Related Experiment Video
Updated: May 26, 2026

Simultaneous Measurement of Turbulence and Particle Kinematics Using Flow Imaging Techniques
Published on: March 12, 2019
Distribution of relative velocities in turbulent aerosols
1Department of Physics, Gothenburg University, S-41296 Gothenburg, Sweden.
Abstract:
We compute the distribution of relative velocities for a one-dimensional model of heavy particles suspended in a turbulent flow, quantifying the caustic contribution to the moments of relative velocities. The same principles determine the corresponding caustic contribution in d spatial dimensions. The distribution of relative velocities Δv at small separations R acquires the universal form ρ(Δv,R)∼R(d-1)|Δv|(D(2)-2d) for large (but not too large) values of |Δv|. Here D(2) is the phase-space correlation dimension. Our conclusions are in excellent agreement with numerical simulations of particles suspended in a randomly mixing flow in two dimensions, and in quantitative agreement with published data on direct numerical simulations of particles in turbulent flows.
Related Concept Videos
Distribution of Molecular Speeds
Relative Velocity in Two Dimensions
Laminar and Turbulent Flow
Maxwell-Boltzmann Distribution: Problem Solving
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy
Turbulent Flow

