Inverse energy transfer in decaying MHD turbulence: A shell-to-shell analysis

In decaying magnetohydrodynamic turbulence, energy can be transported from small to large scales, known as inverse transfer. We explore the mechanism behind this phenomenon using shell-to-shell transfer functions. Independent of magnetic net-helicity, large magnetic scales receive energy directly from the integral scale in both the magnetic and kinetic reservoirs, leading to increasingly non-local transfer for larger receiving scales. The resulting rate of energy increase in each receiving scale is proportional to its energy, resulting in self-similar, multiplicative growth. Even though the system is magnetically dominated, contributions from kinetic-magnetic and magnetic-magnetic energy-exchange are similar in magnitude. In the case of vanishing net-helicity, transfer functions between the positively and negatively helical parts of the field are computed. We find that inverse transfer only occurs within each helical sector, not across them. Our findings are consistent with the theory underlying the conservation of the Hosking integral, which explains inverse transfer as merging of local magnetic islands with equal-signed helicity.