Waves and turbulence in magnetohydrodynamic direct numerical simulations

Abstract

Direct numerical simulations of the incompressible MHD equations with a uniform background magnetic field in a turbulent regime are performed to assess the relative importance of broadband turbulent fluctuations and wavelike fluctuations that are associated with an Alfvén wave dispersion relation. The focus is on properties of the fluctuations in the frequency domain. Eulerian frequency spectra and individual wave number mode frequency spectra show the presence of peaks at the corresponding Alfvén wave frequencies for full nonlinear simulations in a turbulent regime. The peaks are however broad and their power content is compared to the power in the full spectrum as well as a signal to noise ratio is defined and quantified for different values of the background magnetic field. The ratio of power in Alfvén waves to the power in the rest of the spectrum is also quantified and is found to be small for different values of the mean magnetic field. Individual modes in time show a much more complex behavior than that could be expected for linear solutions. Also, nonlinear transfer of energy is evidenced by the existence of peaks at wave numbers perpendicular to the mean magnetic field. Implications are discussed for theories of strong turbulence as well as perturbation theories that assume the leading order behavior is that of propagating Alfvén waves.