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Title:
Joint instability and abrupt nonlinear transitions in a differentially rotating plasma
Authors:
Plummer, A.; Marston, J. B.; Tobias, S. M.
Affiliation:
AA(Department of Physics, Harvard University, Cambridge, MA 02138, USA), AB(Department of Physics, Brown University, Providence, RI 02912, USA), AC(Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK)
Publication:
Journal of Plasma Physics, Volume 85, Issue 1, article id. 905850113, 21 pp.
Publication Date:
02/2019
Origin:
CUP
Keywords:
astrophysical plasmas, plasma dynamics, plasma nonlinear phenomena
Abstract Copyright:
(c) 2019: © Cambridge University Press 2019
DOI:
10.1017/S0022377819000060
Bibliographic Code:
2019JPlPh..85a9013P

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.
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