Joint Instability and Abrupt Nonlinear Transitions in a Differentially Rotating Plasma

TL;DR

This study investigates MHD instabilities in a solar tachocline model, revealing a new long-term energy cycle driven by magnetic and kinetic energy exchanges, which depends on nonlinear interactions and eddy processes.

Contribution

It introduces a comprehensive analysis of joint instabilities and long-term cycles in a differentially rotating plasma using multiple simulation methods, highlighting the importance of eddy scattering.

Findings

Identification of a new long-term energy cycle in the plasma model.

Nonlinear development of instability becomes more complex with decreased magnetic diffusivity.

Periodic energy exchanges resemble solar variability phenomena.

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 analyze the nonlinear development of the instability via fully nonlinear direct numerical simulation, the generalized quasilinear 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 are identified that produce 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.