Author:
BAJER KONRAD,MOFFATT H. K.
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,
Pm[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
Pm[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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
7 articles.
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