Theoretical modeling derives mean velocity profiles from co-spectral budgets in wall-bounded flows, suggesting a unified framework linking logarithmic and power-law scaling theories.
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 ([12pt]{minimal}{document}C^ K{document}CK′), and Rotta (A) constants, namely, [12pt]{minimal}{document}κ = (4 A/7C^ K)-3/4{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.
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Katul et al. (2013) studied this question.
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