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 it’s derivatives $u^{(k)}={\mathrm{\partial }}_x^{k}u$, the general formula is found: $lnP(\mathrm{\mid }{u}^{(k)}\mathrm{\mid })\propto -(\mathrm{\mid }{u}^{(k)}\mathrm{\mid }\mathrm{/}(Re{)}^k{)}^{3\mathrm{/}(k+1)}$.