Phase Mixing of Kink MHD Waves in the Solar Corona: Viscous Dissipation and Heating

Abstract

Magnetohydrodynamic (MHD) kink waves have been observed frequently in solar coronal flux tubes, which makes them a great tool for seismology of the solar corona. Here, the effect of viscosity is studied on the evolution of kink waves. To this aim, we solve the initial value problem for the incompressible linearized viscous MHD equations in a radially inhomogeneous flux tube in the limit of long wavelengths. Using a modal expansion technique the spatio-temporal behavior of the perturbations is obtained. We confirm that for large Reynolds numbers representative of the coronal plasma the decrement in the amplitude of the kink oscillations is due to the resonant absorption mechanism that converts the global transverse oscillation to rotational motions in the inhomogeneous layer of the flux tube. We show that viscosity suppresses the rate of phase mixing of the perturbations in the inhomogeneous region of the flux tube and prevents the continuous building up of small scales in the system once a sufficiently small scale is reached. The viscous dissipation function is calculated to investigate plasma heating by viscosity in the inhomogeneous layer of the flux tube. For Reynolds numbers of the order of 10^6-10^8, the energy of the kink wave is transformed into heat in two to eight periods of the kink oscillation. For larger and more realistic Reynolds numbers, heating happens, predominantly, after the global kink oscillation is damped, and no significant heating occurs during the observable transverse motion of the flux tube.

21 pages, 8 figures

References in corpus (6)

• Nonlinear Instability of kink oscillations due to shear motions
• Magnetohydrodynamic kink waves in nonuniform solar flux tubes: phase mixing and energy cascade to small scales
• The effect of twisted magnetic field on the resonant absorption of MHD waves in coronal loops
• Resonant absorption in expanding coronal magnetic flux tubes with uniform density
• Investigating the damping rate of phase-mixed Alfven waves
• The effect of a twisted magnetic field on the phase mixing of the kink magnetohydrodynamic waves in coronal loops

Cited by in corpus (5)

• Transition to turbulence in nonuniform coronal loops driven by torsional Alfven waves
• Three-dimensional simulations of the inhomogeneous Low Solar Wind
• Damping of slow surface kink modes in solar photospheric waveguides modeled by one-dimensional inhomogeneities
• Transition to turbulence in nonuniform coronal loops driven by torsional Alfvén waves. II. Extended analysis and effect of magnetic twist
• Resonant Absorption of Kink MHD Waves in Inclined and Asymmetric Coronal Loops