Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly

Akshay Bhatnagar, Anupam Gupta, Dhrubaditya Mitra, and Rahul Pandit
Phys. Rev. E 97, 033102 – Published 2 March 2018
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Abstract

We present an extensive numerical study of the time irreversibility of the dynamics of heavy inertial particles in three-dimensional, statistically homogeneous, and isotropic turbulent flows. We show that the probability density function (PDF) of the increment, W(τ), of a particle's energy over a time scale τ is non-Gaussian, and skewed toward negative values. This implies that, on average, particles gain energy over a period of time that is longer than the duration over which they lose energy. We call this slow gain and fast loss. We find that the third moment of W(τ) scales as τ3 for small values of τ. We show that the PDF of power-input p is negatively skewed too; we use this skewness Ir as a measure of the time irreversibility and we demonstrate that it increases sharply with the Stokes number St for small St; this increase slows down at St1. Furthermore, we obtain the PDFs of t+ and t, the times over which p has, respectively, positive or negative signs, i.e., the particle gains or loses energy. We obtain from these PDFs a direct and natural quantification of the slow gain and fast loss of the energy of the particles, because these PDFs possess exponential tails from which we infer the characteristic loss and gain times tloss and tgain, respectively, and we obtain tloss<tgain for all the cases we have considered. Finally, we show that the fast loss of energy occurs with greater probability in the strain-dominated region than in the vortical one; in contrast, the slow gain in the energy of the particles is equally likely in vortical or strain-dominated regions of the flow.

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  • Received 21 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.033102

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Akshay Bhatnagar1,2,*, Anupam Gupta3,†, Dhrubaditya Mitra2,‡, and Rahul Pandit1,§

  • 1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
  • 2Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
  • 3Mechanical Science and Engineering, University of Illinois, 1206 West Green Street, Urbana, Illinois 61801, USA

  • *akshayphy@gmail.com
  • anupam1509@gmail.com
  • dhruba.mitra@gmail.com
  • §rahul@iisc.ac.in

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Issue

Vol. 97, Iss. 3 — March 2018

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