Shock Waves and Shock-Wave Structure in Magneto-Fluid Dynamics

Germain, P.

doi:10.1103/revmodphys.32.951

Cited by 102 publications

(37 citation statements)

References 4 publications

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“…It has been suggested by [9] Germain that, to some degree, there appears to have been two avenues of shock wave studies.…”

Section: Introductionmentioning

confidence: 99%

Study of Two-Sided Similarity Methods Using a Radiation “Switch on” Imploding Shock in a Magnetic Field

NiCastro¹

2018

Journal of Applied Mathematics

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This paper explores aspects of two-sided similarity modeling using cylindrical geometry for radiating shock waves embedded in a medium with a magnetic field. Two-sided similarity solution techniques may be used to link states influenced by long range near instantaneous fields that continually modify the pre-and postshock zones. Emergent radiation scaling relations are immediately available from consistent homologies. For both small angle and large angle measurements, an approximate analytic technique in the vicinity of luminous fronts together with the high symmetry implications delineated in Lemma provides direct access to the homology parameters. The parameters obtained using this process can augment the constraint relations and contribute to establishing relevant similarity homologies.

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“…It has been suggested by [9] Germain that, to some degree, there appears to have been two avenues of shock wave studies.…”

Section: Introductionmentioning

confidence: 99%

Study of Two-Sided Similarity Methods Using a Radiation “Switch on” Imploding Shock in a Magnetic Field

NiCastro¹

2018

Journal of Applied Mathematics

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“…Germain 1960;Anderson 1963;Jeffrey and Taniuti 1964;Liberman and Velikhovich 1986;Sturtevant 1987;Gombosi 1998;Goedbloed 2008) and just express the basic nonlinear conservation laws across a discontinuity. Discontinuous solutions only satisfy the integral form of the MHD equations, i.e.…”

Section: Intermediate Shocks In Mhdmentioning

confidence: 99%

Parameter regimes for slow, intermediate and fast MHD shocks

Delmont

Keppens²

2010

J. Plasma Phys.

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We investigate under which parameter regimes the magnetohydrodynamic (MHD) Rankine-Hugoniot conditions, which describe discontinuous solutions to the MHD equations, allow for slow, intermediate and fast shocks. We derive limiting values for the upstream and downstream shock parameters for which shocks of a given shock-type can occur. We revisit this classical topic in nonlinear MHD dynamics, augmenting the recent time reversal duality finding by in the usual shock frame parametrization.

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“…For dissipative models in simple geometries in the limit of vanishing dissipation, the intermediate shocks were shown not to be stable against certain perturbations. Traditionally ͑Akhiezer, Liubarski, and Polovin, 9 Germain, 10 Jeffrey and Taniuti 11 ͒, this failure of the test of evolutionarity was used to rule out the physical reality of intermediate shocks. However, after Wu 13 showed intermediate shocks to arise in numerical solutions of the dissipative MHD equations, a flurry of numerical and observational papers appeared on the structure and formation of intermediate shocks, [25][26][27][28][29] on their astrophysical implications, 30,31 on their relationship with magnetic reconnection, 32,33 on their significance for the Riemann problem, [34][35][36] on their occurrence in bow-shock flows, 37 and their possible breakup.…”

Section: -17mentioning

confidence: 99%

“…7,8 In the theory of shock conditions in magnetohydrodynamics ͑MHD͒, the so-called intermediate shocks play a prominent role since they continuously connect the slow and fast magnetosonic shocks in parameter space. In the older literature, [9][10][11][12] these shocks were discarded because they were believed to be nonevolutionary. However, in 1988, Wu 13 showed intermediate shocks to arise in a numerical solution of the dissipative MHD equations through nonlinear steepening from a continuous wave.…”

Section: Introductionmentioning

confidence: 99%

Time reversal duality of magnetohydrodynamic shocks

Goedbloed

2008

Physics of Plasmas

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The shock conditions in magnetohydrodynamics ͑MHD͒ are reduced to their most concise, three-parameter, distilled form by consistent use of the scale independence of the MHD equations and of the de Hoffmann-Teller transformation. They then exhibit a distinct time reversal duality between entropy-allowed shocks and entropy-forbidden jumps. This yields a new classification of MHD shocks by means of the monotonicity properties with respect to upstream and downstream Alfvén Mach numbers, it exhibits the central role of intermediate discontinuities, and permits straightforward construction of all relevant dimensionless quantities of the shocks. An exhaustive overview is presented of solutions in the different parameter regimes.

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Shock Waves and Shock-Wave Structure in Magneto-Fluid Dynamics

Cited by 102 publications

References 4 publications

Study of Two-Sided Similarity Methods Using a Radiation “Switch on” Imploding Shock in a Magnetic Field

Study of Two-Sided Similarity Methods Using a Radiation “Switch on” Imploding Shock in a Magnetic Field

Parameter regimes for slow, intermediate and fast MHD shocks

Time reversal duality of magnetohydrodynamic shocks

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