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Joint instability and abrupt nonlinear transitions in a differentially rotating plasma
Plummer, A.; Marston, J. B.; Tobias, S. M.
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)
Journal of Plasma Physics, Volume 85, Issue 1, article id. 905850113, 21 pp.
Publication Date:
astrophysical plasmas, plasma dynamics, plasma nonlinear phenomena
Abstract Copyright:
(c) 2019: © Cambridge University Press 2019
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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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