The signature of initial conditions on magnetohydrodynamic turbulence

Abstract

We demonstrate that the initial correlation between velocity and current density fluctuations can lead to the formation of enormous current sheets in freely evolving magnetohydrodynamic (MHD) turbulence. These coherent structures are observed at the peak of the energy dissipation rate and are the carriers of long-range correlations despite all of the nonlinear interactions during the formation of turbulence. The size of these structures spans our computational domain, dominating the scaling of the energy spectrum, which follows a E k -2 power law. As the Reynolds number increases, the curling of the current sheets due to Kelvin-Helmholtz-type instabilities and reconnection modifies the scaling of the energy spectrum from k -2 toward k -5/3. This transition occurs due to the decorrelation of the velocity and the current density which is proportional to . Finite Reynolds number behavior is observed without reaching a finite asymptote for the energy dissipation rate even for a simulation of Reλ ≃ 440 with 2048 3 grid points. This behavior demonstrates that even state-of-the-art numerical simulations of the highest Reynolds numbers can be influenced by the choice of initial conditions and consequently they are inadequate to deduce unequivocally the fate of universality in MHD turbulence. Implications for astrophysical observations are discussed. © 2014. The American Astronomical Society. All rights reserved..