On Weak and Strong Magnetohydrodynamic Turbulence

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 B₀. 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 bλ the fluctuating field at the scale λ~ 1/k⊥. We find that when the critical balance condition, k\|B₀~ k⊥ bλ, is satisfied, the turbulence is strong, and the energy spectrum is E(k⊥)∝ k-3/2⊥. As the k\| width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit k\|B₀ k⊥ bλ, the spectrum approaches E(k⊥)∝ 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.