Third-order Lagrangian stochastic modeling

Abstract

The formulation of third-order Lagrangian stochastic models for the hyper-accelerations (time derivative of acceleration) of fluid particles in turbulence is presented. Agreement between model predictions and data from direct numerical simulations [Yeung and Pope, J. Fluid Mech. 207, 531 (1989)] for the Lagrangian velocity structure function and Lagrangian acceleration autocorrelation function is excellent and significantly better than that obtained with a second-order Lagrangian stochastic model. The effects of third-order processes on the turbulent dispersion of fluid particles are found to be significant at Reynolds numbers typical of laboratory-scale experiments and direct numerical simulations and comparable in magnitude to the effects of second-order processes.