On Kelvin-Helmholtz and parametric instabilities driven by coronal waves

Abstract

The Kelvin-Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the oscillatory shear flow associated with an MHD wave. We investigate the linear stability of a discontinuous oscillatory shear flow in the presence of a horizontal magnetic field within a Cartesian framework that captures the essential features of MHD oscillations in flux tubes. We derive a Mathieu equation for the Lagrangian displacement of the interface and analyse its properties, identifying two different instabilities: a Kelvin-Helmholtz instability and a parametric instability involving resonance between the oscillatory shear flow and two surface Alfvén waves. The latter occurs when the system is Kelvin-Helmholtz stable, thus favouring modes that vary along the flux tube, and as a consequence provides an important and additional mechanism to extract energy. When applied to flows with the characteristic properties of kink waves in the solar corona, both instabilities can grow, with the parametric instability capable of generating smaller scale disturbances along the magnetic field than possible via the Kelvin-Helmholtz instability. The characteristic time-scale for these instabilities is $\sim 100$ s, for wavelengths of $200$ km. The parametric instability is more likely to occur for smaller density contrasts and larger velocity shears, making its development more likely on coronal loops than on prominence threads.

12 pages, 4 figures, accepted for publication MNRAS

References in corpus (10)

• The Solar Optical Telescope for the Hinode Mission: An Overview
• Nonlinear Instability of kink oscillations due to shear motions
• Fine strand-like structure in the solar corona from MHD transverse oscillations
• Heating by transverse waves in simulated coronal loops
• Damping of nonlinear standing kink oscillations: a numerical study
• The Kelvin-Helmholtz Instability at CME-Boundaries in the Solar Corona: Observations and 2.5D MHD Simulations
• Transverse Wave Induced Kelvin-Helmholtz Rolls in Spicules
• Modelling observed decay-less oscillations as resonantly enhanced Kelvin-Helmholtz vortices from transverse MHD waves and their seismological application
• Quiescent prominence dynamics observed with the Hinode Solar Optical Telescope . II. Prominence Bubble Boundary Layer Characteristics and the Onset of a Coupled Kelvin-Helmholtz Rayleigh-Taylor Instability
• Energetics of the Kelvin-Helmholtz instability induced by transverse waves in twisted coronal loops

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