At high Reynolds numbers, the logarithmic range in wall-bounded flows spans many scales. An important conceptual modeling framework of the logarithmic range is Townsend's attached eddy hypothesis [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976)], where high Reynolds number wall-bounded flows are modeled as assemblies of space-filling, self-similar, and wall-attached eddies. Recently, Yang et al. [Phys. Rev. Fluids 1, 024402 (2016)] reinterpreted this hypothesis and developed the “hierarchical random additive process” model (HRAP), which provides further insights into the scaling implications of the attached eddies. For example, in a recent study [Yang et al., Phys. Rev. Fluids 2, 064602 (2017)], the HRAP model was used for making scaling predictions of the second-order structure function $〈[u_i^{\prime }\left(\mathbf{x}\right)-u_i^{\prime }\left({\mathbf{x}}^{\prime }\right)][u_j^{\prime }\left(\mathbf{x}\right)-u_j^{\prime }\left({\mathbf{x}}^{\prime }\right)]〉$ in the logarithmic range, where $u_i$'s are the velocity fluctuations in the $i\mathrm{th}$ Cartesian direction. Here, we provide empirical support for this HRAP model using high-fidelity experimental data of all three components of velocity in a high Reynolds number boundary layer flow. We show that the spanwise velocity fluctuation can be modeled as a random additive process, and that the wall-normal velocity fluctuation is dominated by the closest neighboring wall-attached eddy. By accounting for all the three velocities in all the three Cartesian directions, the HRAP model is formally a well rounded model for the momentum-carrying scales in wall-bounded flows at high Reynolds numbers.

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• Boundary layers
• Turbulence