Lagrangian chaos and correlated Lévy flights in a non-Beltrami flow: Transient versus long-term transport

Abstract

Long-range transport is studied numerically in a time-independent, three-dimensional (3D) fluid flow composed of the superposition of two chains of alternating vortices, one horizontal and the other vertical. Tracers in this flow follow chaotic trajectories composed of correlated Lévy flights with varying velocities. Locations of the chaotic regimes in the flow are compared with recent theories of chaos in non-Beltrami 3D flows. Growth of the variance of a distribution of tracers is divided into transient and long-term regimes, each with different growth exponents.

Lévy walk description of suprathermal ion transport

“…18 used a constant, unidirectional accelerating electric field, leading to larger Dr for a given Dt. For the diffusion and superdiffusion reported for the fluid model in Fogleman, 16 ¼ 1 by assumption, which is similar to our values for diffusive and superdiffusive c. This is smaller than the Richardson value, ¼ 3=2, reported by Lawrence 17 for solar magnetic bright points. Notably, our subdiffusive ' 0:15 is smaller than any of the values we found in the literature, consistent with the absence of subdiffusive cases in these other studies.…”

“…in fluid turbulence. 16 This is consistent with the presence of fully-developed turbulence, without constant acceleration, common to these three contexts.…”

“…This allows exploration of transport regimes from subdiffusive to superdiffusive. While other authors have used Lévy walks in fluids 16 and in plasma turbulence, 18 we believe that our work constitutes the first application of the Lévy walk to the complete set of applicable transport regimes while using a validated numerical model of suprathermal ions in plasma turbulence.…”

“…However, contrary to the Lévy flight, Lévy walks penalize long steps, since they require more time. Lévy walks have been used to describe transport phenomena in a wide range of systems, from neutral fluids 16 to the motion of magnetic bright points in the Sun. 17 In the context of plasma physics, it has been pointed out that superballistic transport observed in a static reconnecting current-sheet is in agreement with the Lévy walk prediction.…”

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

“…A substantial body of work does exist on experimental analysis of 2D chaotic advection and its impact on transport processes. However, such studies focus predominantly on ramifications and signatures of chaotic advection as, e.g., (exponential) stretching and folding of material elements, [26][27][28] transport enhancement and anomalous diffusion, [29][30][31][32][33] crossing of transport barriers, 34 and the formation of persistent patterns. 35 Laboratory experiments dedicated specifically to the Hamiltonian dynamics and kinematic mechanisms that underly the above phenomena (e.g., emergence of periodic points, formation and breakdown of KAM tori, and manifold dynamics) are rare, on the other hand.…”