Numerical Modeling of the Internal Dispersive Shock Wave in the Ocean

Talipova, Tatiana; Pelinovsky, Efim; Kurkina, Oxana; Kurkin, Andrey

doi:10.1155/2015/875619

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…Such a nonlinear wavetrain is called a dispersive shock wave (DSW). 1 The phenomenon of DSWs is ubiquitous in nature, appearing in dispersive media as diverse as the ocean, 2,3 intense laser light, 4,5,6 electron beams, 7 ultra-cold atoms, 8,9,10 and viscous fluids. 11 It is the superfluid or dispersive hydrodynamic analog of a viscous shock wave in a gas.…”

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confidence: 99%

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

et al. 2017

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The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin-wave step pulse in a low-loss magnetic Y 3 Fe 5 O 12 thin film strip, in which the spin-wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin-wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW selfcavitation, indicated by a point of zero power and a concomitant 180 phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.

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confidence: 99%

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

et al. 2017

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“…The SG dynamics has significant research implications in various physical fields such as optics [5][6][7][8][9], hydrodynamics [10,11], and plasmas [12]. Multiple soliton interactions may lead to the occurrence of rogue waves (RWs), which were actively studied in the context of ocean internal waves [13][14][15][16] and nonlinear optics [7,8,17]. In experiment, the SG can be generated by the synchronous injection of laser pulses inside a passive ring cavity [18], and in long water tank through the disorganization of wave motion induced by the wave maker [19].…”

Section: Introductionmentioning

confidence: 99%

Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

Zhang,

Xu,

Yang

et al. 2024

Preprint

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For the focusing Gardner equation, we investigate the dynamics of soliton gas (SG) incorporating the strongest pairwise soliton interactions that achieve the maximum attainable amplification AI = 2. In our simulated SG, the interactions of positive solitons overtaking negative ones are dominant because the velocities of most of positive solitons are larger than those of negative ones in the initial distribution. As the number of bipolar soliton pairs with AI = 2 increases, the third moment decrease in absolute while the fourth moment increases. Meanwhile, the maximum values in the global wave field increase significantly while the minimum values exhibit a relatively modest increase, owing to the generation of many high positive transient waves during interactions, as compared to the limited production of high negative transient waves. Also, an obvious elevation in the tails of global probability density functions is observed for positive wave amplitudes, which indicates an increase of the number of extreme events in the wave field. In addition, the rogue wave (RW) occurrence probability does not increase but rather decreases, in contrast to the situation in the integrable turbulence. Our findings may be useful for realizing some controllable experiments of the SGs in water waves. PACS: 05.45.Yv; 02.30.Ik; 47.35.Fg.

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“…In their generic form they are a modulated wavetrain, consisting of solitary waves at one edge and linear dispersive waves at the opposite edge, which links two disparate flow states, thus displaying a range of nonlinearities within a single coherent structure 2 . In addition to their theoretical interest as a generic nonlinear wave form, DSWs are readily observable in a wide range of applications, examples including meteorology [3][4][5] , oceanography [6][7][8][9][10] , water waves 7,8,11 , plasmas 12 , geophysics [13][14][15][16] , nonlinear optics [17][18][19][20][21][22][23][24][25][26] , elasticity 27 , Bose-Einstein condensates 28 , magnetic films 29 and Fermionic fluids 30 , see 2 for a summary of these applications.…”

Section: Introductionmentioning

confidence: 99%

Numerical and analytical study of undular bores governed by the full water wave equations and bidirectional Whitham–Boussinesq equations

2021

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Undular bores, also termed dispersive shock waves, generated by an initial discontinuity in height as governed by two forms of the Boussinesq system of weakly nonlinear shallow water wave theory, the standard formulation and a Hamiltonian formulation, two related Whitham-Boussinesq equations and the full water wave equations for gravity surface waves are studied and compared. It is found that the Whitham-Boussinesq systems give solutions in excellent agreement with numerical solutions of the full water wave equations for the positions of the leading and trailing edges of the bore up until the onset on modulational instability. The Whitham-Boussinesq systems, which are far simpler than the full water wave equations, can then be used to accurately model surface water wave undular bores. Finally, comparisons with numerical solutions of the full water wave equations show that the Whitham-Boussinesq systems give a slightly lower threshold for the onset of modulational instability in terms of the height of the initial step generating the undular bore.

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Numerical Modeling of the Internal Dispersive Shock Wave in the Ocean

Cited by 5 publications

References 23 publications

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

Numerical and analytical study of undular bores governed by the full water wave equations and bidirectional Whitham–Boussinesq equations

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