Flat Plate Turbulent Boundary Layer Research Articles

Evidence of quasiequilibrium in pressure-gradient turbulent boundary layers

Two sets of measurements utilizing hot-wire anemometry and oil-film interferometry for flat-plate turbulent boundary layers, exposed to various controlled adverse and favourable pressure gradients, are used to evaluate history effects of the imposed and varying free-stream gradients. The results are from the NDF wind tunnel at Illinois Tech (IIT) and the MTL wind tunnel at KTH, over the range $800 < Re_\tau < 22\,000$ (where $Re_{\tau }$ is the friction Reynolds number). The streamwise pressure-gradient parameter $\beta \equiv (-\ell /\tau _{w}) \cdot (\partial P_{e}/\partial x)$ varied between $-2 < \beta < 7$ , where $\ell$ is an outer length scale for boundary layers equivalent to the half-height of channel flow and the radius of pipe flow, and is estimated for each boundary-layer profile; note that $\tau_w$ is the wall-shear stress and $P_e$ is the free-stream static pressure. Extracting from each profile the three parameters of the overlap region, following the recent work of Monkewitz & Nagib (J. Fluid Mech., vol. 967, 2023, p. A15) that led to an overlap region of combined logarithmic and linear parts, we find minimum history effects in the overlap region. Thus, the overlap region in this range of pressure-gradient boundary layers appears to be in ‘quasiequilibrium’.

On the extension of a Riemann solver for RANS simulations

Purpose Reynolds-averaged Navier–Stokes (RANS) models often perform poorly in shock/turbulence interaction regions, resulting in excessive wall heat load and incorrect representation of the separation length in shockwave/turbulent boundary layer interactions. The authors suggest that this can be traced back to inadequate numerical treatment of the inviscid fluxes. The purpose of this study is an extension to the well-known Harten, Lax, van Leer, Einfeldt (HLLE) Riemann solver to overcome this issue. Design/methodology/approach It explicitly takes into account the broadening of waves due to the averaging procedure, which adds numerical dissipation and reduces excessive turbulence production across shocks. The scheme is derived based on the HLLE equations, and it is tested against three numerical experiments. Findings Sod’s shock tube case shows that the scheme succeeds in reducing turbulence amplification across shocks. A shock-free turbulent flat plate boundary layer indicates that smooth flow at moderate turbulence intensity is largely unaffected by the scheme. A shock/turbulent boundary layer interaction case with higher turbulence intensity shows that the added numerical dissipation can, however, impair the wall heat flux distribution. Originality/value The proposed scheme is motivated by implicit large eddy simulations that use numerical dissipation as subgrid-scale model. Introducing physical aspects of turbulence into the numerical treatment for RANS simulations is a novel approach.

Direct numerical simulations of supersonic flat-plate turbulent boundary layers with uniform blowing

The effect of uniform blowing on a spatially developing flat-plate turbulent boundary layer at Mach 2.25 is investigated using direct numerical simulations. Two values of the wall blowing ratio are considered, corresponding to low and high blowing rates. Uniform blowing is found to significantly reduce the near-wall turbulence anisotropy, although the turbulent kinetic energy still exhibits near-wall asymptotic behavior and the Reynolds analogy is relatively insensitive to changes in the blowing ratio. The pre-multiplied spectra of turbulent kinetic energy production demonstrate that increasing the blowing ratio significantly energizes the large-scale structures in the outer region, while suppressing the inner small-scale structures. An increase in the blowing ratio also has a strong influence on the behavior of the fluctuating wall pressure, amplifying the fluctuation intensity and reducing the dominant frequencies in the power spectrum. Two-point space–time correlations indicate that the characteristic length scale of the pressure fluctuations increases with increasing blowing ratio, whereas the convection velocity exhibits the opposite trend. Analysis of the reduced mean wall heat flux reveals that it is dominated by the relative balance between the work of the Reynolds stress and the turbulent transport of heat, but is insensitive to uniform blowing. Importantly, bidimensional empirical mode decomposition of the turbulent structures highlights the increasingly dominant contributions related to the significantly energized outer large-scale structures in the blowing region.

Characterisation of unsteady separation in a turbulent boundary layer: Reynolds stresses and flow dynamics

The large-eddy simulation technique was used to investigate the dynamics of unsteady flow separation on a flat-plate turbulent boundary layer. The unsteadiness was generated by imposing an oscillating, wall-normal velocity profile at the top of the computational domain, and a range of reduced frequencies ( $k$ ), from a very rapid flutter-like motion to a slow quasi-steady oscillation, was studied. Ambrogi et al. (J. Fluid Mech., vol. 945, 2022, A10) showed that the reduced frequency greatly affects the transient separation process, and at a frequency $k=1$ , the separation region became unstable and was advected periodically out of the domain. In this paper, we discuss the causes of the observed advection process and the effects of the unsteadiness on the second moments. The time evolution of turbulent kinetic energy, for instance, reveals that an advection-like phenomenon is also present at a very low reduced frequency, but its dynamic behaviour is completely different from that of the intermediate frequency ( $k=1$ ). At the intermediate frequency the entire recirculation region is advected downstream, keeping its shape. The advected structure is rotational in nature, and moves at constant speed. In contrast, in the low-frequency case the advected fluid originates at the reattachment point, and the structure is shear-dominated. Particle pathlines reflect the fact that the flow at the low frequency is quasi-steady-state, but show peculiar differences at the intermediate frequency, in which the flow response to the freestream forcing depends on the particle positions in the wall-normal direction.

