Relevance of instantons in Burgers turbulence

T. Grafke, R. Grauer, T. Schäfer, Eric Vanden Eijnden

Research output: Contribution to journalArticle

Abstract

Instanton calculations are performed in the context of stationary Burgers turbulence to estimate the tails of the probability density function (PDF) of velocity gradients. These results are then compared to those obtained from massive direct numerical simulations (DNS) of the randomly forced Burgers equation. The instanton predictions are shown to agree with the DNS in a wide range of regimes, including those that are far from the limiting cases previously considered in the literature. These results settle the controversy of the relevance of the instanton approach for the prediction of the velocity gradient PDF tail exponents. They also demonstrate the usefulness of the instanton formalism in Burgers turbulence, and suggest that this approach may be applicable in other contexts, such as 2D and 3D turbulence in compressible and incompressible flows.

Original languageEnglish (US)
Article number34003
JournalEPL
Volume109
Issue number3
DOIs
StatePublished - Feb 1 2015

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instantons
turbulence
probability density functions
direct numerical simulation
gradients
compressible flow
Burger equation
incompressible flow
predictions
exponents
formalism
estimates

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Relevance of instantons in Burgers turbulence. / Grafke, T.; Grauer, R.; Schäfer, T.; Vanden Eijnden, Eric.

In: EPL, Vol. 109, No. 3, 34003, 01.02.2015.

Research output: Contribution to journalArticle

Grafke, T. ; Grauer, R. ; Schäfer, T. ; Vanden Eijnden, Eric. / Relevance of instantons in Burgers turbulence. In: EPL. 2015 ; Vol. 109, No. 3.
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