Diffusion of Fluid Particles by the Combined Model of Random Fourier Modes and Random Flight

Abstract

To investigate the motion of fluid particles around a cylinder in turbulent flows, we developed a new model for simulating the trajectory of particles : the combined model of kinematic simulation (KS) and random flight (RF). The large-scale turbulence is simulated by a sum of random Fourier modes varying in space and time, and the small-scale turbulent fluctuation is simply modelled by an ITO type of stochastic differential equation with a memory time comparable to the Lagrangian integral time scale T^L_S of small-scale motion. The Lagrangian properties of fluid particles in homogeneous isotropic turbulence with uniform mean flow have been examined. Some new results have been obtained using this new model : (a) the cross-correlation of the displacements due to the large- and small-scale motions is negligibly small ; (b) random small-scale motion causes decorrelation of the large-scale velocity ; (c) the value of T^L_S used in RF can be reasonably estimated from pure KS.