Statistics of decaying Burgers turbulence

Journal Article · Mon Feb 01 04:00:00 EST 1993 · Physics of Fluids A; (United States)

DOI:https://doi.org/10.1063/1.858868· OSTI ID:6832827

Gotoh, T ^[1]; Kraichnan, R H ^[2]

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1. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) Center for Turbulence Research, Stanford University, Stanford, California 94305-3030 (United States)
2. 369 Montezuma 108, Santa Fe, New Mexico 87501-2626 (United States)

Freely decaying Burgers turbulence at low and moderate Reynolds number R is studied by mapping closure and by numerical simulations. Good agreement is found for the single-point probability distribution function (pdf) of velocity gradient [xi], for wave number spectra, and for various integral statistical quantities. The pdf of [xi] exhibits a nearly exponential tail at large negative [xi], and a cusp with sharp cutoff at a positive value of [xi]. The pdf of fluid density has a power-law tail, so that high-order moments of density do not exist. Asymptotic analysis of the mapping closure as R[r arrow][infinity] yields an inertial-range wave number spectrum of kinetic energy with the form [ital E]([ital k])[proportional to][ital k][sup [minus]2]. The pdf cusp becomes infinite as R[r arrow][infinity] and gives rise to a flatness [lt][xi][sup 4][gt]/[lt][xi][sup 2][gt][sup 2][proportional to]R in the limit.

• DOE Contract Number: FG03-90ER14118
• OSTI ID: 6832827
• Journal Information: Physics of Fluids A; (United States), Journal Name: Physics of Fluids A; (United States) Vol. 5:2; ISSN 0899-8213; ISSN PFADEB
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
DECAY
DISTRIBUTION FUNCTIONS
ENERGY SPECTRA
FLUID FLOW
FUNCTIONS
MATHEMATICS
REYNOLDS NUMBER
SHOCK WAVES
SPECTRA
STATISTICS
TURBULENT FLOW