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INVARIANT ASSUMPTION OF PDF AND MEAN VELOCITY PROFILE IN HIGH-REYNOLDS NUMBER TURBULENT BOUNDARY LAYERS

Yoshiyuki Tsuji
KTH Mechanics, Royal Institute of Technology, 100 44 Stockholm, Sweden; Department of Energy Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8503, Japan

Bjorn Lindgren
Department of Mechanics, Royal Institute of Technology, Osquarsbacke 18, SE-100 44 Stockholm, Sweden

Arne V. Johansson
Linne FLOW Centre, Dept. of Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden

Аннотация

The probability density function (pdf) of a streamwise velocity component is studied in zero-pressure gradient boundary layers. From analyzing the data up to Rθ ≈ 13000, it was found that pdfs have self-similar profiles ranging from y+ ≈ 180 to 0.049 · Δ+, where Δ 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 loglaw profile is expected as the mean velocity distribution.