Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow

Finite Larmor radius (FLR) effects on non-diffusive transport in a prototypical zonal flow with drift waves are studied in the context of a simplified chaotic transport model. The model consists of a superposition of drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. High frequency FLR effects are incorporated by gyroaveraging the E×B velocity. Transport in the direction of the density gradient is negligible and we therefore focus on transport parallel to the zonal flows. A prescribed asymmetry produces strongly asymmetric nonGaussian PDFs of particle displacements, with Lévy flights in one direction but not the other. For k⊥ρth = 0, where k⊥ is the characteristic wavelength of the flow and ρth is the thermal Larmor radius, a transition is observed in the scaling of the second moment of particle displacements, σ ∼ t . The transition separates ballistic motion, γ ≈ 2, at intermediate times from superdiffusion, γ = 1.6, at larger times. This change of scaling is accompanied by the transition of the PDF of particle displacements from algebraic decay to exponential decay. However, FLR effects seem to eliminate this transition. In all cases, the Lagrangian velocity autocorrelation function exhibits non-diffusive algebraic decay, C ∼ τ , with ζ = 2 − γ to a good approximation. The PDFs of trapping and flight events show clear evidence of algebraic scaling with decay exponents depending on the value of k⊥ρth. The shape and spatio-temporal self-similar anomalous scaling of the PDFs of particle displacements are reproduced accurately with a neutral, α = β, asymmetric effective fractional diffusion model where α and β are the orders of the spatial and temporal fractional derivatives.