Co-spectrum and mean velocity in turbulent boundary layers

Abstract

Connections are explored between spectral descriptions of turbulence and the mean velocity profile in the equilibrium layer of wall-bounded flows using a modeled budget for the co-spectral density. Using a standard model for the wall normal velocity variance and a Rotta-like return-to-isotropy closure for the pressure-strain effects, the co-spectrum is derived. The approach establishes a relation between the von Kármán (κ), one-dimensional Kolmogorov (\documentclass[12pt]{minimal}\begin{document}$C^\prime _K$\end{document}CK′), and Rotta (A) constants, namely, \documentclass[12pt]{minimal}\begin{document}$\kappa = (4 A/7C^\prime _K)^{-3/4}$\end{document}κ=(4A/7CK′)−3/4. Depending on the choices made about small-scale intermittency corrections, the logarithmic mean velocity profile or a power-law profile with an exponent that depends on the intermittency correction are derived thereby offering a new perspective on a long standing debate.