Co-spectrum and mean velocity in turbulent boundary layers

Katul, G., Porporato, A., Manes, Costantino and Meneveau, C. (2013) Co-spectrum and mean velocity in turbulent boundary layers. Physics of Fluids, 25 (9), 91702. (doi:10.1063/1.4821997).

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 (?), one-dimensional Kolmogorov ( C?K ), and Rotta (A) constants, namely, ?=(4A/7C?K)?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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