http://arxiv.org/abs/1902.01105
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 $B_p^2/(2\m_0) \tc$, 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.
J. Parker and N. Constantinou
Tue, 5 Feb 19
13/86
Comments: 14 pages, 8 figures
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