### Abstract

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. (Formula presented) 1452 (1997)] based on short-time estimations that the left tail of PDF has the form (Formula presented)

Original language | English (US) |
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Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 64 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics