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Session: Lagrangian aspects of turbulence 1
Session starts: Wednesday 26 August, 10:30
Presentation starts: 11:45
Room: Room F

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Akshay Bhatnagar (Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.)
Anupam Gupta (University of Rome ``Tor Vergata'', Rome, Italy.)
Dhrubaditya Mitra (NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.)
Prasad Perlekar (TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India.)
Rahul Pandit (Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.)

Abstract:
We obtain new universal statistical properties of heavy-particle trajectories in three-dimensional, statistically steady, homogeneous, and isotropic turbulent flows by direct numerical simulations. We show that the probability distribution functions (PDFs) $P(\phi)$, of the angle $\phi$ between the Eulerian velocity ${\bf u}$ and the particle velocity ${\bf v}$, at a point and time, scales as $P(\phi) \sim \phi^{-\gamma}$, with a new universal exponent $\gamma \simeq 4$. The PDFs of the trajectory curvature $\kappa$ and modulus $\theta$ of the torsion $\vartheta$ scale, respectively, as $P(\kappa) \sim \kappa^{-h_\kappa}$, as $\kappa \to \infty$, and $P(\theta) \sim \theta^{-h_\theta}$, as $\theta \to \infty$, with exponents $h_\kappa \simeq 2.5$ and $h_\theta \simeq 3$ that do not depend on the Stokes number $St$. We also show that $\gamma$, $h_\kappa$ and $h_\theta$ can be obtained by using simple stochastic models. We show that the number $N_I(t,St)$ of points (up until time $t$), at which $\vartheta$ changes sign, is such that $n_I(St) \equiv \lim_{t\to\infty} \frac{N_I(t,St)}{t} \sim St^{-\Delta}$, with $\Delta \simeq 0.4$ a universal exponent.