Segregation of particles in incompressible random flows:singularities, intermittency and random uncorrelated motion

We report recent measurements of the segregation of small inertial particles advected via Stokes drag in an isotropic homogeneous incompressible turbulent flow using a full Lagrangian method (FLM) to calculate the compressibility of an elemental volume of particles measured along a particle trajectory. The flow field was generated by a random Fourier mode kinematic simulation (KS) and by DNS. Numerical results show that the average compressibility decreases continuously with time if the value of the Stokes number is below a threshold value ~1, indicating that the segregation continues indefinitely. We find that the probability distribution of the compression tends to a Gaussian distribution except in the wings due to the occurrence of singularities in the particle concentration which makes the process highly intermittent. The distribution of singularities over a fixed interval of time for a range of Stoke numbers is shown to be well approximated by a Poisson distribution. Finally, we show that the occurrence of singularities is related to the formation of caustics and the occurrence of random uncorrelated motion (RUM).