Power-law distributions of particle concentration in free-surface flows

Particles floating on the surface of a turbulent incompressible fluid accumulate along string-like structures, while leaving large regions of the flow domain empty. This is reflected experimentally by a very peaked probability distribution function of c(r), the coarse-grained particle concentration at scale r, around c(r)=0, with a power-law decay over two decades of c(r), Pi(c(r)) proportional, variant c(r)(-beta(r)). The positive exponent beta(r) decreases with scale in the inertial range and stays approximately constant in the dissipative range, thus, indicating a qualitative difference between the dissipative and the inertial ranges of scales, also visible in the first moment of c(r).