Intermittency of Burgers' Turbulence

Abstract

We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For the PDFs of velocity and it's derivatives $u^{(k)}={\partial }_x^{k}u$, the general formula is found: $lnP(|u^{(k)}|)\propto -(|u^{(k)}|/(Re{)}^k{)}^{3/(k+1)}$.

4 pages, RevTeX 3.0, short version of chao-dyn/9603015, submitted to Phys. Rev. Lett

References in corpus (2)

• Instantons in Burgers Equation
• Instantons and Intermittency

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