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

Research output: Contribution to journalArticle

Abstract

The statistics of the multivalued solutions of the forced Riemann equation, ut + uux=f, is considered. An exact equation for the signed probability density function of these solutions and their gradient ξ=Ux 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 languageEnglish (US)
Pages (from-to)2149-2153
Number of pages5
JournalPhysics of Fluids
Volume11
Issue number8
DOIs
StatePublished - 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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