Geometrical shock dynamics for magnetohydrodynamic fast shocks

Handle URI:
http://hdl.handle.net/10754/622296
Title:
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Authors:
Mostert, W.; Pullin, D. I.; Samtaney, Ravi ( 0000-0002-4702-6473 ) ; Wheatley, V.
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
KAUST Department:
Mechanical Engineering Program; Physical Sciences and Engineering (PSE) Division
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.
Publisher:
Cambridge University Press (CUP)
Journal:
Journal of Fluid Mechanics
KAUST Grant Number:
URF/1/2162-01
Issue Date:
12-Dec-2016
DOI:
10.1017/jfm.2016.767
Type:
Article
ISSN:
0022-1120; 1469-7645
Sponsors:
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).
Additional Links:
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/div-classtitlegeometrical-shock-dynamics-for-magnetohydrodynamic-fast-shocksdiv/2DC5A580D7CBBC64D563EFEC8FD25200
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Mechanical Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorMostert, W.en
dc.contributor.authorPullin, D. I.en
dc.contributor.authorSamtaney, Ravien
dc.contributor.authorWheatley, V.en
dc.date.accessioned2017-01-02T09:08:24Z-
dc.date.available2017-01-02T09:08:24Z-
dc.date.issued2016-12-12en
dc.identifier.citationMostert 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.en
dc.identifier.issn0022-1120en
dc.identifier.issn1469-7645en
dc.identifier.doi10.1017/jfm.2016.767en
dc.identifier.urihttp://hdl.handle.net/10754/622296-
dc.description.abstractWe 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 Pressen
dc.description.sponsorshipThis 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).en
dc.publisherCambridge University Press (CUP)en
dc.relation.urlhttps://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/div-classtitlegeometrical-shock-dynamics-for-magnetohydrodynamic-fast-shocksdiv/2DC5A580D7CBBC64D563EFEC8FD25200en
dc.subjectcompressible flowsen
dc.subjectMHD and electrohydrodynamicsen
dc.subjectshock wavesen
dc.titleGeometrical shock dynamics for magnetohydrodynamic fast shocksen
dc.typeArticleen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalJournal of Fluid Mechanicsen
dc.contributor.institutionGraduate Aerospace Laboratories, California Institute of Technology, CA 91125, USAen
dc.contributor.institutionSchool of Mechanical and Mining Engineering, University of Queensland, QLD 4072, Australiaen
kaust.authorSamtaney, Ravien
kaust.grant.numberURF/1/2162-01en
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