### 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 s_{n} in the scaling relations (∂u/∂x)^{n} / √(∂u/∂x)^{2n/2} ∝ Re^{sn}, between the velocity gradients ∂u/∂x and the Reynolds number Re, agrees well with experimental data.

Original language | English (US) |
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Pages (from-to) | 147-155 |

Number of pages | 9 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 343 |

Issue number | 1-4 |

DOIs | |

State | Published - Nov 15 2004 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 343, no. 1-4, pp. 147-155. https://doi.org/10.1016/j.physa.2004.07.037

}

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 -