Turbulent cascades

K. R. Sreenivasan, G. Stolovitzky

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)311-333
Number of pages23
JournalJournal of Statistical Physics
Volume78
Issue number1-2
DOIs
StatePublished - Jan 1995

Fingerprint

multipliers
Cascade
Multiplier
cascades
Turbulence
Power Law
turbulence
Weak Singularity
Statistical Independence
high Reynolds number
Energy Dissipation
Strain Rate
Folding
probability density functions
Model
Probability density function
folding
Increment
strain rate
Breakdown

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

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

In: Journal of Statistical Physics, Vol. 78, No. 1-2, 01.1995, p. 311-333.

Research output: Contribution to journalArticle

Sreenivasan, K. R. ; Stolovitzky, G. / Turbulent cascades. In: Journal of Statistical Physics. 1995 ; Vol. 78, No. 1-2. pp. 311-333.
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