On weak and strong magnetohydrodynamic turbulence

JC Perez, S Boldyrev - The Astrophysical Journal, 2007 - iopscience.iop.org
JC Perez, S Boldyrev
The Astrophysical Journal, 2007iopscience.iop.org
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_ {\parallel}, k_ {\perp} characteristic field-parallel and field-perpendicular wavenumbers of …
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_ {\parallel}, k_ {\perp} characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and b_ {\lambda} the fluctuating field at the scale\lambda\sim 1/k_ {\perp}. We find that when the critical balance condition, k_ {\parallel} B_ {0}\sim k_ {\perp} b_ {\lambda}, is satisfied, the turbulence is strong, and the energy spectrum is E (k_ {\perp})\propto k^{-3/2} _ {\perp}. As the k_ {\parallel} width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit k_ {\parallel} B_ {0}\gg k_ {\perp} b_ {\lambda}, the spectrum approaches E (k_ {\perp})\propto k^{-2} _ {\perp}. 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.
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