The one-point statistics of viscous Burgers turbulence initialized with Gaussian data

Reade Ryan, Marco Avellaneda

Research output: Contribution to journalArticlepeer-review

Abstract

We study the statistics of the viscous Burgers turbulence (BT) model, initialized at time t = 0 by a large class of Gaussian data. Using a first-principles analysis of the Hopf-Cole formula for the Burgers equation and the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) for the velocity u(x, t) and the velocity derivatives ∂nu(x,t)/∂xn,n = 1, 2, . . . . The PDF tails have a non-universal structure of the form log P(θ) ∝ -(Re)-ptqθr, where Re is the Reynolds number and p, q, and r depend on the order of differentiation and the infrared behavior of the initial energy spectrum.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalCommunications In Mathematical Physics
Volume200
Issue number1
DOIs
StatePublished - 1999

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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