Whistlerization and anisotropy in two-dimensional electron magnetohydrodynamic turbulence

A detailed numerical simulation to understand the turbulent state of the decaying two-dimensional electron magnetohydrodynamics is presented. It is observed that the evolved spectrum is comprised of a collection of random eddies and a gas of whistler waves, the latter constituting the normal oscillatory modes of such a model. The whistlerization of the turbulent spectra has been quantified by novel diagnostics. In this work, results are presented only in the regime where the spatial excitation scales are longer than the electron skin depth. Simulations suggest that spectra at short scales are comparatively more whistlerized. The long scale field merely acts as the ambient field along which whistler waves propagate. It is also observed that, in the presence of an external magnetic field, the power spectrum acquires a distinct directional dependence. This anisotropy is dominant at short scales. It is shown that such an anisotropy at short scales results from a cascade mechanism governed by the interacting whistlers waves.