### 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 language | English (US) |
---|---|

Pages (from-to) | 1880-1891 |

Number of pages | 12 |

Journal | Physics of Fluids A |

Volume | 3 |

Issue number | 8 |

State | Published - 1991 |

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### ASJC Scopus subject areas

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

### Cite this

*Physics of Fluids A*,

*3*(8), 1880-1891.

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

Research output: Contribution to journal › Article

*Physics of Fluids A*, vol. 3, no. 8, pp. 1880-1891.

}

TY - JOUR

T1 - Diffusion and geometric effects in passive advection by random arrays of vortices

AU - Avellaneda, Marco

AU - Torquato, S.

AU - Kim, I. C.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0347251727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347251727&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347251727

VL - 3

SP - 1880

EP - 1891

JO - Physics of fluids. A, Fluid dynamics

JF - Physics of fluids. A, Fluid dynamics

SN - 0899-8213

IS - 8

ER -