Geometrical shock dynamics for magnetohydrodynamic fast shocks

Mostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V.

Geometrical shock dynamics for magnetohydrodynamic fast shocks

Type

Article

Authors

Mostert, W.
Pullin, D. I.
Samtaney, Ravi

Wheatley, V.

KAUST Department

Fluid and Plasma Simulation Group (FPS)
Mechanical Engineering Program
Physical Science and Engineering (PSE) Division

KAUST Grant Number

URF/1/2162-01

Online Publication Date

2016-12-12

Print Publication Date

2017-01

Date

2016-12-12

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 (Formula presented.), where (Formula presented.) 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. © 2016 Cambridge University Press

Citation

Mostert W, Pullin DI, Samtaney R, Wheatley V (2016) Geometrical shock dynamics for magnetohydrodynamic fast shocks. Journal of Fluid Mechanics 811. Available: http://dx.doi.org/10.1017/jfm.2016.767.

Acknowledgements

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).