Shock Waves in Dispersive Eulerian Fluids

Hoefer, Mark

doi:10.1007/s00332-014-9199-4

Cited by 42 publications

(72 citation statements)

References 79 publications

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“…A positive dispersive shock, on the other hand, will produce a precursor wave train, with a linear wave edge in the upstream region and a standing soliton at the shock front. Such dispersive shock waves are solutions of the nonlinear Korteweg-de Vries equation of dispersive Eulerian fluids [Biskamp, 1973;Hoefer, 2014]. Since the fast magnetosonic oscilliton mode appears on fluid scale (see Figure 1a), our fluid model is able to capture the nonlinear trailing wave train of the thermal ion shock as we show below.…”

Section: Introductionmentioning

confidence: 92%

“…Note that this will give only the initial linear state of the soliton or oscilliton. The nonlinear growth rate and the full analytical solution of the oscilliton can be obtained from the nonlinear Korteweg-de Vries equation of dispersive Eulerian fluids [Biskamp, 1973;Hoefer, 2014]. The growth rate of the nonlinear low-frequency fast mode in a three-fluid model has been derived analytically by Toida and Aota [2013], and it has been shown that the low-frequency fast mode has a maximum amplitude.…”

Section: Appendix B: Derivation Of the Phase Velocity Of Solitons Andmentioning

confidence: 99%

“…An upstream propagating negative dispersive shock will produce a trailing wave train (quasi-stationary nonlinear wave or oscilliton) with a standing soliton (overshoot) at the shock front and a downstream propagating linear wave edge [Hoefer, 2014]. A positive dispersive shock, on the other hand, will produce a precursor wave train, with a linear wave edge in the upstream region and a standing soliton at the shock front.…”

Section: Introductionmentioning

confidence: 99%

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Constraining the pickup ion abundance and temperature through the multifluid reconstruction of the Voyager 2 termination shock crossing

et al. 2015

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Voyager 2 observations revealed that the hot solar wind ions (the so‐called pickup ions) play a dominant role in the thermodynamics of the termination shock and the heliosheath. The number density and temperature of this hot population, however, have remained unknown, since the plasma instrument on board Voyager 2 can only detect the colder thermal ion component. Here we show that due to the multifluid nature of the plasma, the fast magnetosonic mode splits into a low‐frequency fast mode and a high‐frequency fast mode. The coupling between the two fast modes results in a quasi‐stationary nonlinear wave mode, the “oscilliton,” which creates a large‐amplitude trailing wave train downstream of the thermal ion shock. By fitting multifluid shock wave solutions to the shock structure observed by Voyager 2, we are able to constrain both the abundance and the temperature of the undetected pickup ions. In our three‐fluid model, we take into account the nonnegligible partial pressure of suprathermal energetic electrons (0.022–1.5 MeV) observed by the Low‐Energy Charged Particle Experiment instrument on board Voyager 2. The best fitting simulation suggests a pickup ion abundance of 20 ± 3%, an upstream pickup ion temperature of 13.4 ± 2 MK, and a hot electron population with an apparent temperature of ~0.83 MK. We conclude that the actual shock transition is a subcritical dispersive shock wave with low Mach number and high plasma β.

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Section: Introductionmentioning

confidence: 92%

Section: Appendix B: Derivation Of the Phase Velocity Of Solitons Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Constraining the pickup ion abundance and temperature through the multifluid reconstruction of the Voyager 2 termination shock crossing

et al. 2015

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“…The minimum |f m | is found by applying Newton's method to (72), resulting in the amplitude A s . Hoefer [50] obtained general results for DSW solutions for NLS equations with a general nonlinearity f (|u| 2 )u.…”

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confidence: 99%

Optical dispersive shock waves in defocusing colloidal media

Marchant

Smyth

2017

Physica D: Nonlinear Phenomena

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The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocusing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations. AbstractThe propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocussing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.

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“…More recently, Dubrovin's universality conjectures [21] introduced a new direction in the rigorous treatment of the initial stage of DSW formation. Additional progress in the understanding of solutions to the Riemann problem for non-integrable nonlinear dispersive wave equations [22,23] has made possible the analytical description of DSWs in more physically-relevant model equations.…”

mentioning

confidence: 99%