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Geometrical shock dynamics for magnetohydrodynamic fast shocks

Published online by Cambridge University Press:  12 December 2016

W. Mostert ,
D. I. Pullin ,
R. Samtaney  and
V. Wheatley
W. Mostert*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, CA 91125, USA
D. I. Pullin
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, CA 91125, USA
R. Samtaney
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
V. Wheatley
Affiliation:
School of Mechanical and Mining Engineering, University of Queensland, QLD 4072, Australia
*
†Email address for correspondence: wouter.mostert@uqconnect.edu.au
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Abstract

We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as $\unicode[STIX]{x1D716}^{-1}$, where $\unicode[STIX]{x1D716}$ is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Shock waves MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , R2
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Copyright
© 2016 Cambridge University Press 

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