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 Dq(t)Dq(t) (q=1q=1 to 6) of the floating particles starting with the uniform distribution Dq(0)=2Dq(0)=2 for Taylor Microscale Reynolds number Reλ≃160Reλ≃160. Focus is on the time evolution of the correlation dimension D2(t)D2(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.