A refined interpretation of the logarithmic structure function law in wall layer turbulence

• Published in: Physics of fluids (1994) 2006-06, Vol.18 (6)
• Main Authors: Davidson, P. A., Krogstad, P.-Å., Nickels, T. B.
• Format: Article
• Language: English
• Subjects: Boundary layer and shear turbulence; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Turbulent flows, convection, and heat transfer
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.2214087

It has been shown recently that the real-space equivalent of the k − 1 law for near-wall turbulence is a logarithmic law for the second-order longitudinal structure function, ⟨ ( Δ u ) 2 ⟩ ( r ) = u * 2 ( A + B ln ( r ∕ y ) ) . Here y is the distance from the wall, u * is the shear velocity, A and B are coefficients of order unity and r is measured in the streamwise direction. In this paper we provide theoretical arguments to suggest that, in the limit of large Reynolds number, B is a universal constant while A is of the form A = A ′ − B ln ( P ∕ ϵ ) , where A ′ is a universal constant and P and ϵ are the rates of production and dissipation of energy, respectively. Hence A is a weak, universal, function of y . Two independent sets of data are examined and it is shown that, to within experimental error, our predictions are consistent with the data.