Magnetic eddy viscosity of mean sheared flows in two-dimensional magnetohydrodynamics. (arXiv:1902.01105v1 [physics.plasm-ph])
<a href="http://arxiv.org/find/physics/1/au:+Parker_J/0/1/0/all/0/1">Jeffrey B. Parker</a>, <a href="http://arxiv.org/find/physics/1/au:+Constantinou_N/0/1/0/all/0/1">Navid C. Constantinou</a>
Induction of magnetohydrodynamics (MHD) fluids at magnetic Reynolds number
(Rm) less than~1 has long been known to cause magnetic drag. Here, we show that
when $Rm gg 1$, and additionally in a hydrodynamic-dominated regime in which
the magnetic energy is much smaller than the kinetic energy, induction due to a
mean shared flow leads to a magnetic eddy viscosity. The magnetic viscosity is
derived from simple physical arguments, where a coherent response due to shear
flow builds up in the magnetic field until decorrelated by turbulent motion.
The dynamic viscosity coefficient is approximately $B_p^2/(2m_0) tc$, the
poloidal magnetic energy density multiplied by the correlation time. We confirm
the magnetic eddy viscosity through numerical simulations of two-dimensional
incompressible MHD. We also consider the three-dimensional case, and in
cylindrical or spherical geometry we find a nonzero viscosity whenever there is
differential rotation. These results thus serve as a dynamical generalization
of Ferraro’s law of isorotation. The magnetic eddy viscosity leads to transport
of angular momentum and may be of importance to zonal flows in the interior of
gas giants.
Induction of magnetohydrodynamics (MHD) fluids at magnetic Reynolds number
(Rm) less than~1 has long been known to cause magnetic drag. Here, we show that
when $Rm gg 1$, and additionally in a hydrodynamic-dominated regime in which
the magnetic energy is much smaller than the kinetic energy, induction due to a
mean shared flow leads to a magnetic eddy viscosity. The magnetic viscosity is
derived from simple physical arguments, where a coherent response due to shear
flow builds up in the magnetic field until decorrelated by turbulent motion.
The dynamic viscosity coefficient is approximately $B_p^2/(2m_0) tc$, the
poloidal magnetic energy density multiplied by the correlation time. We confirm
the magnetic eddy viscosity through numerical simulations of two-dimensional
incompressible MHD. We also consider the three-dimensional case, and in
cylindrical or spherical geometry we find a nonzero viscosity whenever there is
differential rotation. These results thus serve as a dynamical generalization
of Ferraro’s law of isorotation. The magnetic eddy viscosity leads to transport
of angular momentum and may be of importance to zonal flows in the interior of
gas giants.
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