MODELING OF THE DIFFUSION OF FLUID PARTICLES IN TURBULENT FLOWS APPROACHING A CIRCULAR-CYLINDER BY RANDOM FOURIER MODES AND RANDOM FLIGHT

To investigate the diffusion of fluid particles around a cylinder in a turbulent flow, we have developed two new types of model for simulati ng the trajectory of particles:(1) a model combining random Fourier mo des and random flight (RF); (2) a pure kinematic simulation (KS) by ra ndom Fourier modes. In model 1 the large-scale turbulence is simulated by a sum of random Fourier modes varying in space and time, and the s mall-scale random motion of particles is simply modelled by an Ito typ e of stochastic differential equation with a memory time comparable to the Lagrangian time scale T(s)L of the small-scale motion. In model 2 , both large- and small-scale turbulence is simulated using random Fou rier modes. The change of turbulence around the cylinder is modelled b y rapid distortion theory (RDT), although the small-scale motion of pa rticles in the RF model is simply assumed to keep the homogeneous rand om behaviour. These models give very similar and realistic trajectorie s showing rapid changes of direction due to the small-scale motion.