Scale dependence of multiplier distributions for particle concentration, enstrophy, and dissipation in the inertial range of homogeneous turbulence

Thomas Hartlep, Jeffrey N. Cuzzi, and Brian Weston
Phys. Rev. E 95, 033115 – Published 27 March 2017

Abstract

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

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  • Received 12 December 2016

DOI:https://doi.org/10.1103/PhysRevE.95.033115

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Thomas Hartlep*

  • Bay Area Environmental Research Institute, Petaluma, California 94952, USA

Jeffrey N. Cuzzi

  • NASA Ames Research Center, Moffett Field, California 94035, USA

Brian Weston

  • University of California Davis, Mechanical & Aerospace Engineering, Davis, California 95616, USA

  • *Also, NASA Ames Research Center, Moffett Field, CA 94035, USA; thomas.hartlep@nasa.gov

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Issue

Vol. 95, Iss. 3 — March 2017

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