Motion of axisymmetric magnetic eddies with swirl
Seminar Room 1, Newton Institute
We consider the motion of axisymmetric magnetic eddies with swirl in ideal MHD (magnetohydrodynamics) flow. The magnetic field is assumed to be toroidal, while the velocity field has both toroidal and poloidal components. First, the contour-dynamics formulation by Hattori and Moffatt (2006) for the case without swirl is extended to include swirl velocity so that the cross helicity does not vanish in general. The strength of vortex sheets which appear on the contours varies with time under the influence of the centrifugal force due to swirl and the magnetic tension due to the Lorentz force. Numerical simulation using the contour-dynamics formulation shows that there exist counter-propagating dipolar structures at the radius of balance between the centrifugal force and the magnetic tension; these structures are well described by the steady solutions obtained by perturbation expansion. The effects of vorticity inside the eddy on the motion of the eddies are also investigated. Next, we seek exact steady spherical solutions of magnetic eddies with swirl. A generalized family of exact solutions is found; it includes Hillís spherical vortex, the Hicks-Moffatt family which is a non-MHD vortex with swirl and the family of a MHD vortex without swirl found by Hattori and Moffatt (2006).