A general formula is established for traveling speed of an axisymmetric toroidal vortex with magnetic flux concentrated in a thin core embedded in electrically conducting fluid subject to the Hall effect. We extend Helmholtz-Lamb's method to include magnetic flux. The resulting formula admits viscous diffusion of vorticity and magnetic diffusion. The Hall effect only modifies the distribution of magnetic field. In the other extreme of fat cores, an exact solution is constructed of the ideal Hall-magnetohydrodynamics (HMHD) for a steadily traveling spherical magnetic vortex. This vortex is accompanied by a spherical-boundary vortex sheet as in the MHD case. The toroidal magnetic field acts to enhance the traveling speed, but the Hall effect causes the discrepancy in the traveling speed, whether the magnetic field is parallel or antiparallel to the vorticity, by modifying the distribution of the magnetic field. The traveling speed of a thin vortex ring is increased or decreased for parallel or antiparallel cases, respectively. For the spherical vortex, the opposite trend is brought by the surface vortex sheet. Besides, a particular solution is found for a spherical vortex pertaining only to the HMHD.

Close

PrevNext

View figure in article

• Magnetohydrodynamics
• Vortex dynamics
• Vortex flows