Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence

TL;DR

This study uses high-resolution simulations to analyze two-dimensional electron magnetohydrodynamic turbulence, revealing a $k^{-5/2}$ energy spectrum, scale-dependent anisotropy, and evidence of an inverse energy cascade without dissipative cutoff effects.

Contribution

It demonstrates the presence of an inverse cascade and clarifies the absence of dissipative cutoffs, challenging previous findings influenced by hyperdiffusivity.

Findings

Energy spectrum approaches $k^{-5/2}$ law with increasing $R_B$

No evidence of dissipative cutoff, indicating non-local energy transfer

Inverse cascade partially transfers magnetic energy to larger scales

Abstract

Electron magnetohydrodynamic (EMHD) turbulence in two dimensions is studied via high-resolution numerical simulations with a normal diffusivity. The resulting energy spectra asymptotically approach a $k^{-5/2}$ law with increasing $R_B$, the ratio of the nonlinear to linear timescales in the governing equation. No evidence is found of a dissipative cutoff, consistent with non-local spectral energy transfer. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. Relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further, EMHD turbulence displays scale-dependent anisotropy with reduced energy transfer in the direction parallel to the uniform background field, consistent with previous studies. Finally, the governing equation is found to yield an inverse cascade, at least partially transferring magnetic energy from small to large scales.