Triadic energy transfers in non-helical magnetohydrodynamic turbulence

Abstract

The eddy-damped quasi-normal Markovian (EDQNM) two-point statistical closure model is used to study the non-linear triadic energy transfer processes in three-dimensional, incompressible, isotropic, non-helical magnetohydrodynamic (MHD) turbulence in the primitive variable formulation. The triadic transfer functions, which arise from the closure of the three-point correlations in the kinetic energy and magnetic energy spectrum evolution equations, are calculated for non-helical MHD turbulence as a function of wavenumber $k$ for given values of $(p,q)$ with $q$ fixed and $p$ varied. These functions describe the magnitude of the energy transferred into or out of a given mode with wavenumber $k$ due to all allowed interactions of modes with wavenumbers $p$ and $q$ satisfying ${\bf k}={\bf p}+{\bf q}$, and their integrals over all $p$ and $q$ yield the kinetic energy and magnetic energy transfer spectra. Rather than solving the time-dependent, coupled EDQNM equations using initial, prescribed energy spectra, assumed forms of the kinetic energy spectrum $E_{v}(k)$ and the magnetic energy spectrum $E_{B}(k)$ having both a production subrange spectrum proportional to $k$ and a Kolmogorov inertial subrange spectrum proportional to $k^{-5/3}$ are used to evaluate instantaneous values of the triadic transfer functions. The two cases $r_{A}\,{=}\,1$ and $\frac12$ are considered, where $r_{A}$ is the Alfvén ratio. The individual contributions to the transfer functions are also computed in order to determine the dominant interactions that contribute to the total spectral energy transfers. The triadic transfers exhibit forms similar to those found in previous studies of incompressible, isotropic Navier–Stokes turbulence. The non-local-in-wavenumber triadic interactions dominate the local-in-wavenumber interactions, which indicates that the transfer process in non-helical MHD turbulence is primarily local in scale. As the Alfvén ratio decreases, it was found that the most non-local triadic interactions resulted in kinetic energy input and magnetic energy removal at most wavenumbers $k$. The decomposition of the triadic kinetic and magnetic energy transfer functions into their constituents showed that increasing non-locality of the wavenumber interaction involving modes $p$ and $q$ responsible for the net energy transfer into a given wavenumber $k$ corresponds to a qualitative change in the cascade dynamics; namely, there is less energy removal at smaller $k$ and primarily energy input at nearly all $k$. An increased degree of non-locality also results in more cancellation between constituent triadic transfer functions.