Turbulent transport in a non-Markovian velocity field

Abstract

The commonly used quasilinear approximation allows one to calculate the turbulent transport coefficients for the mean of a passive scalar or a magnetic field in a given velocity field. Formally, the quasilinear approximation is exact when the correlation time of the velocity field is zero. We calculate the lowest-order corrections to the transport coefficients due to the correlation time being nonzero. For this, we use the Furutsu-Novikov theorem, which allows one to express the turbulent transport coefficients in a Gaussian random velocity field as a series in the correlation time. We find that the turbulent diffusivities of both the mean passive scalar and the mean magnetic field are suppressed. Nevertheless, contradicting a previous study, we show that the turbulent diffusivity of the mean magnetic field is smaller than that of the mean passive scalar. We also find corrections to the $\alpha$ effect.