Joint instability and abrupt nonlinear transitions in a differentially rotating plasma. (February 2019)

• Record Type: Journal Article
• Authors: Plummer, A.; Marston, J. B.; Tobias, S. M.
• Is Part Of: Journal of plasma physics. Volume 85:Number 1(2019)
• Publication Date: 2019-02
• Subjects: astrophysical plasmas, -- plasma dynamics, -- plasma nonlinear phenomena; Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S0022377819000060
• Languages: English
• ISSNs: 0022-3778

Abstract

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.