Magnetic Eddy Viscosity of Mean Sheared Flows in Two-Dimensional Magnetohydrodynamics

Journal Article · 27 August 2019 · Physical Review Fluids

DOI: https://doi.org/10.1103/PhysRevFluids.4.083701 · OSTI ID:1568002

Parker, J B ^[1]; Constantinou, N C ^[2]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2. Australian National Univ., Canberra, ACT (Australia)

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 $$\gg 1$$ 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 $$(B^2_p/2_{μ_0}) τ_{corr}$$, 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 flows in astrophysical domains such as the interior of some gas giants.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1568002
• Report Number(s): LLNL-JRNL-767360; 957784
• Journal Information: Physical Review Fluids, Journal Name: Physical Review Fluids Journal Issue: 8 Vol. 4; ISSN 2469-990X
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English