Finite Larmor radius effects on nondiffusive tracer transport in a zonal flow

Gustafson, K.; del-Castillo-Negrete, D.; Dorland, W.
October 2008
Physics of Plasmas;Oct2008, Vol. 15 Issue 10, p102309
Academic Journal
Finite Larmor radius (FLR) effects on nondiffusive 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 from 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 non-Gaussian probability distribution functions (PDFs) of particle displacements, with Lévy flights in one direction only. 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: σ2∼tγ. 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 nondiffusive algebraic decay, C∼τ-κ, with κ=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 spatiotemporal 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, respectively.


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