Simulation of turbulent dispersion using Weierstrass modes

A simple fractal model is proposed for the dispersion of passive scalars in an incompressible homogeneous turbulent flow field. The dispersion process is based on a three-dimensional velocity field which is assumed to be a linear superposition of Taylor-Green vortices with wave numbers and amplitudes as those in a Weierstrass function. The chosen velocity field satisfies the continuity equation as well as Kolmogorov's inertial range power law, and has a fractal dimension D between upper and lower length-scale bounds. A cloud of tracer particles is relased into the flow field and dispersed by the fluid motion, the trajectories are numerically integrated from the velocity field. The puffs which result from this process are used to examine some aspects of turbulent dispersion, through comparisons with integrated concentration wind-tunnel measurements. The agreement between numerical and experimental results indicates the significance of the proposed simulation model.