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Magnetic Eddy Viscosity of Mean Shear Flows in Two-dimensional Magnetohydrodynamics by Parker, Jeffrey B. ;Constantinou, Navid C. is a Engineering article available to read on EtoBox.

What is Magnetic Eddy Viscosity of Mean Shear Flows in Two-dimensional Magnetohydrodynamics about?

Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than 1 has long been known to cause magnetic drag. Here we show that when Rm 1 and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear 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 2 p /2μ 0 )τ corr , the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results 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 fl

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Author

Parker, Jeffrey B. ;Constantinou, Navid C.

Publisher

American Physical Society (APS)

Published

2019

Language

EN

Field

Engineering (Physical Sciences)