Cascades in decaying three-dimensional electron magnetohydrodynamic turbulence

TL;DR

This study uses high-resolution simulations to analyze decaying 3D EMHD turbulence, revealing a consistent energy spectrum, absence of a dissipative cutoff, and the development of stationary structures with anisotropic energy transfer.

Contribution

It provides new insights into 3D EMHD turbulence, including the asymptotic energy spectrum, the absence of dissipative cutoff, and the effects of a background magnetic field on energy cascades.

Findings

Energy spectra approach k^{-2} law with increasing R_B

No evidence of dissipative cutoff, supporting non-local transfer

Development of stationary structures over time

Abstract

Decaying electron magnetohydrodynamic (EMHD) turbulence in three dimensions is studied via high-resolution numerical simulations. The resulting energy spectra asymptotically approach a k^{-2} law with increasing R_B, the ratio of the nonlinear to linear timescales in the governing equation, consistent with theoretical predictions. No evidence is found of a dissipative cutoff, consistent with non-local spectral energy transfer and recent studies of 2D EMHD turbulence. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. In another similarity to 2D EMHD turbulence, relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further, cascades of energy in 3D EMHD turbulence are found to be suppressed in all directions under the influence of a uniform background field. Energy transfer is further reduced in the direction parallel to the field, displaying scale dependent anisotropy. Finally, the governing equation is found to yield a weak inverse cascade, at least partially transferring magnetic energy from small to large scales.