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Evolution of triangles in a two-dimensional turbulent flow.

P Castiglione1, A Pumir

  • 1Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
Summary

Investigating particle swarms in turbulent flow reveals distinct triangle shape distributions. At large scales, shapes are Gaussian; in the inertial range, they become non-Gaussian, favoring elongated triangles.

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Area of Science:

  • Fluid Dynamics
  • Turbulence Research
  • Statistical Mechanics

Background:

  • Turbulent flows distort particle swarms, affecting their shape and separation.
  • Understanding particle dispersion is crucial in various scientific and engineering fields.

Purpose of the Study:

  • To statistically analyze the geometric evolution of particle swarms in turbulent flow.
  • To identify and characterize the probability distributions of triangle shapes formed by three particles.

Main Methods:

  • Experimental investigation of a turbulent two-dimensional flow with a k(-5/3) energy spectrum.
  • Tracking Lagrangian markers (three points) to analyze triangle geometry over time.

Main Results:

  • Two distinct shape distributions were identified for particle triangles.

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  • At large scales (beyond integral scale), shapes follow a Gaussian distribution.
  • In the inertial range, a self-similar, non-Gaussian distribution emerges, showing a higher probability for elongated triangles.

    • Conclusions:

    • The geometry of particle swarms in turbulence exhibits scale-dependent statistical properties.
    • The observed non-Gaussian distribution in the inertial range aligns with predictions from stochastic models.
    • This study provides insights into particle dispersion dynamics in turbulent environments.