A&A 420, 737-749 (2004)
DOI: 10.1051/0004-6361:20041040

Kelvin-Helmholtz and shear instability of a helical flow around a magnetic flux tube

F. Kolesnikov¹, M. Bünte², D. Schmitt¹ and M. Schüssler<sup>1

1</sup>  Max-Planck-Institut für Sonnensystemforschung (Formerly: Max-Planck-Institut für Aeronomie.) , Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany
²  Bodenacherstrasse 33, 8121 Benglen, Switzerland

(Received 15 January 2004 / Accepted 12 March 2004 )

Abstract
Magnetic flux concentrations in the solar (sub)photosphere are surrounded by strong downflows, which come into swirling motion owing to the conservation of angular momentum. While such a whirl flow can stabilize a magnetic flux tube against the MHD fluting instability, it potentially becomes subject to Kelvin-Helmholtz and shear instability near the edge of the flux tube, which may lead to twisting of the magnetic field and perhaps even to the disruption of the magnetic structure. As a first step towards studying the relevance of such instabilities, we investigate the stability of an incompressible flow with longitudinal and azimuthal (whirl) components surrounding a cylinder with a uniform longitudinal magnetic field. We find that a sharp jump of the azimuthal flow component at the cylinder boundary always leads to Kelvin-Helmholtz-type instability for sufficiently small wavelength of the perturbation. On the other hand, a smooth and wide enough transition of the azimuthal velocity towards the surface of the cylinder leads to stable configurations, even for a discontinuous profile of the longitudinal flow.

Key words: magnetohydrodynamics: MHD -- hydrodynamics -- instabilities -- Sun: magnetic fields -- Sun: photosphere

Offprint request: M. Schüssler, msch@linmpi.mpg.de

© ESO 2004

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