Turbulent dispersion with broken reflectional symmetry

We consider dispersion in axisymmetric turbulence which lacks reflectional symmetry. A stochastic equation for the Lagrangian evolution of the velocity of a fluid particle, which is appropriate for infinite Reynolds number turbulence, is used to model the dispersion. Such equations are now common as Lagrangian dispersion models for atmospheric transport problems, but are only strictly well founded for isotropic homogeneous turbulence. It is the minimalist variation from this state of affairs that is considered here. Axisymmetry is the most highly symmetric turbulence that can be suitably analysed by these techniques, spherical symmetry being equivalent to full isotropy in the class of models considered. This simple relaxation of full symmetry leads to oscillations of the Lagrangian velocity autocorrelation, oscillatory growth of the dispersion, significant reduction of dispersion for fixed turbulence kinetic energy and dissipation rate, spiralling fluid-particle trajectories, and tracer fluxes orthogonal to gradients (skew diffusion). The mean fluid-particle angular momentum is an important parameter.