Intermittency of Burgers' Turbulence

Details Intermittency of Burgers' Turbulence Intermittency of Burgers' Turbulence

1996-09-10

arxiv.org/abs/chao-dyn/9609005v1

Phys. Rev. Lett, 78, 1452, (1997)

Physics

Condensed Matter

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

Scientific paper

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 $u^{(k)} = \partial_x^ku$, the general formula is found: $ln P (|u^{(k)}|) \propto -(|u^{(k)}|/(Re)^k)^{3/(k+1)}$.

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