The effect of anisotropic viscosity on the nonlinear MHD kink instability

Abstract

The kink instability of magnetohydrodynamics is believed to be fundamental to many aspects of the dynamic activity of the solar atmosphere, such as the initiation of flares and the heating of the solar corona. In this work, we investigate the importance of viscosity on the kink instability. In particular, we focus on two forms of viscosity; isotropic viscosity (independent of the magnetic field) and anisotropic viscosity (with a preferred direction following the magnetic field). Through the detailed analysis of magnetohydrodynamic simulations of the kink instability with both types of viscosity, we show that the form of viscosity has a significant effect on the nonlinear dynamics of the instability. The different viscosities allow for different flow and current structures to develop, thus affecting the behaviour of magnetic relaxation, the formation of secondary instabilities and the Ohmic and viscous heating produced. Our results have important consequences for the interpretation of solar observations of the kink instability.

Kelvin-Helmholtz instability and collapse of a twisted magnetic null point with anisotropic viscosity

“…for t < 6), suggesting the switching model allows for enhanced reconnection. As in Quinn et al (2020), here too, this is due to the switching model permitting greater velocities, greater compression and thinner, stronger current sheets. It is then unclear whether the generally enhanced reconnection rate in the switching case for times t = 5 to 10 can be attributed to the current-enhancing effect of the switching model or an effect of the KHI.…”

“…The weaker effect of direct damping, by anisotropic viscosity compared to isotropic viscosity, means that the shorter length scales also coincide, in general, with higher magnitudes, thus enhancing the possibility of instability. Even with different dynamical drivers (the null point is twisted in this study whereas the flux tube in Quinn et al (2020) is initially unstable and allowed to relax) the cases with anisotropic viscosity exhibit the fast development of instabilities and reconnection in the way described above. Although anisotropic viscosity does not affect the magnetic field directly, it does have a significant indirect influence through nonlinear interaction.…”

“…The general qualitative behaviour that we have found in this study matches well with our previous study on the effect of anisotropic viscosity on the kink instability in a flux tube. (Quinn et al 2020). The more localised influence of anisotropic viscosity compared to isotropic viscosity allows for the creation of much smaller length scales, both in the magnetic and velocity fields.…”

“…One significant finding is that the velocity shears created by the KHI allow anisotropic viscous heating of comparable levels to that of isotropic viscosity (in contrast to much larger differences observed in other situations e.g. the kink instability of a twisted flux tube (Quinn et al 2020)).…”

“…The reconnection rate is calculated using the same method employed in previous work by the same authors (Quinn et al 2020). In summary, the reconnection rate local to a given magnetic field line is calculated as the local parallel electric field (that is, parallel to the magnetic field) integrated along the field line.…”