The dynamo effect in decaying helical turbulence

TL;DR

This paper demonstrates that in decaying helical turbulence, magnetic fields become fully helical with an inverse cascade, exhibiting slow decay and exponential growth, relevant to astrophysical and experimental dynamos.

Contribution

It reveals the evolution of magnetic helicity and energy in decaying turbulence, showing inverse cascading and dynamo action with new scaling laws and late-time behavior.

Findings

Magnetic helicity becomes fully helical with opposite sign to kinetic helicity.

Magnetic energy decays as approximately t^{-1/2}, slower than in fully helical cases.

Magnetic field experiences exponential growth early on, indicating small-scale dynamo action.

Abstract

We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity - regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t^{-1/2}. This is even slower than in the fully helical case, where it decays like t^{-2/3}. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity, is approximately constant. This scaling of magnetic energy persists over long time scales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a cross-over to the t^{-2/3} decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe.