Alpha effect and diffusivity in helical turbulence with shear

TL;DR

This study investigates how shear affects turbulent transport coefficients like alpha and diffusivity tensors in helical turbulence, revealing quenching and enhancement patterns, and proposes a model for turbulent pumping velocity based on simulation results.

Contribution

It provides new insights into the dependence of turbulent transport coefficients on shear and Reynolds number, and introduces a simple model for turbulent pumping velocity in helical turbulence.

Findings

Diagonal alpha components quench with increasing shear.

Turbulent magnetic diffusivity components increase with shear.

Proposed a model linking turbulent pumping velocity to helicity and vorticity.

Abstract

We study the dependence of turbulent transport coefficients, such as the components of the $\alpha$ tensor ($\alpha_{ij}$) and the turbulent magnetic diffusivity tensor ($\eta_{ij}$), on shear and magnetic Reynolds number in the presence of helical forcing. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity. We find that with increasing shear the diagonal components of $\alpha_{ij}$ quench, whereas those of $\eta_{ij}$ increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or $\gamma$ effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of $\alpha_{ij}$, it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence.