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Chaotic Lagrangian models for turbulent relative dispersion
Guglielmo Lacorata1, Angelo Vulpiani2
1CNR-Istituto di Scienze dell'Atmosfera e del Clima, Via Monteroni, I-73100, Lecce, Italy and Center of Excellence CETEMPS, Università dell'Aquila, Via Vetoio, I-67100, Coppito (AQ), Italy.
Physical Review. E
|May 17, 2017
Summary
This study introduces a deterministic model for turbulent dispersion, controlled by Lagrangian chaos, not stochastic diffusion. This efficient, low-cost model accurately simulates turbulent trajectories and has geophysical applications.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Computational Physics
Background:
- Stochastic diffusion models often suffer from drawbacks like the "sweeping effect."
- Understanding relative dispersion in turbulent flows is crucial for various scientific fields.
Purpose of the Study:
- To introduce a deterministic multiscale dynamical system as a prototype model for relative dispersion.
- To demonstrate that Lagrangian chaos, not stochastic diffusion, can control transport and mixing properties.
- To remove the "sweeping effect" using quasi-Lagrangian coordinates.
Main Methods:
- Development of a deterministic multiscale dynamical system.
- Utilizing quasi-Lagrangian coordinates to eliminate the "sweeping effect."
- Analysis of Lagrangian dispersion statistics using the finite-scale Lyapunov exponent (FSLE).
Main Results:
- The model accurately captures Lagrangian dispersion statistics, validated by FSLE scaling exponents.
- Numerical experiments across a range of Reynolds numbers confirm the model's efficiency and low computational cost.
- Chaotic deterministic flows are shown to be effective models for turbulent trajectories.
Conclusions:
- The deterministic model provides an efficient and numerically low-cost alternative to stochastic models for simulating turbulent dispersion.
- The model's simple mathematics and validated accuracy suggest potential applications in geophysical modeling and predictability studies.
- FSLE serves as a critical tool for assessing the fidelity of turbulence models against theoretical and observational data.
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