### Abstract

A systematic analysis is carried out for the randomly forced Burgers equation in the infinite Reynolds number (inviscid) limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of quantities defined along the shocks. This method allows one to compute the dissipative anomalies, as well as asymptotics for the structure functions and the probability density functions. It is shown that the left tail for the probability density function of the velocity gradient has to decay faster than |ξ|^{-3}. A further argument confirms the prediction of E et al. [Phys. Rev. Lett. 78, 1904 (1997)] that it should decay as |ξ|^{-7/2}.

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

Pages (from-to) | 2572-2575 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 83 |

Issue number | 13 |

State | Published - Sep 27 1999 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*83*(13), 2572-2575.

**Asymptotic theory for the probability density functions in burgers turbulence.** / Weinan, E.; Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 83, no. 13, pp. 2572-2575.

}

TY - JOUR

T1 - Asymptotic theory for the probability density functions in burgers turbulence

AU - Weinan, E.

AU - Vanden Eijnden, Eric

PY - 1999/9/27

Y1 - 1999/9/27

N2 - A systematic analysis is carried out for the randomly forced Burgers equation in the infinite Reynolds number (inviscid) limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of quantities defined along the shocks. This method allows one to compute the dissipative anomalies, as well as asymptotics for the structure functions and the probability density functions. It is shown that the left tail for the probability density function of the velocity gradient has to decay faster than |ξ|-3. A further argument confirms the prediction of E et al. [Phys. Rev. Lett. 78, 1904 (1997)] that it should decay as |ξ|-7/2.

AB - A systematic analysis is carried out for the randomly forced Burgers equation in the infinite Reynolds number (inviscid) limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of quantities defined along the shocks. This method allows one to compute the dissipative anomalies, as well as asymptotics for the structure functions and the probability density functions. It is shown that the left tail for the probability density function of the velocity gradient has to decay faster than |ξ|-3. A further argument confirms the prediction of E et al. [Phys. Rev. Lett. 78, 1904 (1997)] that it should decay as |ξ|-7/2.

UR - http://www.scopus.com/inward/record.url?scp=29444442507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29444442507&partnerID=8YFLogxK

M3 - Article

VL - 83

SP - 2572

EP - 2575

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 13

ER -