Abstract
A new analytical model of axially-symmetric magnetic vortices with both a twisted fluid flow and a magnetic field is proposed. The exact solution for the three-dimensional structure of the fluid velocity and the magnetic field is obtained within the framework of the ideal magnetohydrodynamic equations for an incompressible fluid in a gravitational field. A quasi-stationary localised vortex arises when the radial flow that tends to concentrate vorticity in a narrow column around the axis of symmetry is balanced by the vertical vortex advection in the axial direction. The explicit expressions for the velocity and magnetic field components are obtained. The proposed analytic model may be used to parameterise the observed solar tornadoes and can provide a new indirect way for estimating magnetic twist from the observed azimuthal velocity profiles.
Highlights
A new analytical model of axially-symmetric magnetic vortices with both a twisted fluid flow and a magnetic field is proposed
The exact solution for the three-dimensional structure of the fluid velocity and the magnetic field is obtained within the framework of the ideal magnetohydrodynamic equations for an incompressible fluid in a gravitational field
A quasi-stationary localised vortex arises when the radial flow that tends to concentrate vorticity in a narrow column around the axis of symmetry is balanced by the vertical vortex advection in the axial direction
Summary
A new analytical model of axially-symmetric magnetic vortices with both a twisted fluid flow and a magnetic field is proposed. Gruzinskaya, 123242 Moscow, Russia 2Plasma Dynamics Group, Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S13JD, United Kingdom 3Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada 4The University of Texas at Austin, Austin, Texas 78712, USA 5Plasma Dynamics Group, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom (Received 22 January 2018; accepted 18 April 2018; published online 8 May 2018) A quasi-stationary localised vortex arises when the radial flow that tends to concentrate vorticity in a narrow column around the axis of symmetry is balanced by the vertical vortex advection in the axial direction.
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