Quenching and anisotropy of hydromagnetic turbulent transport

TL;DR

This paper investigates how strong magnetic fields suppress and introduce anisotropy in turbulent magnetic transport coefficients using the test-field method across different turbulent flows, revealing specific quenching exponents and behaviors.

Contribution

It provides detailed quantification of the quenching of turbulent transport coefficients and anisotropies in various hydromagnetic turbulence regimes, using advanced numerical methods.

Findings

Significant quenching occurs only when magnetic fields exceed equipartition values.

Quenching exponents depend on how magnetic fields are scaled, with different values for quenched and unquenched flows.

Turbulent diffusion and pumping exhibit similar quenching behaviors, with variations based on flow type and magnetic Reynolds number.

Abstract

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the $\alpha$ effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the {\it quenched} flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows these quenching exponents become about 4, 1.5, and 2.3, respectively. For the $\alpha$ effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the $\bf \Omega \times \bf J$ effect nearly the same quenching exponent is obtained as for $\alpha$. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.