Turbul Transport

Rep. Prog. Phys., Vol. 46, pp 621-664, 1983. Printed in Great Britain Transport effects associated with turbulence with particular attention to the influence of helicity H K Moffatt Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Abstract The action of turbulence on a passive convected scalar field (e.g. temperature) or vector field (e.g. the magnetic field in an electrically conducting fluid) is reviewed, with particular attention paid to anomalous effects that can arise through the influence of Coriolis forces in a rotating system on the statistics of the turbulence. The simplest such effect (which corresponds to a breaking of the Onsager symmetry relations) is a ‘skew-diffusion’ effect, i.e. the appearance of a component of turbulent heat flux perpendicular to the local mean temperature gradient. The famous a effect of magnetohydrodynamic dynamo theory is also in this category, as is the more subtle Radler effect (the appearance of a mean electromotive force perpendicular to the mean current in a plasma). These effects are all associated with the helicity of a turbulent flow, i.e. the correlation between the velocity field u ( x , t ) and the vorticity field w(x, t ) = curl U. Sections 1-4 are introductory in nature, and discuss the problem of heat spot dispersion, the interaction of molecular and turbulent convective effects, the spectral description of random scalar and vector fields, and the spectral properties of a passive scalar field which is subject to both influences. In 0 5 , the mean-field (or double-length scale) approach is presented for the scalar field problem, and the general theory of eddy diffusivity and skew diffusivity is developed. Sections 6 and 7 are devoted to the Lagrangian approach and the ‘first-order smoothing’ approach-complementary approaches which have some interesting points