PDFs for velocity and velocity gradients in Burgers' turbulence

Marco Avellaneda, R. Ryan, E. Weinan

Research output: Contribution to journalArticle

Abstract

We characterize the tails of the probability distribution functions for the solution of Burgers' equation with Gaussian initial data and its derivatives ∂kv(x,t)/∂xk, k=0,1,2,... . The tails are "stretched exponentials" of the form P(θ)∝exp[-(Re)- ptqθr], where Re is the Reynolds number. The exponents p, q, and r depend on the initial spectrum as well as on the order of differentiation, k. These exact results are compared with those obtained using the mapping closure technique.

Original languageEnglish (US)
Pages (from-to)3067-3071
Number of pages5
JournalPhysics of Fluids
Volume7
Issue number12
StatePublished - 1995

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Burger equation
probability distribution functions
Probability distributions
closures
Distribution functions
Reynolds number
Turbulence
turbulence
exponents
Derivatives
gradients

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

PDFs for velocity and velocity gradients in Burgers' turbulence. / Avellaneda, Marco; Ryan, R.; Weinan, E.

In: Physics of Fluids, Vol. 7, No. 12, 1995, p. 3067-3071.

Research output: Contribution to journalArticle

Avellaneda, M, Ryan, R & Weinan, E 1995, 'PDFs for velocity and velocity gradients in Burgers' turbulence', Physics of Fluids, vol. 7, no. 12, pp. 3067-3071.
Avellaneda, Marco ; Ryan, R. ; Weinan, E. / PDFs for velocity and velocity gradients in Burgers' turbulence. In: Physics of Fluids. 1995 ; Vol. 7, No. 12. pp. 3067-3071.
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