Helical mode interactions and spectral energy transfer in magnetohydrodynamic turbulence

Helical mode interactions and spectral energy transfer in magnetohydrodynamic turbulence

Linkmann, M.F.
Berera, A.
McKay, M.E.
Jäger, J.

2015-08-27

Spectral transfer processes in magnetohydrodynamic (MHD) turbulence are investigated by decomposition of the velocity and magnetic fields in Fourier space into helical modes. In 1992, Waleffe (Phys. Fluids A, 4:350 (1992)) used this decomposition to calculate triad interactions for isotropic hydrodynamic turbulence and determined whether a given triad contributed to forward or reverse energy transfer depending on the helicities of the interacting modes. The problem becomes more difficult in MHD due to the need to treat a coupled system of partial differential equations and the energy transfers between the magnetic and velocity fields. This requires the development of techniques that extend Waleffe's work, which are subsequently used to calculate the direction of energy transfer processes originating from triad interactions derived from the MHD equations. In order to illustrate the possible transfer processes that arise from helical mode interactions, we focus on simplified cases and putting special emphasis on interactions resulting in reverse spectral energy transfer. This approach also proves to be helpful in determining the nature of certain energy transfer processes, where transfer of energy between different fields and between the same field can be distinguished. Reverse transfer of magnetic energy was found if the helicities of two modes corresponding to the smaller wavenumbers are the same, while for reverse transfer of kinetic energy Waleffe's result is recovered. Reverse transfer of kinetic to magnetic energy is facilitated if the interacting magnetic field modes are of opposite helicity, and no reverse transfer of magnetic to kinetic energy was found. More generally, the direction of energy transfer not only depends on helicity but also on the ratio of magnetic to kinetic energy. For the magnetically dominated case reverse transfer occurs of all helicities are the same, the kinetically dominated case two modes need to have the same helicity while the third mode is of opposite helicity to allow reverse transfer.

spectral methods
magnetohydrodynamics
turbulence
helical mode decomposition

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