A Scale-Entropy Diffusion Equation for Wall Turbulence

  • Hassan Kassem
  • Diogo Queiros-Conde
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 14)


We applied on a database of PIV fields obtained at Laboratoire de Mécanique de Lille corresponding to a turbulent boundary layer the statistical and geometrical tools defined in the context of entropic-skins theory. We are interested by the spatial organization of velocity fluctuations. We define the absolute value of velocity fluctuation δ V defined relatively to the mean velocity. For given value δ V s (the threshold), the set Ω(δ V s ) is defined by taking the points on the field where δ Vδ V s . We thus define a hierarchy of sets for the threshold δ V s ranging from the Kolmogorov velocity (the corresponding set is noted Ω K ) to the turbulent intensity U′ (the corresponding set is noted Ω U). We then characterize the multi-scale features of the sets Ω(δ V s ). It is shown that, between Taylor and integral scale, the set Ω(δ V s ) can be considered as self-similar which fractal dimension is noted D s . We found that fractal dimension varies linearly with logarithm of ratio δ V s /U′. The relation is D s =2+βln (δ V s /U′) with β≈0.12–0.26: this result is obtained for all the values y + we worked with. We then defined an equivalent dispersion scale l e such as \(N(\delta V_{s})-N_{K}=l_{e}^{2}\). It is shown that \(\delta V_{s}/U'\sim l_{e}^{1.52}\). We thus can write D s =2+β′ln (l e /l 0) with β′≈0.18–0.39. These results are interpreted in the context of a scale-entropy diffusion equation introduced to characterize multi-scale geometrical features of turbulence.


Fractal Dimension Turbulent Intensity Velocity Fluctuation Integral Scale Wall Turbulence 
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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Unite Chimie et ProcédésENSTA-ParisTechParisFrance

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