Clustering by mixing flows

Duncan, Kevin; Mehlig, Bernhard; Ostlund, Stellan and Wilkinson, Michael (2005). Clustering by mixing flows. Physical Review Letters, 95(24) p. 240602.



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 , a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Padé-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 characterize two distinct clustering effects which occur in that limit.

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