Large negative velocity gradients in Burgers turbulence.

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