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Transport in finite size systems: An exit time approach
P. Castiglione1, M. Cencini, A. Vulpiani
1Dipartimento di Fisica, Universita "La Sapienza," and INFM, Unita di Roma 1, P.le A. Moro 2, I-00185, Roma, Italy.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
Passive tracer transport in finite systems with chaotic scattering is complex. Exit time statistics reveal strong initial condition sensitivity, showing long-tailed probability distributions unsuitable for simple characterization.
Area of Science:
- Physics
- Fluid Dynamics
- Complex Systems
Background:
- Chaotic scattering describes systems where trajectories diverge exponentially.
- Passive tracer transport is crucial for understanding mixing and dispersion in various physical systems.
- Finite systems with open streamlines and recirculation zones present unique challenges for transport analysis.
Purpose of the Study:
- To analyze passive tracer transport in finite systems within the framework of chaotic scattering.
- To investigate models with open streamlines and a finite number of recirculation zones.
- To characterize nonasymptotic dispersion properties when asymptotic quantities are inappropriate.
Main Methods:
- Analysis of chaotic scattering models.
- Study of systems with open streamlines and recirculation zones.
- Characterization using exit time statistics.
Main Results:
- Asymptotic quantities like eddy diffusivity are inappropriate for systems with a small number of recirculation zones.
- Exit time statistics reveal strong sensitivity to initial conditions.
- The resulting probability distribution function exhibits long tails, precluding a unique typical exit time.
Conclusions:
- Nonasymptotic dispersion properties are key in finite chaotic systems.
- Exit time statistics provide a more accurate characterization than traditional methods.
- Understanding these properties is crucial for predicting tracer behavior in complex flows.