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Joint instability and abrupt nonlinear transitions in a differentially rotating plasma

Part of: Focus on Plasma Astrophysics

Published online by Cambridge University Press:  18 February 2019

A. Plummer ,
J. B. Marston Open the ORCID record for J. B. Marston [Opens in a new window]  and
S. M. Tobias
A. Plummer
Affiliation:
Department of Physics, Harvard University, Cambridge, MA 02138, USA
J. B. Marston*
Affiliation:
Department of Physics, Brown University, Providence, RI 02912, USA
S. M. Tobias
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: [email protected]
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Abstract

Global magnetohydrodynamic (MHD) instabilities are investigated in a computationally tractable two-dimensional model of the solar tachocline. The model’s differential rotation yields stability in the absence of a magnetic field, but if a magnetic field is present, a joint instability is observed. We analyse the nonlinear development of the instability via fully nonlinear direct numerical simulation, the generalized quasi-linear approximation (GQL) and direct statistical simulation (DSS) based upon low-order expansion in equal-time cumulants. As the magnetic diffusivity is decreased, the nonlinear development of the instability becomes more complicated until eventually a set of parameters is identified that produces a previously unidentified long-term cycle in which energy is transformed from kinetic energy to magnetic energy and back. We find that the periodic transitions, which mimic some aspects of solar variability – for example, the quasiperiodic seasonal exchange of energy between toroidal field and waves or eddies – are unable to be reproduced when eddy-scattering processes are excluded from the model.

Keywords

astrophysical plasmasplasma dynamicsplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 1 , February 2019 , 905850113
Copyright
© Cambridge University Press 2019 

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