Abstract

Determining the turbulent diffusivity of magnetic fields is one of the most fundamental problems of astrophysical fluid dynamics. I shall argue that a method developed by Angstrom (1861) 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. I shall initially illustrate this method in a two-dimensional system. This geometry is chosen because it is possible to compare the results with (somewhat tried and somewhat trusted) independent methods that are restricted to two-dimensional flows. I shall describe two variants of this method; one (the “Turbulent Angstrom Method”) that is better suited to laboratory experiments the second (the “Method of Oscillatory Sines’‘) that is effective for numerical experiments. If correctly implemented, all methods agree. I shall finish by extending the methods to three dimensional convective flows.