Turbulent Dispersion of Heavy Particles With Nonlinear Drag

Abstract

The analysis of Reeks (1977) for particle dispersion in isotropic turbulence is extended so as to include a nonlinear drag law. The principal issue is the evaluation of the inertial time constants, βα −1 , and the mean slip. Unlike what is found for the Stokesian drag, the time constants are functions of the slip velocity and are anisotropic. For settling velocity, VT , much larger than root-mean-square of the fluid velocity fluctuations, u0 , the mean slip is given by VT . For VT →0, the mean slip is related to turbulent velocity fluctuation by assuming that fluctuations in βα are small compared to the mean value. An interpolation formula is used to evaluate βα and VT in regions intermediate between conditions of VT →0 and VT ≫ u0 . The limitations of the analysis are explored by carrying out a Monte-Carlo simulation for particle motion in a pseudo turbulence described by a Gaussian distribution and Kraichnan’s (1970) energy spectrum.