In this case the soliton amplitude is proportional to h −1 (x); see Ostrovsky and Pelinovsky (1970), Johnson (1973). If the solitary wave has small amplitude, and thus, large wave length, it transforms as a linear wave, and its amplitude is proportional to h −1/4 (x); see Pelinovsky (1971), Nakoulima et al (2005). As a result, the distribution of soliton amplitudes changes with depth, and the portion of largeamplitude waves enhances more significantly than the portion of smaller-amplitude solitons.…”

Section: The Korteweg-de Vries Modelmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework

Sergeeva

Pelinovsky

Talipova

2011

Nat. Hazards Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows.

show abstract

Section: The Korteweg-de Vries Modelmentioning

confidence: 99%

Section: The Korteweg-de Vries Modelmentioning

confidence: 99%

Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework

Sergeeva

Pelinovsky

Talipova

2011

Nat. Hazards Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…В результате нарушается соотношение между дисперсией и нелинейностью, характеризуемое числом Урселла [22,23]:…”

Section: трансформация солитона на уступеunclassified

Wave dynamics in the variable-section channels

Pelinovsky¹,

Didenkulova²,

Shurgalina³

2017

MGZh

View full text Add to dashboard Cite

Динамика длинных морских волн в каналах переменной глубины и переменного прямо-угольного сечения обсуждается в рамках различных приближений от линейных уравнений мелкой воды до уравнений нелинейно-дисперсионной теории. В случае линейной теории мел-кой воды демонстрируется общий подход, позволяющий найти бегущие (безотражательные) волны в неоднородных каналах. Соответствующие условия определяются решением системы обыкновенных дифференциальных уравнений. Изучен в деталях так называемый согласован-ный канал, в котором ширина определенным образом связана с глубиной, при этом в рамках линейной теории мелкой воды волна не отражается от донных неровностей. Форма волны в таком канале остается неизменной на записях в фиксированных точках вдоль канала (марео-графных записях), но меняется в пространстве. Действие нелинейности и дисперсии приводит к деформации волны в таком канале. В рамках слабонелинейной теории мелкой воды форма волны описывается Римановым решением и волна обрушается (градиентная катастрофа), при-чем быстрее в зоне уменьшающейся глубины. Выведено модифицированное уравнение Корте-вега − де Вриза, описывающее эволюцию солитона малой, но конечной амплитуды в самосо-гласованном канале, глубина которого может меняться произвольным образом. Рассмотрены некоторые примеры трансформации уединенной волны в таком канале, в частности адиабати-ческая перестройка солитона в канале с медленно меняющимися параметрами и распад уеди-ненной волны на группу солитонов после прохождения зоны резкого изменения глубины. По-лученные решения расширяют класс решений, представленных ранее в работах С.Ф. Доценко, написанных им в соавторстве с учениками.Ключевые слова: бегущие длинные волны, каналы переменного сечения, уравнения мелкой воды, уравнение Кортевега -де Вриза.

show abstract

“…Since the wave after the bottom step has a soliton-like shape (but it is not a soliton), the calculation of the amplitudes of the emerging solitons is relatively simple (for more details, see [22,23]) and the formula for the secondary soliton amplitudes has the following form:…”

Section: Soliton Transformation On a Bottom Stepmentioning

confidence: 99%

“…As a result, the relationship between dispersion and nonlinearity, characterized by the Ursell number [22,23]:…”

Section: Soliton Transformation On a Bottom Stepmentioning

confidence: 99%

Wave Dynamics in the Channels of Variable Cross-Section

Pelinovsky¹,

Didenkulova²,

Shurgalina³

2017

PhO

View full text Add to dashboard Cite

Dynamics of long sea waves in the channels of variable depth and variable rectangular cross-section is discussed within various approximations -from the shallow water equations to those of nonlinear dispersion theory. General approach permitting to find traveling (non-reflective) waves in inhomogeneous channels is demonstrated within the framework of the shallow water linear theory. The appropriate conditions are determined by solving a system of ordinary differential equations. The so-called self-consistent channel in which the width is connected with its depth in a specific way is studied in detail. Within the linear theory of shallow water, a wave does not reflect from the bottom irregularities. The wave shape remains unchanged on the records of the wave gauges (mareographs) fixed along the channel axis, but it varies in space. Nonlinearity and dispersion lead to the wave transformation in such a channel. Within the framework of the shallow water weakly nonlinear theory, the wave shape is described by the Riemann solution, and the wave breaks (gradient catastrophe) quicker in the zones of decreasing depth. The modified Korteweg -de Vries equation describing evolution of a solitary wave of weak but finite amplitude in a self-consistent channel, the depth of which can vary arbitrary, is derived. Some examples of a solitary wave transformation in such a channel are analyzed (particularly, a soliton adiabatic transformation in the channel with the slowly varying parameters, and a solitary wave fission into the group of solitons after it has passed the zone where the depth changes abruptly. The obtained solutions extend the class of those represented earlier by S.F. Dotsenko and his colleagues.

show abstract

Solitary wave dynamics in shallow water over periodic topography

Cited by 23 publications

References 28 publications

Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework

Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework

Wave dynamics in the variable-section channels

Wave Dynamics in the Channels of Variable Cross-Section

Contact Info

Product

Resources

About