Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles

Akshay Bhatnagar, K. Gustavsson, and Dhrubaditya Mitra
Phys. Rev. E 97, 023105 – Published 15 February 2018

Abstract

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component VR for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D2. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011); J. Turbul. 15, 34 (2014)] that the scale invariant part of the distribution has two asymptotic regimes: (1) |VR|R, where the distribution depends solely on R, and (2) |VR|R, where the distribution is a function of |VR| alone. The probability distributions in these two regimes are matched along a straight line: |VR|=z*R. Our simulations confirm that this is indeed correct. We further obtain D2 and z* as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St0.7 and the latter has only a weak dependence on St.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 16 October 2017

DOI:https://doi.org/10.1103/PhysRevE.97.023105

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Akshay Bhatnagar1,*, K. Gustavsson2,†, and Dhrubaditya Mitra1,‡

  • 1Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
  • 2Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden

  • *akshayphy@gmail.com
  • kristian.gustafsson@physics.gu.se
  • dhruba.mitra@gmail.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 97, Iss. 2 — February 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×