Clustering and collisions in stochastic turbulence

Abstract

This thesis deals with the behaviour of particles in a stochastic model of turbulence. Special attention is given to clustering and collisions of particles. A stochastic model of turbulence is implemented and used to perform simulations of particle dynamics. Both advected particles, and particles with inertia are considered, as well as both incompressible and partly compressible flow. The behaviour of the dynamics is quantified by studying the Lyapunov exponents, and their relation to clustering is discussed. Simulations of the advective dynamics are used to estimate the exponents for different degrees of compressibility. The simulations are shown to be in agreement with theory, and the theory’s regime of validity is discussed in brief. Collision rates are computed for particles advected in incompressible flow. The results agree with previous numerical studies, as well as with theoretical estimates for the initial transient and the long time steady state. It is demonstrated that clustering of particles can occur both as result of compressibility in the field and of particle inertia.