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Geometrical shock dynamics for magnetohydrodynamic fast shocks

Mostert, W. and Pullin, D. I. and Samtaney, R. and Wheatley, V. (2017) Geometrical shock dynamics for magnetohydrodynamic fast shocks. Journal of Fluid Mechanics, 811 . Art. No. R2. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20170112-111948222

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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 ϵ^(-1), where ϵ 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1017/jfm.2016.767DOIArticle
ORCID:
AuthorORCID
Samtaney, R.0000-0002-4702-6473
Additional Information:© 2016 Cambridge University Press. Received 2 September 2016; revised 25 October 2016; accepted 10 November 2016; first published online 12 December 2016. This research was supported by the KAUST Office of Sponsored Research under award URF/1/2162-01. V.W. holds an Australian Research Council Discovery Early Career Researcher Award (project number DE120102942).
Funders:
Funding AgencyGrant Number
King Abdullah University of Science and Technology (KAUST)URF/1/2162-01
Australian Research CouncilDE120102942
Subject Keywords:compressible flows, shock waves, MHD and electrohydrodynamics
Record Number:CaltechAUTHORS:20170112-111948222
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170112-111948222
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73472
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Jan 2017 16:42
Last Modified:03 Oct 2019 16:28

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