On the simulation of particle trajectories in turbulent flows

A different class of stochastic model, comprising of the Langevin equation with a random time scale, for the simulation of fluid velocities along particle trajectories in high Reynolds-number turbulent flows is formulated. These velocities are neither purely Lagrangian nor purely Eulerian in character. The distribution of time scales is chosen to ensure that the modeled form of the fluid-velocity structure function and spectral functions are compatible with Kolmogorov similarity scaling and with the scaling analysis of Fung, Hunt, and Perkins [Proc. R. Soc. London, Ser. A 459, 445 (2003)]. It is shown that the model accounts naturally for the crossing trajectory effect and integral time scales are compatible with the much used parameterizations advocated by Csanady [J. Atmos. Sci. 20, 201 (1963)] and by Frenkiel [Adv. Appl. Mech. 3, 61 (1953)]. Model predictions for particle dispersion in grid generated turbulence are shown to be in close accord with the experimental data of Snyder and Lumley [J. Fluid Mech. 48, 41 (1971)]