Intermittency of Burgers' Turbulence

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 its derivatives u^\(k\) = ∂^k_xu, the general formula is found: lnP\(\|u^\(k\)\|\)~-\(\|u^\(k\)\|/Re^k\)^3/\(k+1\).