Diffusion of passive-scalar and magnetic fields by helical turbulence

Abstract

Computer simulations of fluid-element trajectories in mirror-symmetric and maximally helical turbulence are used to evaluate Moffatt's (1974) formulae for the magnetic diffusivity η(t) and the coefficient κ(t) of the alpha-effect. The passive-scalar diffusivity κ(t) and the mean response functions of scalar and magnetic field wave-vector modes are also computed. The velocity field is normal, stationary, homogeneous and isotropic with spectrum $E(k) = \frac{3}{2}v^2_0\delta(k - k_0)$ and time correlation exp [−1/2ω2/0(t-t)²]. The cases ω₀ = O (frozen turbulence), ω = v_o k₀ and ω₀ = 2v₀ k₀ are followed to t = 4/v₀ k₀. In the ω0 > 0 cases with maximal helicity, κ(t) and a(t) approach steady-state values of order vo/k0 and v0, respectively. They behave anomalously for ω₀ = 0. In the mirror-symmetric: cases, q(t) and κ(t) differ very little from each other. At all the ω₀ values, is bigger in the helical than in the mirror-symmetric case. The difference is marked for ω₀ = 0. The simulation results imply that κ(t) becomes negative in non-normal mirror-symmetric turbulence with strong helicity fluctuations that persist over several correlation lengths and times. The computations of response functions indicate that asymptotic expressions for these functions, valid for k [Lt ]; k₀, retain good accuracy for k ∼ k₀. The mean-square magnetic field is found to grow exponentially, and its kurtosis also grows apidly with t, indicating rapid development of a highly intermittent distribution of magnetic field.