Test-field method for mean-field coefficients with MHD background

TL;DR

This paper extends the test-field method to MHD backgrounds, enabling the calculation of turbulent transport coefficients in magnetohydrodynamic flows where previous methods failed, revealing new effects and quenching behaviors.

Contribution

The paper introduces a generalized test-field method for MHD backgrounds, allowing accurate computation of turbulent coefficients in regimes where earlier methods break down.

Findings

The generalized method matches the imposed-field method in homogeneous mean fields.

Turbulent diffusivity tensor results are obtained, inaccessible to previous methods.

New mean-field effects depend on magnetic and velocity fluctuation cross-correlations.

Abstract

Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results: Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. Furthermore, results for the turbulent diffusivity tensor are given, which are inaccessible to the imposed-field method. For MHD backgrounds, new mean-field effects are found that depend on the occurrence of cross-correlations between magnetic and velocity fluctuations. For strong imposed fields, $\alpha$ is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied.