Diffusion and geometric effects in passive advection by random arrays of vortices

Marco Avellaneda, S. Torquato, I. C. Kim

Research output: Contribution to journalArticle

Abstract

The Lagrangian transport of a passive scalar in a class of incompressible, random stationary velocity fields, termed "random-vortex" models, is studied. These fields generally consist of random distributions of finite-sized elementary vortices in space with zero mean velocity in the presence of molecular diffusion D. The effects of vortex density, vortex strength, and sign of the vorticity on the Lagrangian history of a fluid particle [i.e., mean-square displacement σ 2(t) and velocity autocorrelation function script R(t)] on the specific random-vortex models which possess identical energy spectra but different higher-order statistics for a Péclet number of 100 are investigated. This is done by a combination of Monte Carlo simulations of the Langevin equations and analysis. It is found that the Lagrangian autocorrelation script R(t) and the mean-square displacement σ 2(t) can be significantly different as the density of the vortices increases and when there are long-range correlations in the sign of the vorticity. A simple theory based on a model for script R(t) agrees strikingly well with the present simulations. It is found that D* increases with vortex density, suggesting that Gaussian fields are maximally dissipative among a wide class of vortex flows with given energy spectra.

Original languageEnglish (US)
Pages (from-to)1880-1891
Number of pages12
JournalPhysics of Fluids A
Volume3
Issue number8
StatePublished - 1991

Fingerprint

Advection
advection
Vortex flow
vortices
Vorticity
Autocorrelation
vorticity
autocorrelation
energy spectra
Higher order statistics
molecular diffusion
statistical distributions
simulation
velocity distribution
statistics
histories
scalars
Fluids
fluids

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Physics and Astronomy(all)
  • Mechanics of Materials
  • Computational Mechanics
  • Fluid Flow and Transfer Processes

Cite this

Diffusion and geometric effects in passive advection by random arrays of vortices. / Avellaneda, Marco; Torquato, S.; Kim, I. C.

In: Physics of Fluids A, Vol. 3, No. 8, 1991, p. 1880-1891.

Research output: Contribution to journalArticle

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