A conceptual model for the filtered wall-shear stress statistics in turbulent boundary layers

Abstract eng:
We present near-wall results from zero-pressure gradient boundary layer DNS, at Reynolds numbers up to Reθ = 2000 based on momentum thickness θ and free-stream velocity U ∞ . Statistics and probability distributions of fluctuating skin friction suggest increasing standard deviation and higher moments with increasing Reθ . An algebraic correlation for wall dissipation is proposed, fitting current and previous data. The wall-shear stress angle appears correlated with the streamwise vortex structures which are responsible for rare negative shear stress events. A conceptual model is presented, relating statistics of filtered skin friction fluctuations with velocity structure function in δν ! y ! δ (δν and δ are wall viscous length and boundary layer thickness). According to the model, the fluctuating shear stress influences velocity spectra in the Townsend-Perry attached-eddy range 1/δ < k < 1/y, inducing a higher slope than the classical result E(k) ∝ k−1 .

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