Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits

Maiden, Michelle; Lowman, Nicholas K.; Anderson, Donald G.; Schubert, Marika E.; Hoefer, Mark

doi:10.1103/physrevlett.116.174501

Cited by 47 publications

(64 citation statements)

References 43 publications

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“…Finally, Figure 5D illustrates the leading edge partial DSW at = 50 and its envelope predicted from modulation theory. The envelope was computed using the simple wave solution (19). This solution expresses the wavenumber , mean height and amplitude in terms of the self-similar variable = ∕ .…”

Section: Comparisons Of Kdvmodulation Theory With Numerical Solutionsmentioning

confidence: 99%

“…[15][16][17][18] These equations, in fact, coincide with the long wave interfacial equations for the conduit flow of a buoyant, viscous fluid through a miscible, much more viscous fluid. 18,19 Other DSW application areas include nonlinear optics (photorefractive crystals, [20][21][22][23] nonlinear optical fibers, 24,25 nonlinear thermal optical media, 26,27 and colloidal media, 28,29 ), Bose-Einstein condensates, 30,31 and thin-film magnetic materials. 32 Mathematically, a DSW can be understood as an unsteady, modulated wavetrain that consists of two distinguished limits: the zero wavenumber, solitary wave limit and the zero amplitude, linear dispersive wave limit.…”

Section: Introductionmentioning

confidence: 99%

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Modulation theory solution for nonlinearly resonant, fifth‐order Korteweg–de Vries, nonclassical, traveling dispersive shock waves

2018

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A new class of resonant dispersive shock waves was recently identified as solutions of the Kawahara equationa Korteweg-de Vries (KdV) type nonlinear wave equation with third-and fifth-order spatial derivatives-in the regime of nonconvex, linear dispersion. Linear resonance resulting from the third-and fifth-order terms in the Kawahara equation was identified as the key ingredient for nonclassical dispersive shock wave solutions. Here, nonlinear wave (Whitham) modulation theory is used to construct approximate nonclassical traveling dispersive shock wave (TDSW) solutions of the fifth-order KdV equation without the third derivative term, hence without any linear resonance. A self-similar, simple wave modulation solution of the fifth order, weakly nonlinear KdV-Whitham equations is obtained that matches a constant to a heteroclinic traveling wave via a partial dispersive shock wave so that the TDSW is interpreted as a nonlinear resonance. The modulation solution is compared with full numerical solutions, exhibiting excellent agreement. The TDSW is shown to be modulationally stable in the presence of sufficiently small third-order dispersion. The Kawahara-Whitham modulation equations transition from hyperbolic to elliptic type for sufficiently large third-order dispersion, which provides a possible route for the TDSW to exhibit modulational instability.

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Section: Comparisons Of Kdvmodulation Theory With Numerical Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modulation theory solution for nonlinearly resonant, fifth‐order Korteweg–de Vries, nonclassical, traveling dispersive shock waves

2018

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“…Dispersive shock waves (DSWs) are rapidly oscillating solutions of hyperbolic partial differential equations that contrast the generation of multivalued regions through the formation of undular bores [1][2][3][4][5][6][7][8][9][10][11]. This class of phenomena was investigated in several physical fields, initially in shallow water waves [12] and ion-acoustic waves [13], then in oceanography [14], pulses propagation in photonic fibers [15,16], Bose-Einstein condensates [17][18][19][20][21][22], quantum liquids [23], photorefractive media [24], plasma physics [25], viscous fluids [26], and diffracting optical beams [5,[27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Optical spatial shock waves in nonlocal nonlinear media

Marcucci

Pierangeli

Gentilini

et al. 2019

Advances in Physics: X

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Dispersive shock waves are fascinating phenomena occurring when nonlinearity overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves are still under investigation, as the interplay with noninstantaneity in temporal pulses transmission and nonlocality in spatial beams propagation.Despite the rich and vast literature on nonlinear waves in optical Kerr media, spatial dispersive shock waves in nonlocal materials deserve further attention for their unconventional properties. Indeed, they have been investigated in colloidal matter, chemical physics and biophotonics, for sensing and control of extreme phenomena.Here we review the last developed theoretical models and recent optical experiments on spatial dispersive shock waves in nonlocal media. Moreover, we discuss observations in novel versatile materials relevant for soft matter and biology.

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“…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. 1 In contrast to the entropy production and energy dissipation due to friction in viscous shock waves, however, a DSW conserves energy, converting the potential energy of an initial jump into the kinetic energy of nonlinear oscillations.…”

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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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Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits

Cited by 47 publications

References 43 publications

Modulation theory solution for nonlinearly resonant, fifth‐order Korteweg–de Vries, nonclassical, traveling dispersive shock waves

Modulation theory solution for nonlinearly resonant, fifth‐order Korteweg–de Vries, nonclassical, traveling dispersive shock waves

Optical spatial shock waves in nonlocal nonlinear media

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

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