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Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

Published online by Cambridge University Press:  15 February 2022

Andrey Beresnyak Open the ORCID record for Andrey Beresnyak [Opens in a new window] ,
Alexander L. Velikovich ,
John L. Giuliani  and
Arati Dasgupta
Andrey Beresnyak*
Affiliation:
Plasma Physics Division, US Naval Research Laboratory, Washington, DC 20375, USA
Alexander L. Velikovich
Affiliation:
Plasma Physics Division, US Naval Research Laboratory, Washington, DC 20375, USA
John L. Giuliani
Affiliation:
Plasma Physics Division, US Naval Research Laboratory, Washington, DC 20375, USA Emeritus
Arati Dasgupta
Affiliation:
Plasma Physics Division, US Naval Research Laboratory, Washington, DC 20375, USA
*
†Email address for correspondence: andrey.beresnyak@nrl.navy.mil
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Abstract

The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh (OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$. Our self-similar solutions are indeed realized when we solve the initial value MHD problem with the finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field and a shock wave.

JFM classification

Compressible Flows: Shock waves MHD and Electrohydrodynamics: Plasmas
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A35
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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