On weak and strong magnetohydrodynamic turbulence

Jean Carlos Perez; Stanislav Boldyrev

doi:10.1086/526342

paper

On weak and strong magnetohydrodynamic turbulence

arXiv:0712.2086 · doi:10.1086/526342

Abstract

Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_{0}$ . We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{∥}$ , $k_{⊥}$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_{λ}$ the fluctuating field at the scale $λ \sim 1/ k_{⊥}$ . We find that when the critical balance condition, $k_{∥} B_{0} \sim k_{⊥} b_{λ}$ , is satisfied, the turbulence is strong, and the energy spectrum is $E (k_{⊥}) \propto k_{⊥}^{- 3/2}$ . As the $k_{∥}$ width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit $k_{∥} B_{0} ≫ k_{⊥} b_{λ}$ , the spectrum approaches $E (k_{⊥}) \propto k_{⊥}^{- 2}$ . The observed sensitivity of the spectrum to the balance of linear and nonlinear interactions may explain the conflicting numerical and observational findings where this balance condition is not well controlled.

4 pages, 2 figures

On weak and strong magnetohydrodynamic turbulence

Abstract

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