On spontaneous swirling of MHD flows of Hill--Shafranov vortex type

M. S. Kotel'nikova

Lavrentyev Institute of Hydrodynamics, 15 Lavrentyev pr., Novosibirsk 630090, Russia

Abstract
The problem of spontaneous swirling was first formulated as follows: can a rotationally symmetric flow occur in the absence of obvious external sources of rotation, i.e. under conditions, where axisymmetric irrotational motion is possible {\it a priori}? In this work, the nonlinear evolution of axisymmetric perturbations of a viscous MHD flow, namely, the Hill--Shafranov vortex, is addressed by direct numerical simulation. Axisymmetric azimuthal perturbations of the velocity field are considered as the initial perturbation. Three flow regimes are found: (1) linear growth; (2) decay of perturbation energy; (3) secondary energy growth. The region of instability is determined as a function of the Reynolds number and magnetization. Figs 2, Refs 5.