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Journal Articles Physical Review Fluids Year : 2019

Refinement of the logarithmic law of the wall

Abstract

Available direct numerical simulation of turbulent channel flow at moderately high Reynolds numbers data show that the logarithmic diagnostic function is a linearly decreasing function of the outer-normalized wall distance η = y/δ with a slope proportional to the von Kármán constant, κ = 0.4. The validity of this result for turbulent pipe and boundary layer flows is assessed by comparison with the mean velocity profile from experimental data. The results suggest the existence of a flow-independent logarithmic law U + = U /u τ = (1/κ) ln(y * /a), where y * = yU S /ν with U S = yS(y) being the local shear velocity and the two flow-independent constants κ = 0.4 and a = 0.36. The range of its validity extends from the inner-normalized wall distance y + = 300 up to half the outer-length scale η = 0.5 for internal flows, and η = 0.2 for zero-pressure-gradient turbulent boundary layers. Likewise, and within the same range, the mean velocity deficit follows a flow-dependent logarithmic law as a function of a local mean-shear-based coordinate. Furthermore, it is illustrated how the classical friction laws for smooth pipe and zero-pressure-gradient turbulent boundary layer are recovered from this scaling.
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Dates and versions

hal-02144584 , version 1 (03-06-2019)

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F. Laadhari. Refinement of the logarithmic law of the wall. Physical Review Fluids, 2019, 4 (5), ⟨10.1103/PhysRevFluids.4.054605⟩. ⟨hal-02144584⟩
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