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(2016) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 94 (6), art. no. 063112, .

Deviation-angle and trajectory statistics for inertial particles in turbulence

Bhatnagar, A., Gupta, A., Mitra, D., Perlekar, P., Wilkinson, M., Pandit, R.

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) Pφ of this deviation angle shows a power-law region in which Pφ∼φ-4. We also find that the PDFs of the trajectory curvature κ and modulus θ of the torsion have power-law tails that scale, respectively, as Pκ∼κ-5/2, as κ→∞, and Pθ∼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 NI(t,St) of points (up until time t) at which the torsion changes sign. We present numerical evidence that nI(St)≡limt→∞NI(t,St)t∼St-Δ for large St, with Δ≃0.5. © 2016 American Physical Society.