Time evolution of a fractal distribution: Particle concentrations in free-surface turbulence

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 structure, a rare manifestation of a strange attractor observable in real space. The surface pattern reaches a steady state in approximately 1 s. Measurements are made of the fractal dimensions D q ( t ) ( q = 1 to 6) of the floating particles starting with the uniform distribution D q ( 0 ) = 2 for Taylor Microscale Reynolds number R e λ ≃ 160 . Focus is on the time evolution of the correlation dimension D 2 ( t ) as the steady state is approached. This steady state is reached in several large eddy turnover times and does so at an exponential rate.