On the effect of a central vortex on a stretched magnetic flux tube

Abstract

Experiments and numerical simulations of fully developed turbulence reveal the existence of elongated vortices whose length is of the order of the integral scale of turbulence while the diameter is somewhere between the Kolmogorov scale and the Taylor microscale. These vortices are embedded in quasi-irrotational background flow whose straining action counteracts viscous decay and determines their cross-sectional shape. In the present paper we analyse the effect of a stretched vortex of this kind on a uni-directional magnetic flux tube aligned with vorticity in an electrically conducting fluid. When the magnetic Prandtl number is large, P_m[gsim ]1, the field is concentrated in a flux tube which, like the vortex itself, has elliptical cross-section inclined at 45° to the principal axes of strain. We focus on the limit P_m[Lt ]1 when the magnetic flux tube has radial extent much larger than that of the vortex, which appears like a point vortex as regards its action on the flux tube. We find the steady-state solution valid in the entire plane outside the vortex core. The solution shows that the magnetic field has a logarithmic spiral component and no definite orientation of the inner contours. Such magnetized vortices may be expected to exist in MHD turbulence with weak magnetic field where the field shows a tendency to align itself with vorticity. Magnetized vortices may also be expected to exist on the solar surface near the corners of convection cells where downwelling swirling flow tends to concentrate the magnetic field.