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

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.