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Turbulent particle pair diffusion: Numerical simulations.

PloS one·2019
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Residual sweeping errors in turbulent particle pair diffusion in a Lagrangian diffusion model.

PloS one·2017
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Related Experiment Video

Updated: Feb 4, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Turbulent particle pair diffusion: A theory based on local and non-local diffusional processes.

Nadeem A Malik1

  • 1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhahran 31261, Saudi Arabia.

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|October 4, 2018
PubMed
Summary

Turbulent pair diffusion is not purely local. New research reveals both local and non-local processes govern diffusion, challenging prior assumptions and introducing new scaling laws for turbulent flows.

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Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Statistical Mechanics

Background:

  • Richardson's 1926 dataset on turbulent pair diffusion suggested a locality scaling law.
  • Previous theories assumed pair diffusion was primarily a local phenomenon within the inertial subrange.

Purpose of the Study:

  • To re-examine the foundations of turbulent pair diffusion theory.
  • To investigate the scaling laws governing pair diffusion coefficients.
  • To develop a new theoretical framework incorporating both local and non-local processes.

Main Methods:

  • Re-appraisal of Richardson's 1926 dataset.
  • Development of a new theory for turbulent pair diffusion.
  • Analysis within the context of generalized energy spectra E(k) ~ k^-p (1 < p <= 3).
  • Mathematical approach using Fourier integral decomposition.

Main Results:

  • Unequivocal evidence of non-local scaling for the pair diffusion coefficient, contradicting previous locality assumptions.
  • Identification of two non-Richardson regimes based on inertial subrange size: non-local scaling for asymptotically infinite subranges and local scaling for finite subranges.
  • Prediction of intermediate scaling exponents (gamma) between purely local and non-local limits.

Conclusions:

  • Turbulent pair diffusion is governed by a combination of local and non-local diffusional processes within the inertial subrange.
  • The size of the inertial subrange dictates whether local or non-local scaling laws dominate.
  • A novel mathematical framework provides a more comprehensive understanding of turbulent pair diffusion.