Rogue waves in nonlinear hyperbolic systems (shallow-water framework)

Didenkulova, Ira; Pelinovsky, Efim

doi:10.1088/0951-7715/24/3/r01

Cited by 75 publications

(41 citation statements)

References 43 publications

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“…Moreover, it is shown that this theory explains the dynamics of freak waves on the shore and correlates well with their observations [12]. We point out in particular the fact that nonlinear waves in inclined channels with parabolic cross-section are non-reflective and do not lose energy during the propagation [13].…”

Section: Introductionsupporting

confidence: 81%

Wave Dynamics in the Channels of Variable Cross-Section

Pelinovsky¹,

Didenkulova²,

Shurgalina³

2017

PhO

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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.

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Section: Introductionsupporting

confidence: 81%

Wave Dynamics in the Channels of Variable Cross-Section

Pelinovsky¹,

Didenkulova²,

Shurgalina³

2017

PhO

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“…Analysis of tsunami records showed that reflections due to bottom topography may result in the appearance of resonant mode in the coastal zone, see for instance Neetu et al (2011). The study of the coastal rogue waves is based on the nonlinear theory of shallow water (Kharif et al, 2009;Didenkulova and Pelinovsky, 2011;Slunyaev et al, 2011). To characterize the impact of waves on coastal infrastructure, the systematic study of runup process is undertaken, and a lot of papers summarizing the progress in the analytical solutions of the nonlinear shallow-water theory have been published by now (see for instance Carrier and Greenspan, 1958;Pelinovsky, 1982;Synolakis, 1987;Pelinovsky and Mazova, 1992;Carrier et al, 2003;Kânoglu and Synolakis, 2006;Didenkulova et al, 2007;Madsen and Fuhrman, 2008;Kajiura, 1977).…”

Section: Introductionmentioning

confidence: 99%

Physical simulation of resonant wave run-up on a beach

Ezersky

Abcha

Pelinovsky

2013

Nonlin. Processes Geophys.

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Abstract. Nonlinear wave run-up on the beach caused by a harmonic wave maker located at some distance from the shore line is studied experimentally. It is revealed that under certain wave excitation frequencies, a significant increase in run-up amplification is observed. It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. Frequency and magnitude of the maximum amplification are in good correlation with the numerical calculation results represented in the paper (Stefanakis et al., 2011). These effects are very important for understanding the nature of rogue waves in the coastal zone.

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“…It could be discerned from the above that the majority of the studies on the rogue waves based on in situ measurements merely concentrates on the open seas rather than nearshore areas, although the rogue waves in shallow water have also attracted attention (Sergeeva et al, 2011;Didenkulova et al, 2006;Didenkulova and Pelinovsky, 2011;. Chien et al (2002) once reported about 140 freak wave events in the coastal zone of Taiwan in the past 50 years , which claims the existence of freak waves off the deep water areas.…”

Section: Y Wang Et Al: a Preliminary Investigation Of Rogue Waves Omentioning

confidence: 99%

A preliminary investigation of rogue waves off the Jiangsu coast, China

Wang

Tao

Zheng

et al. 2014

Nat. Hazards Earth Syst. Sci.

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Abstract. Due to the potential disasters induced by rogue waves, research in this field has increased rapidly in the last 2 decades. However, there are still a lot of open questions left, including some classic ones, such as whether the rogues waves are just rare events or not. One of the key reasons is that not enough of the observed rogue waves have been investigated. China has a wide sea area, but none of the research has addressed the observed rogue waves. In the present study, 1 year of observed wave data from Jiangsu coastal area, China, are analyzed. It is found that rogue waves are present, although the wave heights are not very large; furthermore, the probability of their occurrence is similar to the Rayleigh distribution prediction, due to the local silty coastal topography. The characteristics of rouge waves are investigated and the results indicate that a new type of rogue wave may exist.

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Rogue waves in nonlinear hyperbolic systems (shallow-water framework)

Cited by 75 publications

References 43 publications

Wave Dynamics in the Channels of Variable Cross-Section

Wave Dynamics in the Channels of Variable Cross-Section

Physical simulation of resonant wave run-up on a beach

A preliminary investigation of rogue waves off the Jiangsu coast, China

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