Kelvin-Helmholtz instability of twisted magnetic flux tubes in the solar wind

Abstract

Context. Tangential velocity discontinuity near the boundaries of solar wind magnetic flux tubes results in Kelvin-Helmholtz instability, which might contribute to solar wind turbulence. While the axial magnetic field stabilizes the instability, a small twist in the magnetic field may allow sub-Alfvénic motions to be unstable. Aims. We aim to study the Kelvin-Helmholtz instability of twisted magnetic flux tubes in the solar wind with different configurations of the external magnetic field. Methods. We use magnetohydrodynamic equations in cylindrical geometry and derive the dispersion equations governing the dynamics of twisted magnetic flux tubes moving along its axis in the cases of untwisted and twisted external fields. Then, we solve the dispersion equations analytically and numerically and find thresholds for Kelvin-Helmholtz instability in both cases of the external field. Results. Both analytical and numerical solutions show that the Kelvin-Helmholtz instability is suppressed in the twisted tube by the external axial magnetic field for sub-Alfvénic motions. However, even a small twist in the external magnetic field allows the Kelvin-Helmholtz instability to be developed for any sub-Alfvénic motion. The unstable harmonics correspond to vortices with high azimuthal mode numbers that are carried by the flow. Conclusions. Twisted magnetic flux tubes can be unstable to Kelvin-Helmholtz instability when they move with small speed relative to the main solar wind stream, then the Kelvin-Helmholtz vortices may significantly contribute to the solar wind turbulence. © 2013 ESO.