Scaling of the Hosking integral in decaying magnetically-dominated turbulence

Abstract

The Saffman helicity invariant of Hosking and Schekochihin (2021, PRX 11, 041005), which we here call the Hosking integral, has emerged as an important quantity that may govern the decay properties of magnetically dominated nonhelical turbulence. Using a range of different computational methods, we confirm that this quantity is indeed gauge-invariant and nearly perfectly conserved in the limit of large Lundquist numbers. For direct numerical simulations with ordinary viscosity and magnetic diffusivity operators, we find that the solution develops in a nearly self-similar fashion. In a diagram quantifying the instantaneous decay coefficients of magnetic energy and integral scale, we find that the solution evolves along a line that is indeed suggestive of the governing role of the Hosking integral. The solution settles near a line in this diagram that is expected for a self-similar evolution of the magnetic energy spectrum. The solution will settle in a slightly different position when the magnetic diffusivity decreases with time, which would be compatible with the decay being governed by the reconnection time scale rather than the Alfvén time.

19 pages, 7 figures, 2 tables; accepted by JPP

References in corpus (14)

• Instability of current sheets and formation of plasmoid chains
• The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained
• Nonhelical inverse transfer of a decaying turbulent magnetic field
• Progress on Cosmological Magnetic Fields
• Classes of hydrodynamic and magnetohydrodynamic turbulent decay
• Evolution of hydromagnetic turbulence from the electroweak phase transition
• Inverse cascade of non-helical magnetic turbulence in a relativistic fluid
• Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence
• Numerical simulations of the decay of primordial magnetic turbulence
• Nonhelical turbulence and the inverse transfer of energy: A parameter study
• Scaling of the Hosking integral in decaying magnetically-dominated turbulence
• Inverse energy transfer in decaying, three dimensional, nonhelical magnetic turbulence due to magnetic reconnection
• Statistical description of coalescing magnetic islands via magnetic reconnection
• Self-similar scaling in decaying numerical turbulence

Cited by in corpus (19)

• Scaling of the Hosking integral in decaying magnetically-dominated turbulence
• Primordial magnetic field as a common solution of nanohertz gravitational waves and the Hubble tension
• Dark Matter Minihalos from Primordial Magnetic Fields
• Resistively controlled primordial magnetic turbulence decay
• Decay law of magnetic turbulence with helicity balanced by chiral fermions
• Hints of Primordial Magnetic Fields at Recombination and Implications for the Hubble Tension
• Chiral magnetohydrodynamics with zero total chirality
• Turbulence with Magnetic Helicity that is Absent on Average
• Growth or Decay -- I: universality of the turbulent dynamo saturation
• Hosking integral in nonhelical Hall cascade
• Parameter study of decaying magnetohydrodynamic turbulence
• Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor
• Turbulent magnetic decay controlled by two conserved quantities
• Revisiting constraints on primordial magnetic fields from spectral distortions of cosmic microwave background
• Spectra of magnetic fields from electroweak symmetry breaking
• LISA and $\gamma$-ray telescopes as multi-messenger probes of a first-order cosmological phase transition
• Inverse cascade from helical and nonhelical decaying columnar magnetic fields
• Conservation of magnetic-helicity fluctuations due to spatial decorrelation of fluxes in decaying MHD turbulence
• Revisiting constraints on magnetogenesis from baryon asymmetry