Energy fluxes and shell-to-shell transfers in three-dimensional decaying magnetohydrodynamic turbulence

Abstract

A spectral analysis of the energy cascade in magnetohydrodynamics (MHD) is presented using high-resolution direct numerical simulation of decaying isotropic turbulence. The Fourier representations of both the velocity and the magnetic fields are split into subsets that correspond to shells of wave vectors. A detailed study of the shell-to-shell interactions is performed and a comparison with theoretical prediction based on field-theoretic method is proposed. Two different definitions for the forward and backward energy transfers are suggested. They provide diagnostics that can be used in order to assess subgrid-scale modeling in large eddy simulation for turbulent MHD systems.

Anisotropic fluxes and nonlocal interactions in magnetohydrodynamic turbulence

“…Note however that for the B = 5 flow, there is also some trace of an inverse cascade (energy transfer from the wavenumber Q = 10 to the wavenumber K = 8). This local behavior has also been found in isotropic (B = 0) decaying MHD turbulence simulations [31]. Nevertheless, we need to note that in forced MHD turbulence where the magnetic field is generated by dynamo action, strong nonlocal transfers also exist [6,8].…”

“…As a result, the coupling between modes that travel in the same direction is local and the energy exchange occurs between similar size eddies. This behavior has been shown to hold in decaying isotropic MHD turbulence simulations (with B = 0) [31]. However, in the presence of a mechanical forcing, strong nonlocal interactions have been observed with a direct energy transfer from the forced scale to the inertial range scales [6,8].…”

Testing for Markovian character and modeling of intermittency in solar wind turbulence

“…The question is also important for modeling MHD flows and numerical simulations, e.g., in large-eddy simulations, where lowpass filtering with respect to a cutoff wave number requires some assumptions concerning the transfer of energy around the cutoff wavenumber. Local and nonlocal transfer mechanisms can be distinguished in theoretical studies of turbulence via shell models or numerical simulations (see, e.g., [22,23,24]), but it is very difficult to study the property of turbulence using experimental data. The Markov processes approach seems to provide such a method.…”

Statistical analysis of transfer of fluctuations in solar wind turbulence

“…For example, this is essential in largeeddy simulations, where low-pass filtering with respect to a cutoff wave number requires some assumptions concerning the transfer of energy around the cutoff wavenumber. Local and nonlocal transfer mechanisms can be distinguished in theoretical studies of turbulence by shell models or numerical simulations (see, e.g., Alexakis et al, 2005;Debliquy et al, 2005;Mininni et al, 2005;Verma et al, 2005), but it is difficult to study the property of turbulence directly using experimental data. Here we argue that a method of statistical analysis based on the Markov processes theory provides a tool that allows to distinguish between local and nonlocal transfer mechanisms in an experimental situation.…”