Refinement of the logarithmic law of the wall

F. Laadhari (1)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique

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.

Domaines: Mécanique des fluides [physics.class-ph]

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