This MPhil thesis explores two themes associated with the dynamics of inertial particles in turbulent fluids. Firstly, we consider an optimal partial covering of fractal sets in a two-dimensional space using ellipses which become increasingly anisotropic as their size is reduced. If the semi-minor axis is ϵ and the semi-major axis is δ, we set δ = ϵα, where 0 s and the angular velocity ω about the vorticity axis. We find that when τsω >> 1, the rods are predominantly either perpendicular or parallel to the vorticity. We also review the current literature on the dynamics of inertial particles in turbulent flows
