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Self-similar profile of probability density functions in zero-pressure gradient turbulent boundary layers
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.ORCID iD: 0000-0002-2711-4687
2005 (English)In: Fluid Dynamics Research, ISSN 0169-5983, E-ISSN 1873-7005, Vol. 37, no 5, 293-316 p.Article in journal (Refereed) Published
Abstract [en]

The probability density function (pdf) of a streamwise velocity component is studied in zero-pressure gradient boundary layers. From analyzing the data up to R-0 similar or equal to-- 13, 000, it is found that pdfs have self-similar profiles ranging from y(+) +/- 180 to 0.049 Delta(+), where Delta is Rotta-Clauser boundary layer thickness. Pdf profiles asymptote to the universal shape very close to the Gaussian, but are positively skewed at the core region, indicating smaller values in the tail parts. Based on this experimental fact, the mean velocity profile is reconsidered from the standpoint of pdf equation. The log-law profile is expected as the mean velocity distribution. The Karman constant is evaluated to be 0.38, and the log-region starts at y(s)(+) = 180 and ends at y(+) = 0.021 Delta(+) + 96.5 for R-0 > 4000. The end point locates in 0.15 delta(+) <= y(r)(+) <= 0.26(+). The relation to the new scaling law derived from Lie-group theory is also discussed.

Place, publisher, year, edition, pages
2005. Vol. 37, no 5, 293-316 p.
Keyword [en]
turbulent boundary layer, probability density function, log-law region, universality, low-reynolds-number, viscous sublayer, overlap region, channel flow, shear flows, pdf methods, power-law, stress, distributions, universality
URN: urn:nbn:se:kth:diva-15242DOI: 10.1016/j.fluiddyn.2005.06.003ISI: 000233841600001ScopusID: 2-s2.0-29944446942OAI: diva2:333283
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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