Abstract
We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. With direct numerical simulations, we demonstrate that the rate of turbulent decay is governed by the reconnection of magnetic structures, and not necessarily by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy-decay laws by proposing that turbulence decays on reconnection timescales while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an invariant for initially helical field configurations, but it does not constrain nonhelical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant, analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence, that expresses the conservation of the random (scaling as ) magnetic helicity contained in any sufficiently large volume. We verify that this invariant is indeed well conserved in our numerical simulations. Our treatment leads to novel predictions for the magnetic-energy-decay laws: In particular, while we expect the canonical power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower decay in the slow “Sweet-Parker” reconnection regime, in better agreement with existing numerical simulations. For nonhelical fields, for which there currently exists no definitive theory, we predict power laws of and in the fast- and slow-reconnection regimes, respectively. 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 MHD turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.
- Received 15 March 2021
- Revised 28 May 2021
- Accepted 10 August 2021
DOI:https://doi.org/10.1103/PhysRevX.11.041005
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Much of the visible matter in the Universe exists as magnetized plasma in a state of chaotic, turbulent motion. We present a theory of how such plasma behaves when its source of energy is removed and the turbulence decays. This process may be key to understanding a wide variety of astrophysical systems, from the solar wind to primordial magnetic fields in the early Universe.
It is well known that the magnetic-field topology restricts the possible motions available to a turbulent plasma. In particular, “magnetic helicity,” which encodes the number of times magnetic flux tubes interlink or twist, must remain constant as the plasma relaxes. This fact may be used to predict how the energy decays.
However, not all field configurations possess magnetic helicity; it is expected only in strongly asymmetric systems, such as those that rotate rapidly. So far, it has been unclear how to predict the system’s evolution when the magnetic field is nonhelical. Here, we propose that the plasma evolution is controlled by local fluctuations in the magnetic helicity. The implications of this idea agree with our simulation results and those of previous authors, of which we argue our theoretical analysis provides the first convincing explanation.
Our suggested formalism is very general, being applicable to any kind of turbulence with a conserved quantity that does not have a definite sign. We anticipate that its applications may be many and varied.
