Reduced magnetohydrodynamics and parallel spectral transfer

Abstract

The self-consistency of the reduced magnetohydrodynamics ͑RMHD͒ model is explored by examining whether ͑parallel͒ spectral transfer might invalidate the assumptions employed in deriving it. Using direct numerical simulations we find that transfer of energy to structures with high parallel wavenumber is in fact limited by ongoing perpendicular transfer. Thus, the dynamics associated with RMHD models remains consistent with the underlying assumptions of RMHD. In particular, in well-resolved simulations it is neither necessary nor correct to introduce additional dissipation terms that ͑artificially͒ damp spectral transfer parallel to the mean magnetic field B 0 .

A two-component phenomenology for homogeneous magnetohydrodynamic turbulence

“…[12][13][14][15] In terms of these time scales, the condition nl ͑k͒ Ͻ A ͑k͒ serves to define the quasi-2D, or low-frequency fluctuations. 10,[16][17][18][19][20][21] For the H c = 0 case, this is equivalent to k ʈ V A Ͻ ku k . Conversely, the wave-like fluctuations are defined by the opposite inequality: k ʈ V A Ͼ ku k .…”

MHD Dynamos and Turbulence

“…Depending on the k spectral width of the forcing, the driven turbulence is weak if the fluctuations satisfy the inequality (3.2), and it is strong if approximate equality holds in (3.2) instead. Further examples of numerical simulations of various regimes of MHD turbulence in the RMHD framework are available (e.g., Oughton et al 2004, Rappazzo et al 2007, Rappazzo et al 2008, Dmitruk et al 2003.…”

Energy spectrum, dissipation, and spatial structures in reduced Hall magnetohydrodynamic

“…The self-consistency of the RMHD approximation has been analyzed in ref. [26]. Moreover, numerical simulations have studied the validity of the RMHD equations by directly comparing its predictions with the compressible MHD equations in a turbulent regime [27].…”