Helical mode interactions and spectral transfer processes in magnetohydrodynamic turbulence

Abstract

Spectral transfer processes in homogeneous magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of the interacting modes is derived. As expected from the inverse cascade of magnetic helicity in 3-D MHD turbulence, mode interactions with like helicities lead to transfer of energy and magnetic helicity to smaller wavenumbers. However, some interactions of modes with unlike helicities also contribute to an inverse energy transfer. As such, an inverse energy cascade for non-helical magnetic fields is shown to be possible. Furthermore, it is found that high values of the cross-helicity may have an asymmetric effect on forward and reverse transfer of energy, where forward transfer is more quenched in regions of high cross-helicity than reverse transfer. This conforms with recent observations of solar wind turbulence. For specific helical interactions the relation to dynamo action is established. The present analysis provides new theoretical insights into physical processes where inverse cascade and dynamo action are involved, such as the evolution of cosmological and astrophysical magnetic fields and laboratory plasmas.

Nonhelical turbulence and the inverse transfer of energy: A parameter study

“…But this nonhelical inverse transfer requires high Reynolds numbers. Hence, previous studies of nonhelical MHD turbulence decay have not seen this effect clearly [11,[20][21][22] whereas latest numerical studies seem to confirm the result by Brandenburg et al [23,24].…”

Fully resolved array of simulations investigating the influence of the magnetic Prandtl number on magnetohydrodynamic turbulence

“…Analyses of triad interactions and shell-to-shell energy transfers show that energy is transferred from the velocity field at the forcing scale to the magnetic and velocity fields at all scales in a way that depends on the separation between the giving and receiving scales and the energy contained in the involved scales, amongst other things [29,[36][37][38][39][40]. Therefore it is reasonable to expect a consistent scaling of ε K /ε M with Pm that is not affected by whether Pm < 1 or Pm > 1, as we see in Fig.…”

Triad interactions and the bidirectional turbulent cascade of magnetic helicity

“…This is the so-called helical decomposition [22][23][24]. To study the triad interaction of helical modes, we use the formalism that was developed by Waleffe [26] for the Navier-Stokes equations and extended by Linkmann et al [20,21] to the MHD equations. This is essentially a linear stability analysis of a dynamical system obtained from the MHD equations in the limits of ν → 0 and η → 0.…”

“…Note that two triads are required to describe the interactions that correspond to the term ∇ × (u × b) due to a necessary symmetrization of the convolution in Fourier space. However, this symmetrization does not allow one to disentangle the triadic interactions of the advection term u · ∇b and the stretching term b · ∇u of the magnetic field [20]. Different interactions of helical modes can now be studied via Eqs.…”