Towards a dynamical theory of multifractals in turbulence

Victor Yakhot, K. R. Sreenivasan

Research output: Contribution to journalArticle

Abstract

Making use of the exact equations for structure functions, supplemented by the equations for dissipative anomaly as well as an estimate for the Lagrangian acceleration of fluid particles, we obtain a main result of the multifractal theory of turbulence. The central element of the theory is a dissipation cut-off that depends on the order of the structure function. An expression obtained for the exponents sn in the scaling relations (∂u/∂x)n / √(∂u/∂x)2n/2 ∝ Resn, between the velocity gradients ∂u/∂x and the Reynolds number Re, agrees well with experimental data.

Original languageEnglish (US)
Pages (from-to)147-155
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Volume343
Issue number1-4
DOIs
StatePublished - Nov 15 2004

Fingerprint

Structure-function
Turbulence
turbulence
Central Element
Scaling Relations
Anomaly
Reynolds number
Dissipation
cut-off
dissipation
Exponent
Experimental Data
exponents
anomalies
Gradient
scaling
Fluid
gradients
fluids
estimates

Keywords

  • Dynamical systems
  • Turbulence

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Towards a dynamical theory of multifractals in turbulence. / Yakhot, Victor; Sreenivasan, K. R.

In: Physica A: Statistical Mechanics and its Applications, Vol. 343, No. 1-4, 15.11.2004, p. 147-155.

Research output: Contribution to journalArticle

@article{af6e82cba0f04861a9e3ee20b80c8ca7,
title = "Towards a dynamical theory of multifractals in turbulence",
abstract = "Making use of the exact equations for structure functions, supplemented by the equations for dissipative anomaly as well as an estimate for the Lagrangian acceleration of fluid particles, we obtain a main result of the multifractal theory of turbulence. The central element of the theory is a dissipation cut-off that depends on the order of the structure function. An expression obtained for the exponents sn in the scaling relations (∂u/∂x)n / √(∂u/∂x)2n/2 ∝ Resn, between the velocity gradients ∂u/∂x and the Reynolds number Re, agrees well with experimental data.",
keywords = "Dynamical systems, Turbulence",
author = "Victor Yakhot and Sreenivasan, {K. R.}",
year = "2004",
month = "11",
day = "15",
doi = "10.1016/j.physa.2004.07.037",
language = "English (US)",
volume = "343",
pages = "147--155",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "1-4",

}

TY - JOUR

T1 - Towards a dynamical theory of multifractals in turbulence

AU - Yakhot, Victor

AU - Sreenivasan, K. R.

PY - 2004/11/15

Y1 - 2004/11/15

N2 - Making use of the exact equations for structure functions, supplemented by the equations for dissipative anomaly as well as an estimate for the Lagrangian acceleration of fluid particles, we obtain a main result of the multifractal theory of turbulence. The central element of the theory is a dissipation cut-off that depends on the order of the structure function. An expression obtained for the exponents sn in the scaling relations (∂u/∂x)n / √(∂u/∂x)2n/2 ∝ Resn, between the velocity gradients ∂u/∂x and the Reynolds number Re, agrees well with experimental data.

AB - Making use of the exact equations for structure functions, supplemented by the equations for dissipative anomaly as well as an estimate for the Lagrangian acceleration of fluid particles, we obtain a main result of the multifractal theory of turbulence. The central element of the theory is a dissipation cut-off that depends on the order of the structure function. An expression obtained for the exponents sn in the scaling relations (∂u/∂x)n / √(∂u/∂x)2n/2 ∝ Resn, between the velocity gradients ∂u/∂x and the Reynolds number Re, agrees well with experimental data.

KW - Dynamical systems

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=4544370772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544370772&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2004.07.037

DO - 10.1016/j.physa.2004.07.037

M3 - Article

VL - 343

SP - 147

EP - 155

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-4

ER -