The non-modal onset of the tearing instability

MacTaggart, D. (2018) The non-modal onset of the tearing instability. Journal of Plasma Physics, 84(5), 905840501. (doi: 10.1017/S0022377818001009)

Abstract

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number S increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the L2 -norm, for the classical set-up of current sheets unstable to the TI, scales as O(S1/4) on time scales of O(S1/4) for S≫1 . This behaviour is much faster than the time scale O(S1/2) when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mactaggart, Dr David
• Authors: MacTaggart, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Plasma Physics
• Publisher: Cambridge University Press
• ISSN: 0022-3778
• ISSN (Online): 1469-7807
• Published Online: 18 September 2018
• Copyright Holders: Copyright © 2018 Cambridge University Press
• First Published: First published in Journal of Plasma Physics 84(5): 905840501
• Publisher Policy: Reproduced in accordance with the publisher copyright policy