Time-Evolution of a Fractal Distribution: Particle Concentrations in Free-Surface Turbulence
arXiv:1010.5463 · doi:10.1016/j.physd.2009.11.005
Abstract
Steady-state turbulence is generated in a tank of water and the trajectories of particles forming a compressible system on the surface are tracked in time. The initial uniformly distributed floating particles coagulate and form a fractal distribution, a rare manifestation of a fractal object observable in real-space. The surface pattern reaches a steady state in approximately 1 s. Measurements are made of the fractal dimensions ( to ) of the floating particles starting with the uniform distribution = 2 for Taylor Microscale Reynolds number . Focus is on the the time-evolution of the correlation dimension as the steady state is approached. This steady state is reached in several large eddy turnover times and does so at an exponential rate.