Universality in fully developed turbulence

Journal Article · Sat Oct 01 04:00:00 EDT 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.50.2784· OSTI ID:6910036

Grossmann, S; Lohse, D ^[1]

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1. Fachbereich Physik, Philipps-Universitaet, Renthof 6, D-35032 Marburg (Germany) The James Franck Institute, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637 (United States)

We extend the numerical simulations of She [ital et] [ital al]. [Phys. Rev. Lett. 70, 3251 (1993)] of highly turbulent flow with 15[le]Taylor-Reynolds numbers Re[sub [lambda]][le]200 up to Re[sub [lambda]][approx]45 000, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers Re[sub [lambda]], the energy spectra as well as the higher moments---when scaled by the spectral intensity at the wave number [ital k][sub [ital p]] of peak dissipation---can be described by [ital one] [ital universal] function of [ital k]/[ital k][sub [ital p]] for all Re[sub [lambda]]. Second, the [ital k]-space inertial subrange scaling exponents [zeta][sub [ital m]] of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the larger Re[sub [lambda]] is), as is the Re[sub [lambda]] dependence of [ital k][sub [ital p]]. Only around [ital k][sub [ital p]], viscous damping leads to a slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).

• OSTI ID: 6910036
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 50:4; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
ENERGY SPECTRA
EQUATIONS
FLUID FLOW
MATHEMATICS
NAVIER-STOKES EQUATIONS
NUMERICAL ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
REYNOLDS NUMBER
SCALING LAWS
SPECTRA
TURBULENT FLOW