Calculating turbulent transport tensors by averaging single-plume dynamics and application to dynamos

Abstract

ABSTRACT Transport coefficients in turbulence are comprised of correlation functions between turbulent fluctuations and efficient methods to calculate them are desirable. For example, in mean-field dynamo theories used to model the growth of large-scale magnetic fields of stars and galaxies, the turbulent electromotive force is commonly approximated by a series of tensor products of turbulent transport coefficients with successively higher order spatial derivatives of the mean magnetic field. One ingredient of standard models is the kinematic coefficient of the zeroth-order term, namely the averaged kinetic pseudo-tensor $\boldsymbol \alpha$, that converts toroidal to poloidal fields. Here we demonstrate an efficient way to calculate this quantity for rotating stratified turbulence, whereby the pre-averaged quantity is calculated for the motion of a single plume, and the average is then taken over an ensemble of plumes of different orientations. We calculate the plume dynamics in the most convenient frame, before transforming back to the lab frame and averaging. Our concise configuration space calculation gives essentially identical results to previous lengthier approaches. The present application exemplifies what is a broadly applicable method.