PDFs for velocity and velocity gradients in Burgers' turbulence

M. 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
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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