On the motion of suspended particles in stationary homogeneous turbulence

Abstract

The closed equations for the velocity correlation tensor and for the mean-squared displacement of a particle suspended in a stationary homogeneous turbulent flow, with an arbitrary linear law of fluid-particle interaction, are obtained using two assumptions suggested previously for the problem of turbulent self-diffusion: the ‘independence approximation’ and the Gaussian property of the functional distribution of particle velocities. The numerical solution of the derived equations is given for an isotropic system with a model turbulence spectrum. The following characteristics of the particle motion are obtained: ( a ) the mean kinetic energy, ( b ) diffusivity, ( c ) rate of energy dissipation, ( d ) velocity correlation function, and ( e ) the correlation function of the relative fluid-particle velocity. The impact of various spectral modes on the characteristics of the particle motion is discussed.