Enhancement of small-scale turbulent dynamo by large-scale shear

TL;DR

This study demonstrates through high-resolution simulations that large-scale shear significantly enhances small-scale dynamo action in turbulent flows, with growth rates scaling with shear rate and independent of magnetic Prandtl number.

Contribution

The paper reveals that large-scale shear supports and amplifies small-scale dynamo growth, providing new scaling laws for growth rate and turbulence velocity in shear flows.

Findings

Dynamo growth rate increases with shear rate.

Shear enhances turbulence, which further boosts dynamo action.

Scaling laws for growth rate and turbulence velocity with shear.

Abstract

Small-scale dynamos are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology and structure formation. Using high-resolution direct numerical simulations we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports small-scale dynamo action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the dynamo growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate $\gamma$ of the small-scale dynamo and the turbulent velocity $u_{\rm rms}$ with shear rate $S$ that are independent of the magnetic Prandtl number: $\gamma \propto |S|$ and $u_{\rm rms} \propto |S|^{2/3}$. For large fluid and magnetic Reynolds numbers, $\gamma$, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the small-scale dynamo exhibits the scaling, $\widetilde{\gamma}\propto |S|^{2/3}$, arising solely from the induction equation for a given velocity field.