Transient magnetorotational instability in rotating shear flows of plasma

Author: davit kaladze
Keywords: Magnetohydrodynamics, plasma shear flow, instability, turbulence
Annotation:

Linear dynamics of perturbations in a rotating constant shear flow of incompressible plasma with a parallel background uniform magnetic field is investigated. This type of plasma flow is ubiquitous in laboratory, in fusion devices, in the atmosphere as well as in a variety of astrophysical objects, so their stability analysis is of paramount importance in understanding dynamics and evolution of these systems. By linearizing equations of ideal magnetohydrodynamics, we obtain evolution equations for small perturbations. For the analysis we employ a special type of nonmodal approach – Kelvin mode formalism. First, in the asymptotic (WKB) approximation we derive dispersion relation and classify modes present in the flow. These are: 1. inertial waves – driven by rotation, but modified by the magnetic field, 2. magnetic mode – driven by magnetic tension force, but modified by rotation. Then, using numerical integration, we analyze time-evolution of both modes. Inertial waves undergo only moderate transient algebraic growth due to shear. By contrast, the magnetic mode exhibits strong (exponential) amplification due to magnetorotational instability (MRI) during a finite time. We characterize such transient MRI as a function of vertical and streamwise wavenumbers of harmonics. We discuss implications of our results for laboratory and astrophysical plasma flows, in particular, the role of the transient instability in the onset and maintenance of subcritical turbulence in these flows.

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