Structure functions in the stochastic Burgers equation

F. Hayot, C. Jayaprakash

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We study analytically and numerically structure functions Sq(r) in the one-dimensional Burgers equation, driven by noise with variance ∞|k|β in Fourier space, (a) when the noise is cut off at some length l and (b) when it is not. We present exact relations satisfied by S3(r) (the von Karman-Howarth relation) and S4(r) that form the basis of our analysis. When there is a cutoff length, shocks occur and Sq(r) ∞r for q≥2 for δ<r <lc where δ is the shock thickness for all β between -1 and 2. We deduce this behavior from the exact relations along with an ansatz that is verified numerically. When there is no cutoff length, multifractal behavior is known to occur only when β<0. Through a study of exact expression S3 we highlight the difference between ltifractality in this case as compared to the case with a cutoff.

Original languageEnglish
Pages (from-to)227-234
Number of pages8
JournalPhysical Review E
Issue number1 SUPPL. A
StatePublished - 1997
Externally publishedYes


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