title: Deviation-angle and trajectory statistics for inertial particles in turbulence.
abstract: Small particles in suspension in a turbulent fluid have trajectories that do not follow the pathlines of the flow exactly. We investigate the statistics of the angle of deviation ϕ between the particle and fluid velocities. We show that, when the effects of particle inertia are small, the probability distribution function (PDF) P_{ϕ} of this deviation angle shows a power-law region in which P_{ϕ}∼ϕ^{-4}. We also find that the PDFs of the trajectory curvature κ and modulus θ of the torsion ϑ have power-law tails that scale, respectively, as P_{κ}∼κ^{-5/2}, as κ→∞, and P_{θ}∼θ^{-3}, as θ→∞: These exponents are in agreement with those previously observed for fluid pathlines. We propose a way to measure the complexity of heavy-particle trajectories by the number N_{I}(t,St) of points (up until time t) at which the torsion changes sign. We present numerical evidence that n_{I}(St)≡lim_{t→∞}N_{I}(t,St)/t∼St^{-Δ} for large St, with Δ≃0.5.
authors.affiliation: Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.|Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden.
authors.forename: Akshay
authors.initials: A
authors.lastname: Bhatnagar
authors.affiliation: Laboratoire de Génie Chimique, FERMAT, Université de Toulouse, INPT-UPS, 31030, Toulouse, France.
authors.forename: Anupam
authors.initials: A
authors.lastname: Gupta
authors.affiliation: Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden.
authors.forename: Dhrubaditya
authors.initials: D
authors.lastname: Mitra
authors.affiliation: TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India.
authors.forename: Prasad
authors.initials: P
authors.lastname: Perlekar
authors.affiliation: Department of Mathematics and Statistics, The Open University, Milton Keynes MK6 7AA, United Kingdom.
authors.forename: Michael
authors.initials: M
authors.lastname: Wilkinson
authors.affiliation: Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
authors.forename: Rahul
authors.initials: R
authors.lastname: Pandit