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

Reade Ryan, Marco Avellaneda

Research output: Contribution to journalArticle

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
StatePublished - 1999

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probability distribution functions
Probability Distribution Function
Turbulence
Tail
turbulence
statistics
Statistics
Burger equation
turbulence models
Turbulence Model
First-principles
Energy Spectrum
Burgers Equation
Gaussian Process
Large Deviations
Reynolds number
energy spectra
Infrared
deviation
Derivative

ASJC Scopus subject areas

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

Cite this

The one-point statistics of viscous Burgers turbulence initialized with Gaussian data. / Ryan, Reade; Avellaneda, Marco.

In: Communications in Mathematical Physics, Vol. 200, No. 1, 1999, p. 1-23.

Research output: Contribution to journalArticle

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