Studying random differential equations as a tool for turbulent diffusion

Research output: Contribution to journalArticle

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 languageEnglish (US)
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume58
Issue number5 SUPPL. A
StatePublished - 1998

Fingerprint

Random Differential Equation
Turbulent Diffusion
turbulent diffusion
differential equations
Approximation
approximation
Interaction
Valid
Sweeping
Linear partial differential equation
interactions
Advection
advection
partial differential equations
Random Field
Velocity Field
velocity distribution
Scalar
scalars

ASJC Scopus subject areas

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

Cite this

@article{a1d476cbe6254fabb1b4c9947f8f0f9a,
title = "Studying random differential equations as a tool for turbulent diffusion",
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.",
author = "{Vanden Eijnden}, Eric",
year = "1998",
language = "English (US)",
volume = "58",
journal = "Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "5 SUPPL. A",

}

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 -