Large negative velocity gradients in Burgers turbulence
Chaotic Dynamics
2013-10-01 v3 Statistical Mechanics
Fluid Dynamics
Abstract
We consider 1D 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 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 [Phys. Rev. Lett. 78 (8) 1452 (1997) [chao-dyn/9609005]] based on short-time estimations that the left tail of PDF has the form ln P(u_x) \propto -|u_x|^(3/2).
Keywords
Cite
@article{arxiv.nlin/0001023,
title = {Large negative velocity gradients in Burgers turbulence},
author = {A. I. Chernykh and M. G. Stepanov},
journal= {arXiv preprint arXiv:nlin/0001023},
year = {2013}
}
Comments
10 pages, RevTeX, 10 figures