Turbulent dispersion of heavy particles with nonlinear drag

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, β^α-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, V^T. much larger than root-mean-square of the fluid velocity fluctuations, Uo, the mean slip is given by V^T. For V^T→ 0, the mean slip is related to turbulent velocity fluctuation by assuming that fluctuations in β^αare small compared to the mean value. An interpolation formula is used to evaluate β^αand V^Tin regions intermediate between conditions of V^T→O and V^T⪢u^o. 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 Kraichnans (1970) energy spectrum.