Solitonic Dispersive Hydrodynamics: Theory and Observation

Maiden, Michelle; Anderson, Donald G.; Franco, Nevil; El, Gennady; Hoefer, Mark

doi:10.1103/physrevlett.120.144101

Cited by 51 publications

(153 citation statements)

References 28 publications

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“…The transmission through a DSW is then determined by the same conditions as in the RW case by way of hydrodynamic reciprocity, a notion recently described in the context of soliton–mean flow interactions (Maiden et al. 2018).…”

Section: Introductionmentioning

confidence: 99%

Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

Congy

Hoefer

2019

J. Fluid Mech.

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A new type of wave-mean flow interaction is identified and studied in which a smallamplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, largescale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg-de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket-mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wave packet by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (2018) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.

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Section: Introductionmentioning

confidence: 99%

Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

Congy

Hoefer

2019

J. Fluid Mech.

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“…In the derivation of the conduit equation, no restriction is placed on the magnitude of the nondimensional, circular cross-sectional area a(z, t), where z, t are the scaled height and time, respectively, assumed to be much larger than the conduit diameter and a characteristic advective time scale. This equation is also an asymptotic, long-wave model of magma flows rising through the Earth's mantle (Barcilon & Richter 1986;Whitehead & Helfrich 1988;Helfrich & Whitehead 1990) and to a comparatively simple laboratory experiment (Olson & Christensen 1986;Scott et al 1986;Whitehead & Helfrich 1988;Helfrich & Whitehead 1990;Lowman & Hoefer 2013a;Maiden et al , 2018Anderson et al 2019). Equation (1.1) fails the so-called Painlevé test for integrability (Harris & Clarkson 2006) and has at least two conservation laws (Harris 1996) therefore is an excellent candidate to test the more broadly applicable solitary wave resolution method for the initial value problem consisting of (1.1) and a(z, 0) = 1 + a 0 (z), lim |z|→∞ a 0 (z) = 0, (…”

Section: Introductionmentioning

confidence: 99%

Solitary wave fission of a large disturbance in a viscous fluid conduit

et al. 2019

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This paper presents a theoretical and experimental study of the long-standing fluid mechanics problem involving the temporal resolution of a large, localised initial disturbance into a sequence of solitary waves. This problem is of fundamental importance in a range of applications including tsunami and internal ocean wave modelling. This study is performed in the context of the viscous fluid conduit system-the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Due to buoyancy induced nonlinear self-steepening balanced by stress induced interfacial dispersion, the disturbance evolves into a slowly modulated wavetrain and further, into a sequence of solitary waves. An extension of Whitham modulation theory, termed the solitary wave resolution method, is used to resolve the fission of an initial disturbance into solitary waves. The developed theory predicts the relationship between the initial disturbance's profile, the number of emergent solitary waves, and their amplitude distribution, quantifying an extension of the well-known soliton resolution conjecture from integrable systems to non-integrable systems that often provide a more accurate modelling of physical systems. The theoretical predictions for the fluid conduit system are confirmed both numerically and experimentally. The number of observed solitary waves is consistently within 1-2 waves of the prediction, and the amplitude distribution shows remarkable agreement. Universal properties of solitary wave fission in other fluid dynamics problems are identified.

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“…Soliton tunneling was recently studied in the context of DSWs in defocusing media in [36]. Also, soliton trapping by an initial discontinuity was recently studied in [37,38]. Note, however, that phenomena governed by the Korteweg-deVries (KdV) equation or the defocusing NLS equation are very different from those described by the focusing NLS equation.…”

mentioning

confidence: 99%

Soliton trapping, transmission, and wake in modulationally unstable media

Biondini

Mantzavinos

2018

Phys. Rev. E

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Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrödinger equation. Two main interaction regimes are identified based on the relative value of the velocity of the incident soliton compared to the amplitude of the background: soliton transmission and soliton trapping. Specifically, when the incident soliton velocity exceeds a certain threshold, the soliton passes through the coherent structure and emerges on the other side with its velocity unchanged. Conversely, when the incident soliton velocity is below the threshold, once the soliton enters the coherent structure, it remains confined there forever. It is demonstrated that the soliton is not destroyed, but its velocity inside the coherent structure is different from its initial one. Moreover, it is also shown that, depending on the location of the discrete eigenvalue associated to the soliton, these phenomena can also be accompanied by the generation of additional, localized propagating waves in the coherent structure, akin to a soliton-generated wake.

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Solitonic Dispersive Hydrodynamics: Theory and Observation

Cited by 51 publications

References 28 publications

Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

Solitary wave fission of a large disturbance in a viscous fluid conduit

Soliton trapping, transmission, and wake in modulationally unstable media

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