2D enslaving of MHD turbulence

Abstract

At odds with its name, the classical weak turbulence theory only works for turbulence which is strong enough. Namely, the nonlinear resonance broadening has to be greater than the Fourier mode spacing Δk = 2π/L, where L is the size of the bounding box. I will revise the wave turbulence theory by extending it to the finite-size systems and by generalizing the description, traditionally done for the energy spectra, to higher wave-mode moments and its probability density functions. I show that when the perturbations of the external magnetic field are so small that the nonlinear resonance broadening is smaller than the Fourier mode spacing, the finite k∥ modes get slaved to the k∥ = 0 modes. In other words, evolution in the perpendicular to the external field direction is identical to purely two-dimensional (2D) turbulence, whereas there is no evolution in the parallel direction, i.e. the parallel structure remains the same as in the initial condition (or forcing). In terms of the relative magnetic field perturbations, the condition of such a 2D enslaving is b̃/B0 < 1. In the wide intermediate range of intensities σ2D < k⊥ L⊥σ2D turbulence has a mesoscopic nature such that the wave correlation time remains of the order of the inverse Fourier-mode spacing and independent on the wave amplitude. Both the 2D and the wave components are present in this regime and constancy of the wave correlation time hints at the possibility that the wave dynamics is linear. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.