Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers

Abstract

In a one-dimensional model for a turbulent aerosol (inertial particles suspended in a random flow) we compute the distributions of particle-velocity gradients and the rate of caustic formation at finite but small Kubo numbers Ku, for arbitrary Stokes numbers St. Our results are consistent with those obtained earlier in the limit of small Ku and and large St, such that Ku^2 St remains constant. We show how finite-time correlations and non-ergodic effects influence the inertial-particle dynamics at finite but small Kubo numbers.