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Image-based Lagrangian Particle Tracking in Bed-load Experiments

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Published on: July 20, 2017

Inertial particles driven by a telegraph noise.

G Falkovich¹, S Musacchio, L Piterbarg

¹Weizmann Institute of Science, Rehovot, 76100 Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 13, 2007

Summary

We developed a model for inertial particle dynamics in compressible flow, revealing how flow time correlation influences particle aggregation. This transition is identified by changes in the Lyapunov exponent based on Stokes (St) and Kubo (Ku) numbers.

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Area of Science:

Fluid Dynamics
Particle Dynamics
Statistical Physics

Background:

Understanding inertial particle behavior in turbulent flows is crucial for various applications.
The role of flow time correlations in particle dynamics, particularly aggregation-disorder transitions, remains an active research area.
Previous models often simplify flow characteristics, limiting analytical insights into complex dynamics.

Purpose of the Study:

To introduce a novel model for Lagrangian particle dynamics in compressible flow.
To analytically investigate the influence of flow time correlation on particle aggregation-disorder transitions.
To identify critical parameter regimes governing particle behavior using Lyapunov exponents.

Main Methods:

Developed a mathematical model for Lagrangian dynamics of inertial particles.
Modeled fluid velocity gradients using telegraph noise to incorporate time correlation.
Analyzed particle trajectory Lyapunov exponents as a function of Stokes (St) and Kubo (Ku) numbers.

Main Results:

Identified a parameter space region (St, Ku) where the leading Lyapunov exponent changes sign, indicating a transition.
Demonstrated that flow time correlation significantly impacts the aggregation-disorder transition of inertial particles.
Derived asymptotic behaviors for short- and long-correlated flows, and the fluid-tracer limit.

Conclusions:

The proposed model provides an analytical framework to study particle dynamics in correlated flows.
Flow time correlation is a key factor determining inertial particle aggregation and disorder.
The study offers insights into the transition dynamics relevant to geophysical and industrial flows.