### Abstract

Turbulent cascades at high Reynolds numbers are explained briefly in terms of multipliers and multiplier distributions. Two properties of the multipliers ensure the existence of power laws for locally averaged energy dissipation rate: (a) the existence of a multiplier probability density function that is independent of the level of the cascade, and (b) the statistical independence of multipliers at one level on those at previous levels. Under certain conditions described in the paper, the same two properties of multipliers guarantee that velocity increments over inertial-range separation distances also possess power laws. This work is specifically motivated by the need to understand the influence on scaling of the experimental observations that property (a) is true for turbulence, but property (b) is not; and additional motivation is the need to relate cascade models to intermittent vortex stretching (and folding). This effect has been modeled by allowing the multiplier distribution to depend on the magnitude of the local strain rate, and it is demonstrated that this rate-dependent model accounts for the statistical dependence observed in experiments. It is also shown that this model is consistent with the uncorrelated cascade models except for very weak singularity strengths (or for negative moments below a certain order), leading to the conclusion that, for all practical purposes, the uncorrelated level-independent multipliers abstract the essence of the breakdown process in turbulence.

Original language | English (US) |
---|---|

Pages (from-to) | 311-333 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 78 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1995 |

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### Keywords

- cascades
- multiplier distributions
- multipliers
- multiscale interaction
- nonlinear interaction
- statistical physics of turbulence
- Turbulence
- turbulent energy transfer

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*78*(1-2), 311-333. https://doi.org/10.1007/BF02183351

**Turbulent cascades.** / Sreenivasan, K. R.; Stolovitzky, G.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 78, no. 1-2, pp. 311-333. https://doi.org/10.1007/BF02183351

}

TY - JOUR

T1 - Turbulent cascades

AU - Sreenivasan, K. R.

AU - Stolovitzky, G.

PY - 1995/1

Y1 - 1995/1

N2 - Turbulent cascades at high Reynolds numbers are explained briefly in terms of multipliers and multiplier distributions. Two properties of the multipliers ensure the existence of power laws for locally averaged energy dissipation rate: (a) the existence of a multiplier probability density function that is independent of the level of the cascade, and (b) the statistical independence of multipliers at one level on those at previous levels. Under certain conditions described in the paper, the same two properties of multipliers guarantee that velocity increments over inertial-range separation distances also possess power laws. This work is specifically motivated by the need to understand the influence on scaling of the experimental observations that property (a) is true for turbulence, but property (b) is not; and additional motivation is the need to relate cascade models to intermittent vortex stretching (and folding). This effect has been modeled by allowing the multiplier distribution to depend on the magnitude of the local strain rate, and it is demonstrated that this rate-dependent model accounts for the statistical dependence observed in experiments. It is also shown that this model is consistent with the uncorrelated cascade models except for very weak singularity strengths (or for negative moments below a certain order), leading to the conclusion that, for all practical purposes, the uncorrelated level-independent multipliers abstract the essence of the breakdown process in turbulence.

AB - Turbulent cascades at high Reynolds numbers are explained briefly in terms of multipliers and multiplier distributions. Two properties of the multipliers ensure the existence of power laws for locally averaged energy dissipation rate: (a) the existence of a multiplier probability density function that is independent of the level of the cascade, and (b) the statistical independence of multipliers at one level on those at previous levels. Under certain conditions described in the paper, the same two properties of multipliers guarantee that velocity increments over inertial-range separation distances also possess power laws. This work is specifically motivated by the need to understand the influence on scaling of the experimental observations that property (a) is true for turbulence, but property (b) is not; and additional motivation is the need to relate cascade models to intermittent vortex stretching (and folding). This effect has been modeled by allowing the multiplier distribution to depend on the magnitude of the local strain rate, and it is demonstrated that this rate-dependent model accounts for the statistical dependence observed in experiments. It is also shown that this model is consistent with the uncorrelated cascade models except for very weak singularity strengths (or for negative moments below a certain order), leading to the conclusion that, for all practical purposes, the uncorrelated level-independent multipliers abstract the essence of the breakdown process in turbulence.

KW - cascades

KW - multiplier distributions

KW - multipliers

KW - multiscale interaction

KW - nonlinear interaction

KW - statistical physics of turbulence

KW - Turbulence

KW - turbulent energy transfer

UR - http://www.scopus.com/inward/record.url?scp=21844481588&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844481588&partnerID=8YFLogxK

U2 - 10.1007/BF02183351

DO - 10.1007/BF02183351

M3 - Article

AN - SCOPUS:21844481588

VL - 78

SP - 311

EP - 333

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -