Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor

Abstract

In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic field, the spectral magnetic energy density is known to increase with time at small wavenumbers $k$, provided the spectrum at low $k$ is sufficiently steep. This process is called inverse cascading and occurs for an initial Batchelor spectrum, where the magnetic energy per linear wavenumber interval increases like $k^4$. For an initial Saffman spectrum that is proportional to $k^2$, however, inverse cascading has not been found in the past. We study here the case of an intermediate $k^3$ spectrum, which may be relevant for magnetogenesis in the early Universe during the electroweak epoch. This case is not well understood in view of the standard Taylor expansion of the magnetic energy spectrum for small $k$. Using high resolution MHD simulations, we show that also in this case there is inverse cascading with a strength just as expected from the conservation of the Hosking integral, which governs the decay of an initial Batchelor spectrum. Even for shallower $k^{\alpha }$ spectra with spectral index $\alpha >3/2$, our simulations suggest a spectral increase at small $k$ with time $t$ proportional to $t^{4\alpha /9-2/3}$. The critical spectral index of $\alpha =3/2$ is related to the slope of the spectral envelope in the Hosking phenomenology. Our simulations with $2048^3$ mesh points now suggest inverse cascading even for an initial Saffman spectrum.

arXiv comment18 pages, 9 figures, 3 tables, submitted to J. Plasma Physics, improved evidence for inverse cascading for nonhelical $k^2$ spectrum

References in corpus (18)

• The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
• Primordial Magnetic Fields and Causality
• The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained
• Progress on Cosmological Magnetic Fields
• Classes of hydrodynamic and magnetohydrodynamic turbulent decay
• Evolution of hydromagnetic turbulence from the electroweak phase transition
• From primordial seed magnetic fields to the galactic dynamo
• Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer
• Magnetic island merger as a mechanism for inverse magnetic energy transfer
• 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
• Hall cascade with fractional magnetic helicity in neutron star crusts
• Decay law of magnetic turbulence with helicity balanced by chiral fermions
• Turbulence with Magnetic Helicity that is Absent on Average
• Hosking integral in nonhelical Hall cascade
• Parameter study of decaying magnetohydrodynamic turbulence
• Kibble mechanism for electroweak magnetic monopoles and magnetic fields

Cited by in corpus (7)

• Resistively controlled primordial magnetic turbulence decay
• Turbulent magnetic decay controlled by two conserved quantities
• Analytic solutions for the linearized first-order magnetohydrodynamics and implications for causality and stability
• Revisiting constraints on primordial magnetic fields from spectral distortions of cosmic microwave background
• Spectra of magnetic fields from electroweak symmetry breaking
• Can WIMPs Survive the Legacy of a Magnetised Early Universe?
• Inverse cascade from helical and nonhelical decaying columnar magnetic fields