Transport effects associated with turbulence with particular attention to the influence of helicity

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 alpha 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 omega (x,t)=curl u.