The mesolayer and reynolds number dependencies of boundary layer turbulence

Spectral measurements from the WALLTURB Lille experiment in a flat plate turbulent boundary layer at R_θ = 19,100 are used to evaluate the role of viscosity on the turbulence in different parts of the boundary layer. The measurements support the idea of a mesolayer from 30 ≤ y⁺ ≤ 300 in which viscosity affects all scales of motion. An approximately k⁻¹ range emerges near the outer part of the mesolayer and over inertial sublayer (220 ≤ y + ≤ 890). But in spite of the relatively high value of R_θ , the spectra in neither the inertial sublayer (300 ≤ y⁺ ≤ 0.1δ_0.99) nor the main part of the boundary layer show a true inertial subrange behavior; i.e., a k^−5/3 spectrum. The spectra outside of y⁺ ≈ 0.12δ⁺₉₉ were shown to be consistent with a k^−5/3+μ behavior where μ>0 and decreases as the inverse of the logarithm of the Reynolds number. An immediate consequence is that the asymptotic state of the boundary layer can be reached only at very high values of R_θ , probably near 10⁵.