Asymptotic theory for the probability density functions in burgers turbulence

Research output: Contribution to journalArticle

Abstract

A systematic analysis is carried out for the randomly forced Burgers equation in the infinite Reynolds number (inviscid) limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of quantities defined along the shocks. This method allows one to compute the dissipative anomalies, as well as asymptotics for the structure functions and the probability density functions. It is shown that the left tail for the probability density function of the velocity gradient has to decay faster than |ξ|-3. A further argument confirms the prediction of E et al. [Phys. Rev. Lett. 78, 1904 (1997)] that it should decay as |ξ|-7/2.

Original languageEnglish (US)
Pages (from-to)2572-2575
Number of pages4
JournalPhysical Review Letters
Volume83
Issue number13
StatePublished - Sep 27 1999

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probability density functions
turbulence
gradients
Burger equation
decay
closures
Reynolds number
shock
statistics
anomalies
predictions
approximation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Asymptotic theory for the probability density functions in burgers turbulence. / Weinan, E.; Vanden Eijnden, Eric.

In: Physical Review Letters, Vol. 83, No. 13, 27.09.1999, p. 2572-2575.

Research output: Contribution to journalArticle

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