### Abstract

We study the statistics of the viscous Burgers turbulence (BT) model, initialized at time t = 0 by a large class of Gaussian data. Using a first-principles analysis of the Hopf-Cole formula for the Burgers equation and the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) for the velocity u(x, t) and the velocity derivatives ∂^{n}u(x,t)/∂x^{n},n = 1, 2, . . . . The PDF tails have a non-universal structure of the form log P(θ) ∝ -(Re)^{-ptqθr}, where Re is the Reynolds number and p, q, and r depend on the order of differentiation and the infrared behavior of the initial energy spectrum.

Original language | English (US) |
---|---|

Pages (from-to) | 1-23 |

Number of pages | 23 |

Journal | Communications in Mathematical Physics |

Volume | 200 |

Issue number | 1 |

State | Published - 1999 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

**The one-point statistics of viscous Burgers turbulence initialized with Gaussian data.** / Ryan, Reade; Avellaneda, Marco.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 200, no. 1, pp. 1-23.

}

TY - JOUR

T1 - The one-point statistics of viscous Burgers turbulence initialized with Gaussian data

AU - Ryan, Reade

AU - Avellaneda, Marco

PY - 1999

Y1 - 1999

N2 - We study the statistics of the viscous Burgers turbulence (BT) model, initialized at time t = 0 by a large class of Gaussian data. Using a first-principles analysis of the Hopf-Cole formula for the Burgers equation and the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) for the velocity u(x, t) and the velocity derivatives ∂nu(x,t)/∂xn,n = 1, 2, . . . . The PDF tails have a non-universal structure of the form log P(θ) ∝ -(Re)-ptqθr, where Re is the Reynolds number and p, q, and r depend on the order of differentiation and the infrared behavior of the initial energy spectrum.

AB - We study the statistics of the viscous Burgers turbulence (BT) model, initialized at time t = 0 by a large class of Gaussian data. Using a first-principles analysis of the Hopf-Cole formula for the Burgers equation and the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) for the velocity u(x, t) and the velocity derivatives ∂nu(x,t)/∂xn,n = 1, 2, . . . . The PDF tails have a non-universal structure of the form log P(θ) ∝ -(Re)-ptqθr, where Re is the Reynolds number and p, q, and r depend on the order of differentiation and the infrared behavior of the initial energy spectrum.

UR - http://www.scopus.com/inward/record.url?scp=0033248331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033248331&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033248331

VL - 200

SP - 1

EP - 23

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -