PDFs for velocity and velocity gradients in Burgers' turbulence

M. Avellaneda; R. Ryan; E. Weinan

doi:10.1063/1.868683

PDFs for velocity and velocity gradients in Burgers' turbulence

M. Avellaneda, R. Ryan, E. Weinan

Mathematics

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

Abstract

We characterize the tails of the probability distribution functions for the solution of Burgers' equation with Gaussian initial data and its derivatives ∂^kv(x,t)/∂x^k, k=0,1,2,... . The tails are "stretched exponentials" of the form P(θ)∝exp[-(Re)- ^pt^qθ^r], where Re is the Reynolds number. The exponents p, q, and r depend on the initial spectrum as well as on the order of differentiation, k. These exact results are compared with those obtained using the mapping closure technique.

Original language	English (US)
Pages (from-to)	3067-3071
Number of pages	5
Journal	Physics of Fluids
Volume	7
Issue number	12
DOIs	https://doi.org/10.1063/1.868683
State	Published - 1995

ASJC Scopus subject areas

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

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author = "M. Avellaneda and R. Ryan and E. Weinan",

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T1 - PDFs for velocity and velocity gradients in Burgers' turbulence

AU - Avellaneda, M.

AU - Ryan, R.

AU - Weinan, E.

PY - 1995

Y1 - 1995

N2 - We characterize the tails of the probability distribution functions for the solution of Burgers' equation with Gaussian initial data and its derivatives ∂kv(x,t)/∂xk, k=0,1,2,... . The tails are "stretched exponentials" of the form P(θ)∝exp[-(Re)- ptqθr], where Re is the Reynolds number. The exponents p, q, and r depend on the initial spectrum as well as on the order of differentiation, k. These exact results are compared with those obtained using the mapping closure technique.

AB - We characterize the tails of the probability distribution functions for the solution of Burgers' equation with Gaussian initial data and its derivatives ∂kv(x,t)/∂xk, k=0,1,2,... . The tails are "stretched exponentials" of the form P(θ)∝exp[-(Re)- ptqθr], where Re is the Reynolds number. The exponents p, q, and r depend on the initial spectrum as well as on the order of differentiation, k. These exact results are compared with those obtained using the mapping closure technique.

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PDFs for velocity and velocity gradients in Burgers' turbulence

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