On the Composite Velocity Profile in Zero Pressure Gradient Turbulent Boundary Layer: Comparison with DNS Datasets

Abstract

Data obtained by direct numerical simulations (DNS) of the Zero-Pressure-Gradient Turbulent Boundary Layer were analyzed and compared to a mathematical model of the mean velocity profile (MVP) in the range 1000 ≤ Reθ ≤ 6500. The mathematical model is based on the superposition of an accurate description of the inner law and Coles’ wake function with appropriately chosen parameters. It is found that there is excellent agreement between the mathematical model and the DNS data in the inner layer when the Reynolds number based on momentum thickness, Reθ, is greater than 1000. Furthermore, there is very good agreement over the entire boundary layer thickness, when Reθ is greater than 2000. The diagnostic functions Ξ and Γ based on DNS data are examined and their characteristics are discussed in relation to the existence of a logarithmic layer or a power law behavior of the MVP. The diagnostic functions predicted by the mathematical model are also presented.

Keywords

• turbulent boundary layer
• direct numerical simulation (DNS)
• composite mean velocity profile
• diagnostic functions