A note on third-order structure functions in turbulence

Authors
Citation
Q. Nie et S. Tanveer, A note on third-order structure functions in turbulence, P ROY SOC A, 455(1985), 1999, pp. 1615-1635
Citations number
28
Categorie Soggetti
Multidisciplinary
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
ISSN journal
13645021 → ACNP
Volume
455
Issue
1985
Year of publication
1999
Pages
1615 - 1635
Database
ISI
SICI code
1364-5021(19990508)455:1985<1615:ANOTSF>2.0.ZU;2-I
Abstract
Starting from the Navier-Stokes equation, we rigorously prove that a modifi ed third-order structure function, (S) over tilde(3)(r), asymptotically equ als -4/3 epsilon r (epsilon is the dissipation rate) in an inertial regime. From this result, we rigorously confirm the Kolmogorov four-fifths law, wi thout the Kolmogorov assumption on isotropy. Our definition of the structur e function involves a solid angle averaging over all possible orientations of the displacement vector y, besides space-time-averaging. Direct:numerica l simulation for a highly symmetric flow for a Taylor Reynolds number of up to 155 shows that the flow remains significantly anisotropic and that, wit hout solid angle averaging, the resulting structure functions approximately satisfy these scaling relations over some range of r = \y\ for some orient ation of y, but not for another.