Energy spectra stemming from interactions of Alfvén waves and turbulent eddies

Abstract

We present a numerical analysis of an incompressible decaying magnetohydrodynamic turbulence run on a grid of 15363 points. The Taylor Reynolds number at the maximum of dissipation is 1100, and the initial condition is a superposition of large-scale Arn'old-Beltrami-Childress flows and random noise at small scales, with no uniform magnetic field. The initial kinetic and magnetic energies are equal, with negligible correlation. The resulting energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectral law compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfvén waves; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k-2 spectrum, the perpendicular direction referring to the local quasiuniform magnetic field. © 2007 The American Physical Society.