Europhys. Lett.
Volume 74, Number 1, April 2006
Page(s) 62 - 68
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 22 February 2006
Europhys. Lett., 74 (1), pp. 62-68 (2006)
DOI: 10.1209/epl/i2005-10503-6

Multifractal clustering of passive tracers on a surface flow

G. Boffetta1, 2, J. Davoudi3 and F. De Lillo4

1  Dipartimento di Fisica Generale and INFN, Università degli Studi di Torino Via Pietro Giuria 1, 10125 Torino, Italy
2  ISAC-CNR, Sezione di Torino - Italy
3  Fachbereich Physik, Philipps-Universität - Renthof 6, D-35032 Marburg, Germany
4  INLN-CNRS - 1361 route des Lucioles, Sophia Antipolis, 06560 Valbonne, France

received 24 October 2005; accepted in final form 6 February 2006
published online 22 February 2006

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 $n_c \simeq 0.86$ 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.

47.27.Gs - Isotropic turbulence; homogeneous turbulence.
47.52.+j - Chaos in fluid dynamics.

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