Inverse transfer of magnetic helicity in isothermal supersonic turbulence

The inverse transfer of magnetic helicity is studied through direct numerical simulations of the isothermal magnetohydrodynamics equations. Turbulent systems driven at large scales by either a solenoidal or a compressive forcing are considered, exhibiting root mean square Mach numbers ranging from 0.1 to about 10. The Fourier spectra of magnetic helicity present scaling exponents which become flatter with increasing compressibility. Considering the Alfvén velocity in place of the magnetic field leads however to more invariant spectra. A shell-to-shell transfer analysis reveals the presence of a subdominant direct transfer in the global picture of the inverse transfer, and that the inverse transport entails both local and non-local aspects. These three features (direct transfer, local inverse transfer, non-local inverse transfer) can be clearly associated with velocity fluctuations in distinct intervals of scale.

The results have been gained through a high-order finite-volume solver. Some practical aspects, benefits and challenges linked to the use of high-order numerics will also be discussed.