### 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) |
---|---|

Pages (from-to) | 3067-3071 |

Number of pages | 5 |

Journal | Physics of Fluids |

Volume | 7 |

Issue number | 12 |

State | Published - 1995 |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*7*(12), 3067-3071.

**PDFs for velocity and velocity gradients in Burgers' turbulence.** / Avellaneda, Marco; Ryan, R.; Weinan, E.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 7, no. 12, pp. 3067-3071.

}

TY - JOUR

T1 - PDFs for velocity and velocity gradients in Burgers' turbulence

AU - Avellaneda, Marco

AU - Ryan, R.

AU - Weinan, E.

PY - 1995

Y1 - 1995

N2 - We characterize the tails of the probability distribution functions for the solution of Burgers' equation with Gaussian initial data and its derivatives ∂kv(x,t)/∂xk, k=0,1,2,... . The tails are "stretched exponentials" of the form P(θ)∝exp[-(Re)- ptqθr], 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.

AB - We characterize the tails of the probability distribution functions for the solution of Burgers' equation with Gaussian initial data and its derivatives ∂kv(x,t)/∂xk, k=0,1,2,... . The tails are "stretched exponentials" of the form P(θ)∝exp[-(Re)- ptqθr], 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.

UR - http://www.scopus.com/inward/record.url?scp=0029529362&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029529362&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 3067

EP - 3071

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 12

ER -