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

Journal Article · Sun Aug 01 00:00:00 EDT 1999 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.870076· OSTI ID:351857

E, W; Vanden Eijnden, E ^[1]

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1. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)

The statistics of the multivalued solutions of the forced Riemann equation, u{sub t}+uu{sub x}=f, is considered. An exact equation for the signed probability density function of these solutions and their gradient {xi}=u{sub 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 {vert_bar}{xi}{vert_bar}{sup {minus}3} for large {vert_bar}{xi}{vert_bar}. Further considerations give bounds on the cumulative probability density function for the velocity gradient of the solution of Burgers equation. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 351857
• Journal Information: Physics of Fluids (1994), Vol. 11, Issue 8; Other Information: PBD: Aug 1999
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
PROBABILITY
RIEMANN FUNCTION
TURBULENCE
ANALYTICAL SOLUTION
STATISTICAL MODELS
BURGERS VECTOR
FLUIDS