Dresden 2003 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 13: Fluid dynamics II
DY 13.4: Vortrag
Montag, 24. März 2003, 12:00–12:15, G\"OR/229
Lévy-flights in turbulent diffusion: Power law contributions in the statistics of particle dispersion and the influence of diffusive corrections — •Julia Dräger — Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden — I. Institut für theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg
Motivated by the original work of Richardson on the dispersion of a pair of passive scalars in atmospheric diffusion, we show by means of a stochastical model based on Lévy-distributions, how so-called ballistic contributions, due to Lévy-flight trajectories, lead to an additional power law factor, s−(β+1) with β=2/3 , in the distribution P(s|t) of pair separations s as well as to a pure power law regime, x−(β+1) with the same exponent β, in the distribution W(x|t) of single particle displacements. We demonstrate that for times t, where P(s|t) including its tails is entirely in the self-similar regime, the power law stretched exponential, P(s|t)∼ t s−(β+1) exp[− b sβ/t], which we propose for the pair dispersion process, is in very good agreement with recent experimental data, and, in contrast to a pure stretched exponential, yields a consistent constant C in Richardson-Obukhows law, ⟨s2(t)⟩=Cε t3. For larger times it is shown that diffusive corrections lead to a strong scaling violation in the experimental data. We derive empirically a new scaling relation for the transient regime which points at an anomalous slow deplition of the self similar regime in agreement with our model.