Large negative velocity gradients in Burgers turbulence - art. no. 026306

We consider one-dimensional Burgers equation driven by large-scale white-in -time random force. The tails of the velocity gradients probability distrib ution function (PDF) are analyzed by saddle point approximation in the path integral describing the velocity statistics. The structure of the saddle-p oint (instanton), that is, the velocity field configuration realizing the m aximum of probability, is studied numerically in details. The numerical res ults allow us to find analytical solution for the long-time part of the ins tanton. Its careful analysis confirms the result of Balkovsky et at. [Phys. Rev. Lett. 78, 1452 (1997)] based on short-time estimations that the left tail of PDF has the form ln P(u(x)) proportional to - \u(x)\(3/2).