A numerical investigation of the mean wall shear stress properties on a spatially developing turbulent boundary layer over a smooth flat plate was carried out by means of a zonal detached eddy simulation (ZDES) technique for the Reynolds number range 3060 Re θ 13 650. Some asymptotic trends of global parameters are suggested. Consistently with previous findings, the calculation confirms the occurrence of very large-scale motions approximately 5δ to 6δ long which are meandering with a lateral amplitude of 0.3δ and which maintain a footprint in the near-wall region. It is shown that these large scales carry a significant amount of Reynolds shear stress and their influence on the skin friction, denoted C f ,2 , is revisited through the FIK identity by Fukagata, Iwamoto & Kasagi (Phys. Fluids, vol. 14, 2002, p. L73). It is argued that C f ,2 is the relevant parameter to characterize the high-Reynolds-number turbulent skin friction since the term describing the spatial heterogeneity of the boundary layer also characterizes the total shear stress variations across the boundary layer. The behaviour of the latter term seems to follow some remarkable self-similarity trends towards high Reynolds numbers. A spectral analysis of the weighted Reynolds stress with respect to the distance to the wall and to the wavelength is provided for the first time to our knowledge and allows us to analyse the influence of the largest scales on the skin friction. It is shown that structures with a streamwise wavelength λ x > δ contribute to more than 60 % of C f ,2 , and that those larger than λ x > 2δ still represent approximately 45 % of C f ,2 .

A Wall-Modeled Large Eddy Simulation (WMLES) of a spatially developing zero-pressure gradient smooth flat plate turbulent boundary layer is performed by means of the third mode of the Zonal Detached Eddy Simulation technique. The outer layer is resolved by a Large Eddy Simulation whereas the wall is modeled by a RANS simulation zone, with a RANS/LES interface prescribed at a fixed location. A revisited cost assessment of the Direct Numerical Simulation of high Reynolds numbers (Reθ ⩾ 10 000) wall-bounded flows emphasizes how moderate the cost of the WMLES approach is compared to methods resolving the near-wall dynamics. This makes possible the simulation over a wide Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000, leaving quite enough space for very large scale motions to develop. For a better skin friction prediction, it is shown that the RANS/LES interface should be high enough in the boundary layer and at a location scaling in boundary layer thickness units (e.g., 0.1δ) rather than in wall units. Velocity spectra are compared to experimental data. The outer layer is well resolved, except near the RANS/LES interface where the very simple and robust passive boundary treatment might be improved by a more specific treatment. Besides, the inner RANS zone also contains large scale fluctuations down to the wall. It is shown that these fluctuations fit better to the experimental data for the same interface location that provides a better skin friction prediction. Numerical tests suggest that the observed very large scale motions may appear in an autonomous way, independently from the near-wall dynamics. It still has to be determined whether the observed structures have a physical or a numerical origin. In order to assess how the large scale motions contribute to skin friction, the Reynolds shear stress contribution is studied as suggested by the FIK identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)]. Scale decomposition is achieved thanks to the co-spectrum of the Reynolds shear stress in function of the length scale and of the wall distance. The contribution of the large scales to streamwise turbulence intensity and to the Reynolds shear stress is assessed. At the considered Reynolds numbers, the observed largest scales contribute significantly to the Reynolds shear stress in the outer layer but are almost inactive in the sense of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, 1976)] closer to the wall. The modeled Cf amounts to only 11% of the total Cf: most of the skin friction is resolved by the present simulations rather than modeled. The large scales, defined by λx > δ, represent the largest contribution to the resolved Cf. It is surmised that there is a correlation between the large scale motions being closer to the experimental data and the better skin friction prediction enabled by a proper interface positioning.

A numerical investigation of the flow dynamics around a two-dimensional high-lift configuration was carried out by means of a zonal detached eddy simulation (ZDES) technique for flow conditions corresponding to aircraft approach. Both slat and flap regions have been scrutinized and compared with experimental data available in the literature. It is shown that slat and flap coves behave like shallow cavities. The distance between the upstream cusp and the downstream edge is the relevant length scale for each cove taken separately. Consistently with previous findings, this study indicates that the maximum of the broadband spectrum of slat (respectively flap) pressure fluctuations occurs for Strouhal numbers 0.5 St 4 when based on slat chord (respectively on flap chord) and free-stream velocity. It is shown that mode (n) of the slat cove and mode (n + 1) of the flap cove are very close making a coherent phase relationship possible. A large-scale coupled self-sustained oscillations mechanism between slat and flap cavities, evidenced by spectral analysis, occurs at a Strouhal number St = 3-6 based on the main wing chord and free-stream velocity. This yields to an acoustic feedback mechanism characterized by a normalized frequency depending on the free stream Mach number like St = (1 − M 2 0 )/2M 0 . The present result appears to line up with the findings by Hein et al. (J. Fluid Mech., vol. 582, 2007, pp. 179-202) who showed that two types of resonance could exist: surface waves ones, scaling with the total aerofoil length and longitudinal cavity-type resonances, scaling with the slat cove length.

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