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Deviation-angle and trajectory statistics for inertial particles in turbulence.

Akshay Bhatnagar1,2, Anupam Gupta3, Dhrubaditya Mitra2

  • 1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.

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Particle trajectories in turbulent fluid flows deviate from fluid pathlines. This study reveals power-law distributions for velocity deviation angles and trajectory properties, offering insights into particle dynamics in turbulence.

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Area of Science:

  • Fluid Dynamics
  • Particle Physics
  • Turbulence Research

Background:

  • Particles in turbulent fluids do not perfectly follow fluid pathlines due to inertia.
  • Understanding particle trajectory deviations is crucial for various applications, including pollutant dispersion and multiphase flow analysis.

Purpose of the Study:

  • To investigate the statistical properties of particle velocity deviation angles in turbulent flows.
  • To analyze the probability distribution functions (PDFs) of trajectory curvature and torsion for suspended particles.
  • To propose a metric for quantifying the complexity of heavy-particle trajectories.

Main Methods:

  • Numerical simulations of particle trajectories in turbulent fluid.
  • Statistical analysis of particle velocity deviation angles.
  • Examination of probability distribution functions (PDFs) for trajectory curvature and torsion.
  • Development and numerical validation of a complexity measure based on torsion sign changes.

Main Results:

  • A power-law region P_{ϕ}∼ϕ^{-4} was identified for the PDF of the velocity deviation angle (ϕ) for small particle inertia.
  • PDFs of trajectory curvature (κ) and torsion modulus (θ) exhibit power-law tails: P_{κ}∼κ^{-5/2} and P_{θ}∼θ^{-3}.
  • The number of torsion sign changes per unit time (n_{I}) scales as St^{-Δ} for large Stokes numbers (St), with Δ≃0.5, indicating a measure of trajectory complexity.

Conclusions:

  • Particle trajectories in turbulence exhibit universal scaling laws similar to fluid pathlines.
  • The proposed measure based on torsion sign changes effectively quantifies heavy-particle trajectory complexity in relation to Stokes number.
  • These findings contribute to a deeper understanding of particle dynamics and dispersion in turbulent environments.