Clustering in mixing flows

Abstract

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Pade-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterise two distinct clustering effects which occur in that limit.

5 pages, 1 figure

References in corpus (6)

• Caustics in turbulent aerosols
• Fractal clustering of inertial particles in random flows
• Slow modes in passive advection
• Large scale inhomogeneity of inertial particles in turbulent flow
• The path-coalescence transition and its applications
• Coagulation by Random Velocity Fields as a Kramers Problem

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