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