2006/12/27 by M. Wilkinson, B. Mehlig, S. Ostlund +2 · 46 citations
Engineering · Physics and Astronomy · #Cluster (spacecraft) #Dimensionless quantity #Fluid Dynamics and Turbulent Flows #Fluid dynamics and aerodynamics studies #Fractal dimension #Limit (mathematics) #Lyapunov exponent #Particle Dynamics in Fluid Flows #Perturbation (astronomy) #Randomness #Series (stratigraphy) #Stokes number #Turbulence #cond-mat.dis-nn #nlin.CD
paper · pdf · doi:10.1063/1.2766740
published in Physics of Fluids 19(11) (American Institute of Physics) · 39 pages, 8 figures
arxiv created 2006/12/27 · openalex publication_date 2007/11/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider particles suspended in a randomly stirred or turbulent fluid. When effects of the inertia of the particles are significant, an initially uniform scatter of particles can cluster together. We analyze this “unmixing” effect by calculating the Lyapunov exponents for dense particles suspended in such a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time of the random flow (that is, the regime of large Stokes number). In this limit Lyapunov exponents are obtained as a power series in a parameter which is a dimensionless measure of the inertia. We report results for the first seven orders. The perturbation series is divergent, but we obtain accurate results from a Padé-Borel summation. We deduce that particles can cluster onto a fractal set and show that its dimension is in satisfactory agreement with previously reported simulations of turbulent Navier-Stokes flows. We also investigate the rate of formation of caustics in the particle flow.