### Abstract

We characterize the tails of the probability distribution functions for the solution of Burgers' equation with Gaussian initial data and its derivatives ∂^{k}v(x,t)/∂x^{k}, k=0,1,2,... . The tails are "stretched exponentials" of the form P(θ)∝exp[-(Re)- ^{p}t^{q}θ^{r}], where Re is the Reynolds number. The exponents p, q, and r depend on the initial spectrum as well as on the order of differentiation, k. These exact results are compared with those obtained using the mapping closure technique.

Original language | English (US) |
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Pages (from-to) | 3067-3071 |

Number of pages | 5 |

Journal | Physics of Fluids |

Volume | 7 |

Issue number | 12 |

DOIs | |

State | Published - 1995 |

### ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes

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## Cite this

Avellaneda, M., Ryan, R., & Weinan, E. (1995). PDFs for velocity and velocity gradients in Burgers' turbulence.

*Physics of Fluids*,*7*(12), 3067-3071. https://doi.org/10.1063/1.868683