On the measurement of the turbulent diffusivity of a large-scale magnetic field

We argue that a method developed by Ångström (Ann. Phys. Chem., vol. 114, 1861, pp. 513–530) to measure the thermal conductivity of solids can be adapted to determine the effective diffusivity of a large-scale magnetic field in a turbulent electrically conducting fluid. The method consists of applying an oscillatory source and measuring the steady-state response. We illustrate this method in a two-dimensional system. This geometry is chosen because it is possible to compare the results with independent methods that are restricted to two-dimensional flows. We describe two variants of this method: one (the ‘turbulent Ångström method’) that is better suited to laboratory experiments and a second (the ‘method of oscillatory sines’) that is effective for numerical experiments. We show that, if correctly implemented, all methods agree. Based on these results we argue that these methods can be extended to three-dimensional numerical simulations and laboratory experiments.