Spectral properties of decaying turbulence in electron magnetohydrodynamics

Abstract

The spectral properties of decaying turbulence in 212-dimensional electron magnetohydrodynamics are studied numerically. In the range kde<1 the energy exhibits a direct cascade while mean square momentum exhibits an inverse cascade. Their spectra are characterized by k−7/3 and k−13/3, respectively. The self-similar decay state of the turbulence is reached after an initial phase of fast exchange between the axial and poloidal magnetic energies. The time behavior t−2/3 of the total energy is found to be consistent with that obtained from selective decay. The maximum of the energy spectrum shifts towards low mode numbers and decays in time as t−1, in agreement with the infrared scaling of the turbulence. In the large de limit, both energy and mean square generalized momentum exhibit direct cascades. No stationary turbulent state could be found as long as the axial kinetic energy is large as compared to the poloidal kinetic energy initially. The global physical quantities decay well before turbulent macroscopic quantities have established similar space–time behavior, and the turbulence is infected by the lack of stationarity. The system decouples into a Navier–Stokes equation and a passive scalar equation only if the poloidal kinetic energy is larger than or equal to the axial kinetic energy. In this limit the k−5/3 and k−3 spectra of the poloidal kinetic energy are recovered.