Sticky particles in compressible flows: aggregation and Richardson's law

The evolution of the distance r(t) between a pair of passive tracer particles in rough compressible velocity fields is studied. The scaling behavior depends on the stickiness of the particles. Sticky particles start aggregating in moderately compressible flows, which can be realized on the free-slip surface of a turbulent fluid; nonsticky particles can aggregate only in less common strongly compressible flows (even then, the aggregation rate remains lower). Aggregation gives rise to an anomalous scaling law for the mean-square-distance growth rate, slower than Richardson's law. These findings help understand the results of recent experiments.