Incompressible models of magnetohydrodynamic Richtmyer-Meshkov instability in cylindrical geometry

Bakhsh, Abeer; Samtaney, Ravi

doi:10.1103/physrevfluids.4.063906

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…Surprisingly, the eigenvalues l i associated with the Hall-MHD model found in (14) where d L > 0, does not enter the solution. Indeed, taking the inverse Laplace transform of Eq.…”

Section: Oscillatory Solutionsmentioning

confidence: 93%

“…The RMI, however, gives rise to mixing between the capsule material and the fuel within, compromising the chance of achieving energy break-even or production. 8 Converging shock-driven RMI in both gases [9][10][11][12][13][14] and solids 15,16 has therefore received attention. Moreover, the high temperatures associated with ICF implosion inevitably cause rapid ionization of the involved materials, which then leads to the interaction between the conducting fluids and magnetic fields that are imposed or self-generated.…”

Section: Introductionmentioning

confidence: 99%

“…Several theoretical descriptions have been proposed in order to model the coupled evolution of plasmas and magnetic fields. One framework is the single-fluid ideal magnetohydrodynamic (MHD) system, where it is demonstrated that the growth of the RMI is suppressed in the presence of an initially uniform magnetic field either normal 14,[23][24][25] or tangential 26,27 to the interface. The cylindrically and spherically converging MHD RMI is also suppressed under a range of seed magnetic field configurations, as investigated numerically by Mostert et al 28,29 In the cylindrical geometry, it is shown that while the suppression occurs along the entire density interface, its extent and the behavior of the interface are highly dependent on the local orientation of the magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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Magnetohydrodynamic Richtmyer–Meshkov instability under an arbitrarily oriented magnetic field

et al. 2020

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The effect of an initially uniform magnetic field of arbitrary orientation on the Richtmyer-Meshkov instability in Hallmagnetohydrodynamics (MHD) and ideal MHD is considered. Attention is restricted to the case where the initial density interface has a single-mode sinusoidal perturbation in amplitude and is accelerated by a shock traveling perpendicular to the interface. An incompressible Hall-MHD model for this flow is developed by solving the relevant impulse-driven linearized initial value problem. The ideal MHD theory is naturally obtained by taking the limit of vanishing ion skin depth. It is shown that the out-of-plane magnetic field component normal to both the impulse and the interface perturbation does not affect the evolution of the flow. For all field orientations other than strictly out-ofplane, the growth of interface perturbations is suppressed. However, the suppression is most effective for near tangential fields but becomes less effective with increasing ion skin depth and Larmor radius. The modeled suppression mechanism is transport of vorticity along magnetic field lines via Alfv en fronts in ideal MHD, and via a dispersive wave system in Hall-MHD. Oscillation of the interface growth rate is caused by a continuous phase change of the induced velocities at the interface due to vorticity transport parallel to the perturbation direction in ideal MHD, while it can also result from interfacial vorticity production associated with the ion cyclotron effect in Hall-MHD with a finite Larmor radius. The limiting flow behavior of a large ion-skin-depth is explored. To assess the accuracy and appropriateness of the incompressible model, its ideal MHD predictions are compared to the results of the corresponding shock-driven nonlinear compressible simulations.

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“…Surprisingly, the eigenvalues l i associated with the Hall-MHD model found in (14) where d L > 0, does not enter the solution. Indeed, taking the inverse Laplace transform of Eq.…”

Section: Oscillatory Solutionsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Magnetohydrodynamic Richtmyer–Meshkov instability under an arbitrarily oriented magnetic field

et al. 2020

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The Richtmyer–Meshkov instability of concave circular arc density interfaces in hydrodynamics and magnetohydrodynamics

Qin

Dong

2021

Physics of Fluids

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Concave circular arc density interfaces (CDIs) are relevant to a deformed diaphragm separating different pressure gases in a shock tunnel or an expansion tube, where it is known that the Richtmyer–Meshkov instability (RMI) limits facility performance. Considering CDIs characterized by different curvatures (κ), numerical investigations of the RMI in both hydrodynamics (hydro) and magnetohydrodynamics (MHD) are performed. In the hydro cases, the largest curvature case appears to be the most unstable one, with the largest amounts of vorticities deposited on the CDIs. In the MHD cases, the interplay between the RMI and the magnetic field is investigated. On the one hand, the RMI can be compressed by magnetic fields. The stronger the magnetic field is, the smoother the density interface will be. The magnetic pressure alleviates pressure deviations along two sides of the CDIs, reducing baroclinic effects. Meanwhile, the magnetic tension force induces Alfvén waves, which transport vorticities away from density interfaces. On the other hand, magnetic fields can be amplified by the RMI, indicating that more amplification occurs when the initial magnetic field is weak, and magnetic lines are severely distorted in such cases. Besides, the evolutions of the kinetic energy and the magnetic energy are discussed. The results indicate that there is no energy transfer between them, and the magnetic energy mainly concentrates on the MHD wave fronts. The change of the enstrophy against time demonstrates that the vorticity energy decreases when the strength of initial magnetic fields increases.

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Linear analysis of magnetohydrodynamic Richtmyer–Meshkov instability in cylindrical geometry for double interfaces in the presence of an azimuthal magnetic field

Bakhsh

2022

Physics of Fluids

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Richtmyer-Meshkov instability (RMI) occurs when a shock wave impulsively accelerates a perturbed density interface between different fluids. The present work investigates the suppression of RMI of double interfaces in terms of linear analysis in cylindrical geometry. An exponential increase/decrease in a growth rate is related to the Rayleigh-Taylor instability (RTI) that occurs without a magnetic field as the lighter fluid penetrates the heavier one. The research program of inertial confinement fusion (ICF) is one of the advanced applications where fluid mixing is the main mechanize of producing energy. The investigations represent the effects of different Atwood numbers or magnetic strengths on the suppression of the instabilities. Three different cases are considered with the hydrodynamics (HD) and magnetohydrodynamics (MHD). In MHD case, the instability's growth rate reduces proportion to the Atwood ratios or the strength of the magnetic field. Two waves are interfering and running parallel and anti-parallel to the interfaces and transport the generated vorticity at the interfaces, causing the perturbed interfaces' growth rate to oscillate in time, which is the essential suppression mechanism.

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Incompressible models of magnetohydrodynamic Richtmyer-Meshkov instability in cylindrical geometry

Cited by 6 publications

References 25 publications

Magnetohydrodynamic Richtmyer–Meshkov instability under an arbitrarily oriented magnetic field

Magnetohydrodynamic Richtmyer–Meshkov instability under an arbitrarily oriented magnetic field

The Richtmyer–Meshkov instability of concave circular arc density interfaces in hydrodynamics and magnetohydrodynamics

Linear analysis of magnetohydrodynamic Richtmyer–Meshkov instability in cylindrical geometry for double interfaces in the presence of an azimuthal magnetic field

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