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Home > Teams > Turbulence & Instabilities > Publications T&I et posters doctorants > Publications T&I 2019

Article in Phys. Rev. Fluids (2019)

Refinement of the logarithmic law of the wall

Faouzi Laadhari

Refinement of the logarithmic law of the wall

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 $\eta=y/\delta$ with a slope proportional to the von Kármán constant, $\kappa=0.4$. 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 $U^+=U/u_\tau=(1/\kappa)\ln(y^\star/a)$, where $y^\star=y\,U_S/\nu$ with $U_S=y\,S(y)$ the local shear velocity and the two flow-independent constants $\kappa=0.4$ 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 $\eta=0.5$ for internal flows, and $\eta=0.2$ 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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