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Diffusion of passive-scalar and magnetic fields byhelical turbulence

Published online by Cambridge University Press:  11 April 2006

Robert H. Kraichnan
Affiliation:
Dublin, Now Hampshire 03444

Abstract

Computer simulations of fluid-element trajectories inmirror-symmetric and maximally helical turbulence are used toevaluate Moffatt's (1974) formulae for the magnetic diffusivity η(t)and the coefficient κ(t) of the alpha-effect. The passive-scalardiffusivity κ(t) and the mean response functions of scalar andmagnetic field wave-vector modes are also computed. The velocityfield 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 (frozenturbulence), ω = vo k0 andω0 = 2v0 k0 are followed to t =4/v0 k0. In the ω0 > 0 cases withmaximal helicity, κ(t) and a(t) approach steady-state values oforder vo/k0 and v0, respectively. They behave anomalously forω0 = 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. Thedifference is marked for ω0 = 0. The simulation resultsimply that κ(t) becomes negative in non-normal mirror-symmetricturbulence with strong helicity fluctuations that persist overseveral correlation lengths and times. The computations of responsefunctions 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 growexponentially, and its kurtosis also grows apidly with t, indicatingrapid development of a highly intermittent distribution of magneticfield.

Information

Type
Research Article
Copyright
© 1976 Cambridge University Press

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