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AuthorSamtaney, Ravi (7)Wheatley, V. (6)Pullin, D. I. (5)Mostert, W. (3)Bakhsh, Abeer (2)View MoreDepartmentMechanical Engineering Program (8)Physical Sciences and Engineering (PSE) Division (8)Applied Mathematics and Computational Science Program (2)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (1)JournalJournal of Fluid Mechanics (3)Physical Review Fluids (2)Journal of Fluids Engineering (1)Matter and Radiation at Extremes (1)Physics of Fluids (1)KAUST Acknowledged Support UnitKAUST Office of Sponsored Research (2)KAUST Grant Number

URF/1/2162-01 (8)

PublisherCambridge University Press (CUP) (3)AIP Publishing (2)American Physical Society (APS) (2)ASME International (1)SubjectMHD and electrohydrodynamics (3)compressible flows (2)Magnetohydrodynamics (2)shock waves (2)converging shock (1)View MoreTypeArticle (8)Year (Issue Date)2018 (2)2017 (3)2016 (3)Item AvailabilityOpen Access (5)Metadata Only (3)

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Spontaneous singularity formation in converging cylindrical shock waves

Mostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V. (Physical Review Fluids, American Physical Society (APS), 2018-07-23) [Article]

We develop a nonlinear, Fourier-based analysis of the evolution of a perturbed, converging cylindrical strong shock using the approximate method of geometrical shock dynamics (GSD). This predicts that a singularity in the shock-shape geometry, corresponding to a change in Fourier-coefficient decay from exponential to algebraic, is guaranteed to form prior to the time of shock impact at the origin, for arbitrarily small, finite initial perturbation amplitude. Specifically for an azimuthally periodic Mach-number perturbation on an initially circular shock with integer mode number q and amplitude proportional to ϵ1, a singularity in the shock geometry forms at a mean shock radius Ru,c∼(q2ϵ)-1/b1, where b1(γ)<0 is a derived constant and γ the ratio of specific heats. This requires q2ϵ1, q≫1. The constant of proportionality is obtained as a function of γ and is independent of the initial shock Mach number M0. Singularity formation corresponds to the transition from a smooth perturbation to a faceted polygonal form. Results are qualitatively verified by a numerical GSD comparison.

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

Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field

Mostert, W.; Pullin, D. I.; Wheatley, V.; Samtaney, Ravi (Physical Review Fluids, American Physical Society (APS), 2017-01-26) [Article]

We present numerical simulations of ideal magnetohydrodynamics showing suppression of the Richtmyer-Meshkov instability in spherical implosions in the presence of an octahedrally symmetric magnetic field. This field configuration is of interest owing to its high degree of spherical symmetry in comparison with previously considered dihedrally symmetric fields. The simulations indicate that the octahedral field suppresses the instability comparably to the other previously considered candidate fields for light-heavy interface accelerations while retaining a highly symmetric underlying flow even at high field strengths. With this field, there is a reduction in the root-mean-square perturbation amplitude of up to approximately 50% at representative time under the strongest field tested while maintaining a homogeneous suppression pattern compared to the other candidate fields.

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.

The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

Li, Yuan; Samtaney, Ravi; Wheatley, Vincent (Matter and Radiation at Extremes, AIP Publishing, 2018-04-13) [Article]

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal magnetohydrodynamics. Three fluids of differing densities are initially separated by the two perturbed cylindrical interfaces. The initial incident converging shock is generated from a Riemann problem upstream of the first interface. The effect of the magnetic field on the instabilities is studied through varying the field strength. It shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field, however, the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations. The degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.

Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma

Bond, D.; Wheatley, V.; Samtaney, Ravi; Pullin, D. I. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017-11-03) [Article]

We computationally investigate the Richtmyer–Meshkov instability of a density interface with a single-mode perturbation in a two-fluid, ion–electron plasma with no initial magnetic field. Self-generated magnetic fields arise subsequently. We study the case where the density jump across the initial interface is due to a thermal discontinuity, and select plasma parameters for which two-fluid plasma effects are expected to be significant in order to elucidate how they alter the instability. The instability is driven via a Riemann problem generated precursor electron shock that impacts the density interface ahead of the ion shock. The resultant charge separation and motion generates electromagnetic fields that cause the electron shock to degenerate and periodically accelerate the electron and ion interfaces, driving Rayleigh–Taylor instability. This generates small-scale structures and substantially increases interfacial growth over the hydrodynamic case.

Linear Analysis of Converging Richtmyer-Meshkov Instability in the Presence of an Azimuthal Magnetic Field

Bakhsh, Abeer; Samtaney, Ravindra (Journal of Fluids Engineering, ASME International, 2017-12-20) [Article]

We investigate the linear stability of both positive and negative Atwood ratio interfaces accelerated either by a fast magnetosonic or hydrodynamic shock in cylindrical geometry. For the magnetohydrodynamic (MHD) case, we examine the role of an initial seed azimuthal magnetic field on the growth rate of the perturbation. In the absence of a magnetic field, the Richtmyer-Meshkov growth is followed by an exponentially increasing growth associated with the Rayleigh-Taylor instability. In the MHD case, the growth rate of the instability reduces in proportion to the strength of the applied magnetic field. The suppression mechanism is associated with the interference of two waves running parallel and anti-parallel to the interface that transport of vorticity and cause the growth rate to oscillate in time with nearly a zero mean value.

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