Ergodic and non-ergodic clustering of inertial particles

We compute the fractal dimension of clusters of inertial particles in random flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic "centrifuge effect". In the limit of St -> 8 and Ku -> 0 (so that Ku(2)St remains finite) it explains clustering in terms of ergodic "multiplicative amplification". In this limit, the theory is consistent with the asymptotic perturbation series in MEHLIG B. et al., Phys. Rev. Lett., 92 (2004) 250602. The new theory allows to analyse how the two clustering mechanisms compete at finite values of St and Ku. For particles suspended in two-dimensional random Gaussian incompressible flows, the theory yields excellent results for Ku < 0.2 for St similar to 1. The ergodic mechanism is found to contribute significantly unless St is very small. For higher values of Ku the new series is likely to require resummation. But numerical simulations show that for Ku similar to St similar to 1, ergodic multiplicative amplification makes a substantial contribution to clustering. Copyright (C) EPLA, 2011