On the statistical solution of the Riemann equation and its implications for Burgers turbulence

E. Weinan; Eric Vanden Eijnden

doi:10.1063/1.870076

On the statistical solution of the Riemann equation and its implications for Burgers turbulence

E. Weinan, Eric Vanden Eijnden

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The statistics of the multivalued solutions of the forced Riemann equation, u_t + uu_x=f, is considered. An exact equation for the signed probability density function of these solutions and their gradient ξ=U_x is derived, and some properties of this equation are analyzed. It is shown in particular that the tails of the signed probability density function generally decay as |ξ|^-3 for large |ξ|. Further considerations give bounds on the cumulative probability density function for the velocity gradient of the solution of Burgers equation.

Original language	English (US)
Pages (from-to)	2149-2153
Number of pages	5
Journal	Physics of Fluids
Volume	11
Issue number	8
DOIs	https://doi.org/10.1063/1.870076
State	Published - Aug 1999

ASJC Scopus subject areas

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

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10.1063/1.870076

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On the statistical solution of the Riemann equation and its implications for Burgers turbulence

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