### Abstract

A modification of Kraichnan's direct interaction approximation (DIA) [R. H. Kraichnan, J. Math. Phys. 2, 124 (1961)] for random linear partial differential equations is proposed. The approximation is tested on the specific example of the turbulent advection of a scalar quantity by a random velocity field. It is shown to account for the sweeping more correctly than the DIA. As a result, it is valid for all times and it is able to describe nonstandard diffusive processes (i.e., superdiffusive and non-Gaussian) for which the DIA is not valid.

Original language | English (US) |
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Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 58 |

Issue number | 5 SUPPL. A |

State | Published - 1998 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

**Studying random differential equations as a tool for turbulent diffusion.** / Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Studying random differential equations as a tool for turbulent diffusion

AU - Vanden Eijnden, Eric

PY - 1998

Y1 - 1998

N2 - A modification of Kraichnan's direct interaction approximation (DIA) [R. H. Kraichnan, J. Math. Phys. 2, 124 (1961)] for random linear partial differential equations is proposed. The approximation is tested on the specific example of the turbulent advection of a scalar quantity by a random velocity field. It is shown to account for the sweeping more correctly than the DIA. As a result, it is valid for all times and it is able to describe nonstandard diffusive processes (i.e., superdiffusive and non-Gaussian) for which the DIA is not valid.

AB - A modification of Kraichnan's direct interaction approximation (DIA) [R. H. Kraichnan, J. Math. Phys. 2, 124 (1961)] for random linear partial differential equations is proposed. The approximation is tested on the specific example of the turbulent advection of a scalar quantity by a random velocity field. It is shown to account for the sweeping more correctly than the DIA. As a result, it is valid for all times and it is able to describe nonstandard diffusive processes (i.e., superdiffusive and non-Gaussian) for which the DIA is not valid.

UR - http://www.scopus.com/inward/record.url?scp=0347334644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347334644&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347334644

VL - 58

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 5 SUPPL. A

ER -