2006 Multifractal clustering of passive tracers on a surface flow

PACS. 47.27.Gs – Isotropic turbulence; homogeneous turbulence. PACS. 47.52.+j – Chaos in fluid dynamics. Abstract. – We study the anomalous scaling of the mass density measure of Lagrangian tracers in a compressible flow realized on the free surface on top of a three-dimensional flow. The full two-dimensional probability distribution of local stretching rates is measured. The intermittency exponents which quantify the fluctuations of the mass measure of tracers at small scales are calculated from the large deviation form of stretching-rate fluctuations. The results indicate the existence of a critical exponent nc 0.86 above which exponents saturate, in agreement with what has been predicted by an analytically solvable model. Direct evaluation of the multi-fractal dimensions by reconstructing the coarse-grained particle density supports the results for low-order moments. Advection of homogeneous distribution of passive particles in a compressible flow gener-ically results in clusters of particles ’ concentration [1–3]. The effects of compressibility in three-dimensional flows are typically relevant only at Mach numbers near or larger than 1 when density inhomogeneity reacts back on the fluid velocity. However, there are simpl