The decay of MHD turbulence and the primordial origin of magnetic fields in cosmic voids - Hosking, DN (2022)
The central result of this thesis is the solution of a decades-old problem in magnetohydrodynamic (MHD) turbulence theory: in the absence of energy injection, how do chaotic magnetic fields decay with time? We obtain novel predictions for the evolution of the magnetic energy and correlation scale by proposing that the field decays on reconnection timescales while respecting certain integral invariants that represent topological constraints. As is well known, the magnetic helicity is such an invariant for initially helical field configurations (Taylor, 1974), but does not constrain non-helical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant — the “Saffman helicity invariant” — which is analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence (Loitsyansky, 1939; Saffman, 1967), and that expresses the conservation of the random (scaling as volume^1/2) magnetic helicity contained in any sufficiently large volume. We verify that the Saffman helicity invariant is indeed well-conserved in our numerical simulations. We formulate a general principle of decay of turbulent systems subject to conservation of Saffman-like invariants, and propose how it may be applied to magnetohydrodynamic (MHD) turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.