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Jets, stickiness, and anomalous transport
Xavier Leoncini1, George M Zaslavsky
1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA. leoncini@cims.nyu.edu
Summary
Investigating chaotic flows from point vortices reveals anomalous superdiffusion in particle transport. Coherent structures and "jets" cause sticky regions, leading to quasiballistic tracer motion and explaining the observed superdiffusion.
Area of Science:
- Fluid Dynamics
- Chaos Theory
- Statistical Mechanics
Background:
- Chaotic flows are complex systems where particle trajectories are highly sensitive to initial conditions.
- Understanding passive particle advection is crucial for predicting transport phenomena in various physical systems.
- Vortex dynamics play a significant role in shaping flow structures and influencing particle movement.
Purpose of the Study:
- To investigate the dynamical and statistical properties of passive particle advection in chaotic flows.
- To analyze the anomalous transport behaviors and their origins in flows generated by multiple point vortices.
- To characterize the coherent structures, termed 'jets', responsible for observed stickiness and superdiffusion.
Main Methods:
- Simulation of chaotic flows generated by 4- and 16-point vortices.
- Analysis of passive tracer motion, including mutual relative evolution of nearby tracers.
- Quantification of transport properties using the second moment exponent and investigation of 'jet' structures.
Main Results:
- Anomalous superdiffusive behavior (second moment exponent μ ≈ 1.75) was observed in general transport properties.
- Coherent structures, specifically vortex cores and regions far from vortices, exhibit 'stickiness' and quasiballistic tracer motion.
- Localized 'jets' within sticky regions were identified, characterized by nested structures, and their trapping time statistics agreed with transport exponents.
Conclusions:
- The anomalous superdiffusion in these chaotic flows originates from coherent structures leading to stickiness and quasiballistic motion.
- The identified 'jets' represent a form of hidden order in tracer motion, explaining the observed transport anomalies.
- The study provides a quantitative link between jet dynamics and the statistical properties of anomalous transport in chaotic flows.