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AuthorSamtaney, Ravi (3)Wheatley, V. (3)Mostert, W. (2)Pullin, D. I. (2)Bakhsh, Abeer (1)View MoreDepartmentMechanical Engineering Program (3)Physical Sciences and Engineering (PSE) Division (3)Applied Mathematics and Computational Science Program (1)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (1)JournalJournal of Fluid Mechanics (2)Physics of Fluids (1)KAUST Acknowledged Support UnitKAUST Office of Sponsored Research (2)KAUST Grant Number

URF/1/2162-01 (3)

PublisherCambridge University Press (CUP) (2)AIP Publishing (1)Subjectcompressible flows (2)MHD and electrohydrodynamics (2)shock waves (2)View MoreTypeArticle (3)Year (Issue Date)
2016 (3)

Item AvailabilityMetadata Only (2)Open Access (1)

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Geometrical shock dynamics for magnetohydrodynamic fast shocks

Mostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016-12-12) [Article]

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

Converging cylindrical magnetohydrodynamic shock collapse onto a power-law-varying line current

Mostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016-03-16) [Article]

We investigate the convergence behaviour of a cylindrical, fast magnetohydrodynamic (MHD) shock wave in a neutrally ionized gas collapsing onto an axial line current that generates a power law in time, azimuthal magnetic field. The analysis is done within the framework of a modified version of ideal MHD for an inviscid, non-dissipative, neutrally ionized compressible gas. The time variation of the magnetic field is tuned such that it approaches zero at the instant that the shock reaches the axis. This configuration is motivated by the desire to produce a finite magnetic field at finite shock radius but a singular gas pressure and temperature at the instant of shock impact. Our main focus is on the variation with shock radius, as, of the shock Mach number and pressure behind the shock as a function of the magnetic field power-law exponent, where gives a constant-in-time line current. The flow problem is first formulated using an extension of geometrical shock dynamics (GSD) into the time domain to take account of the time-varying conditions ahead of the converging shock, coupled with appropriate shock-jump conditions for a fast, symmetric MHD shock. This provides a pair of ordinary differential equations describing both and the time evolution on the shock, as a function of, constrained by a collapse condition required to achieve tuned shock convergence. Asymptotic, analytical results for and are obtained over a range of for general, and for both small and large . In addition, numerical solutions of the GSD equations are performed over a large range of, for selected parameters using . The accuracy of the GSD model is verified for some cases using direct numerical solution of the full, radially symmetric MHD equations using a shock-capturing method. For the GSD solutions, it is found that the physical character of the shock convergence to the axis is a strong function of . For μ≤0.816, and both approach unity at shock impact owing to the dominance of the strong magnetic field over the amplifying effects of geometrical convergence. When (for γ=5/3 ), geometrical convergence is dominant and the shock behaves similarly to a converging gas dynamic shock with singular and. For <μ≤0.816 three distinct regions of variation are identified. For each of these is singular at the axis. © 2016 Cambridge University Press.

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

Bakhsh, Abeer; Gao, Song; Samtaney, Ravi; Wheatley, V. (Physics of Fluids, AIP Publishing, 2016-03-09) [Article]

Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability(RMI) is suppressed in ideal magnetohydrodynamics(MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2p/B^2_r) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.

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