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Clustering by mixing flows.

Kevin Duncan1, Bernhard Mehlig, Stellan Ostlund

  • 1Faculty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom.

Physical Review Letters
|December 31, 2005
PubMed
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Particles suspended in random flows exhibit clustering at high Stokes numbers. This study reveals two distinct clustering effects using Lyapunov exponents and Padé-Borel summation for random flow dynamics.

Area of Science:

  • Fluid dynamics
  • Statistical physics
  • Particle dynamics

Background:

  • Understanding particle behavior in turbulent or random flows is crucial for various applications.
  • Lyapunov exponents quantify chaotic dynamics and sensitive dependence on initial conditions.

Purpose of the Study:

  • To calculate Lyapunov exponents for particles in a random 3D flow.
  • To investigate particle clustering in the limit of small viscous damping and large particle inertia.

Main Methods:

  • Calculation of Lyapunov exponents using a power series expansion in particle inertia (epsilon).
  • Application of Padé-Borel summation to handle asymptotic series and obtain accurate results.
  • Analysis of particle dynamics in incompressible random mixing flows.

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Main Results:

  • Lyapunov exponents were accurately determined using Padé-Borel summation.
  • Pronounced particle clustering was observed for large Stokes numbers.
  • Two distinct types of clustering phenomena were identified in the large Stokes number limit.

Conclusions:

  • The study provides a robust method for calculating Lyapunov exponents in random flows.
  • Demonstrates that particle inertia and flow properties significantly influence clustering.
  • Offers insights into the complex dynamics of suspended particles in turbulent environments.