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. We perform numerical simulations of the reduced MHD equations in a B 0 special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote, k(parallel to), characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and b(lambda) the fluctuating field at the scale lambda similar to 1/k(perpendicular to). We find that when the critical balance condition, k parallel to B-0 similar to k(perpendicular to)b lambda, is satisfied, the turbulence is strong, and the energy spectrum is E(k(perpendicular to)) proportional to k(perpendicular to)(-3/2). As the k(parallel to) width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit k(parallel to)B(0) >> k(perpendicular to)b(lambda), the spectrum approaches E(k(perpendicular to)) proportional to k(perpendicular to)(-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.