A theoretical decomposition of mean skin friction generation into physical phenomena across the whole profile of the incompressible zero-pressure-gradient smooth-flat-plate boundary layer is derived from a mean streamwise kinetic-energy budget in an absolute reference frame (in which the undisturbed fluid is not moving). The Reynolds-number dependences in the laminar and turbulent cases are investigated from direct numerical simulation datasets and Reynolds-averaged Navier-Stokes simulations, and the asymptotic trends are consistently predicted by theory. The generation of the difference between the mean friction in the turbulent and laminar cases is identified with the total production of turbulent kinetic energy (TKE) in the boundary layer, represented by the second term of the proposed decomposition of the mean skin friction coefficient. In contrast, the analysis introduced by Fukagata et al. on a streamwise momentum budget in the wall reference frame, relates the turbulence-induced excess friction to the Reynolds shear stress weighted by a linear function of the wall distance. The wall-normal distribution of the linearly-weighted Reynolds shear stress differs from the distribution of TKE production involved in the present discussion, which consequently draws different conclusions on the contribution of each layer to the mean skin friction coefficient. At low Reynolds numbers, the importance of the buffer-layer dynamics is confirmed. At high Reynolds numbers, the present decomposition quantitatively shows for the first time that the generation of the turbulence-induced excess friction is dominated by the logarithmic layer. This is caused by the well-known decay of the relative contributions of the buffer layer and wake region to TKE production with increasing Reynolds numbers. This result on mean skin friction, with a physical interpretation relying on an energy budget, is consistent with the well-established general importance of the logarithmic layer at high Reynolds numbers, contrary to the friction breakdown obtained from the approach of Fukagata et al. based on a momentum budget. The new decomposition suggests that it may be worth investigating new drag reduction strategies focusing on TKE production and on the nature of the logarithmic layer dynamics. The decomposition is finally extended to the pressure-gradient case and to channel and pipe flows.

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 turbulent inflow for a rapid and low noise switch from RANS to Wall-Modelled LES on curvilinear grids with compressible flow solvers is presented. It can be embedded within the computational domain in practical applications with WMLES grids around three-dimensional geometries in a flexible zonal hybrid RANS/LES modelling context. It relies on a physics-motivated combination of Zonal Detached Eddy Simulation (ZDES) as the WMLES technique together with a Dynamic Forcing method processing the fluctuations caused by a Zonal Immersed Boundary Condition describing roughness elements. The performance in generating a physically-sound turbulent flow field with the proper mean skin friction and turbulent profiles after a short relaxation length is equivalent to more common inflow methods thanks to the generation of large-scale streamwise vorticity by the roughness elements. Comparisons in a low Mach-number zeropressure-gradient flat-plate turbulent boundary layer up to Re θ = 6 100 reveal that the pressure field is dominated by the spurious noise caused by the synthetic turbulence methods (Synthetic Eddy Method and White Noise injection), contrary to the new low-noise approach which may be used to obtain the low-frequency component of wall pressure and reproduce its intermittent nature. The robustness of the method is tested in the flow around a three-element airfoil with WMLES in the upper boundary layer near the trailing edge of the main element. In spite of the very short relaxation distance allowed, self-sustainable resolved turbulence is generated in the outer layer with significantly less spurious noise than with the approach involving White Noise. The ZDES grid count for this latter test case is more than two orders of magnitude lower than the Wall-Resolved LES requirement and a unique mesh is involved, which is much simpler than some multiple-mesh strategies devised for WMLES or turbulent inflow.

A robust strategy for the RANS shielding of attached boundary layers in a hybrid RANS/LES context is presented, addressing two major issues. Firstly, the attached boundary layers must be detected to ensure their RANS treatment, but the original shielding function used by automatic methods such as DDES (2006) or ZDES mode 2 (2012) fails for fine meshes and/or with adverse pressure gradients, motivating the present study. Secondly, even with a stronger shielding, there should not be an excessive delay in the formation of instabilities and resolved LES content in free shear layers. Both objectives cannot be simultaneously reached by only tuning a constant in the original shielding function. The proposed new ZDES mode 2 consequently involves three main ingredients, namely a second shielding function detecting the outer part of the wake layer including with strong adverse pressure gradients, an inhibition function which switches off the second shielding when flow separation is detected, and a significant enhancement of the destruction of eddy viscosity in grey areas. The calibration of the method relies on a set of boundary layers at various Reynolds numbers and pressure gradients conditions and is confirmed by a priori tests in three-dimensional flows around curved geometries. The resulting case-independent model, the new ZDES mode 2, is assessed on four test cases, namely a flat-plate boundary layer, a mixing layer, a backward facing step and transonic buffet over a supercritical airfoil. Overall, it is shown that the new ZDES mode 2 is relevant with respect to four objectives: protection of attached boundary layers for any grid cell size (including infinite mesh refinement) and pressure gradient, RANS shielding at least as broad as the original shielding in any situation, minimum delay in the formation of resolved LES content, and full compatibility of the resulting subgrid scale model in the LES branch with the other modes of ZDES (modes 1 and 3) ensuring a continuous treatment of resolved turbulence across zones treated with different ZDES modes. The new robust ZDES mode 2 consequently is a case-independent answer to the demand for a general automatic and robust RANS/LES treatment of attached and massively separated flows.

= friction Reynolds number Re θ = Reynolds number based on the momentum thickness x center = streamwise coordinate of the cell center x, y, z = streamwise, wall-normal, and spanwise coordinates α = Reynolds-averaged Navier-Stokes/large-eddy simulation interface function parameter Δ vol = mesh characteristic length based on cell volume δ = boundary-layer thickness δ 0 = inlet boundary-layer thickness

The scale-dependent turbulent convection velocity of streamwise velocity fluctuations resolved by large eddy simulation is investigated for the first time across the whole profile of a zero-pressure-gradient spatially developing smooth flat plate boundary layer at Re θ = 13 000. The high Reynolds number and streamwise heterogeneity constraints motivate the derivation of a dedicated new method to assess the frequency-dependent convection velocity from time signals and their local streamwise derivative, using estimates of power spectral densities (PSDs). This method is inspired by del Álamo & Jiménez (J. Fluid Mech., vol. 640, 2009, pp. 5-26), who treated a lower Reynolds number channel flow with a method suited to spectral direct numerical simulations of streamwise homogeneous flows. Reconstruction of the streamwise spectrum from the time spectrum using the scale-dependent convection velocity is illustrated and compared with classical strategies. The new method inherently includes not only the assessment of the validity of Taylor's hypothesis, whose trend is remarkably consistent with theoretical predictions by Lin (Q. Appl. Maths, vol. X(4), 1953, 154-165), but also the definition of a global convection velocity accounting for any arbitrary frequency band. This global velocity is shown to coincide with a correlation-based method widely used in experiments. In addition to the mathematical least-squares definition of this velocity, new interpretations based on the flow physics and turbulent micro time scales are presented. Further, the group velocity is assessed and its relation to convection is discussed.

No abstract