Investigation of Lagrangian Areas of Minimal Stretching (LAMS) in a turbulent boundary layer

In this paper the three-dimensional finite-time Lyapunov exponent (FTLE) field of a direct numerical simulation of a flat-plate turbulent boundary layer is analysed in several wall-parallel sections. The data consider a case at a low subsonic Mach number with a moderate positive pressure gradient in the streamwise direction. In contrast to other studies mainly focusing on the maxima of the FTLE field, particular emphasis is placed on the regions of minimal stretching between the vortices and shear layers of the three-dimensional turbulent flow field. These visually appear as contiguous islands or ‘valleys’ between the ‘ridges’ of the FTLE maxima, both at forward and backward integration of the flow field in time. To clearly distinguish the structures investigated from their more common counterparts (e.g. Lagrangian coherent structures, LCS), the acronym LAMS (Lagrangian areas of minimal stretching) is proposed to denote the associated cohesive fluid regions. Consistent with intuition, the largest LAMS occur near the boundary-layer edge, where large regions of homogeneous laminar external flow coexist with upwelling turbulent structures. Compensating for turbulent regions pushing upward, they sink from there down toward the wall, becoming smaller and longer. This process is associated with an increased relative velocity of the LAMS compared with the mean flow, which is observed over the whole boundary layer in the range $y^+ \gtrsim 10$ . Furthermore, it is observed that the Q4 (sweep) events contained in the LAMS clearly dominate over Q2 (ejection) events above $y^+ \approx 10$ . Thereby, local maxima occur at $y^+ \approx 20$ and near the boundary-layer edge. Below $y^+ \approx 10$ , the relationship reverses. Sweeping LAMS from above $y^+ \approx 10$ and ejecting LAMS from below meet in the layer where the maximal vortical activity occurs. The latter is caused by mostly streamwise oriented vortices with maximal vortex stretching in the streamwise direction. Overall, LAMS are associated with cohesive fluid regions between the surrounding vortices and shear layers that both drop down from the boundary-layer edge toward the wall in the outer region of the boundary layer and lift from the wall in the near-wall region.

Smoothed particle hydrodynamics with κ-ε closure for simulating wall-bounded turbulent flows at medium and high Reynolds numbers

In this study, an improved SPH (smoothed particle hydrodynamics) method coupling the κ-ε turbulence model and the wall function is proposed to simulate wall-bounded turbulent flows at medium and high Reynolds numbers. The second-order partial derivative term of the composite function containing the turbulent viscosity coefficient is decomposed into the sum of two terms, which helps SPH to avoid numerical errors and difficulties in dealing with boundary conditions in the nested approximation of first-order partial derivatives. Particle shifting technique, δ-SPH method, and graphics processing unit parallel technology are used in the simulations to ensure uniform particles, smooth pressure field, and high computational efficiency, respectively. The SPH method with the κ-ε turbulence model and the wall function is tested and validated by simulating four classical wall-bounded turbulent flows at medium and high Reynolds numbers, which are the turbulent flat plate boundary layer at Re = 4.2 × 106 and Re = 107, backward step separation flow at ReH = 3025, the flow around the airfoil at Re = 3 × 106, and the flow around the pitching airfoil at Re = 1.35 × 105, respectively. The simulation results are consistent with the references, validating the suitability of the current SPH method for simulating wall-bounded turbulent flows at medium and high Reynolds numbers. Finally, the airfoil motion combining the pitching and deforming at Re = 3 × 106 is investigated by the current SPH method. The results show that the deformation of the airfoil's relative thickness affects the lift coefficients of the pitching airfoil. Furthermore, the increase in the relative thickness increment reduces the amplitude of the lift coefficient, while the increase in the deformation period has little effect on the amplitude of the lift coefficient.

Study on the separation in the shock wave/boundary layer interaction induced by a curved fin

The effect of an isentropic compression wave fan on shock wave/turbulent boundary layer interaction induced by a curved fin is studied by the nanoparticle-based planar laser scattering method, oil flow method, and numerical method. The curved fin consists of two parts: A curved surface generating an isentropic compression fan and a planar surface ensuring the compression fan focuses into a swept shock wave. The flowfield is compared with the three-dimensional separation flowfield induced by a planar fin with the same deflection angle. The results show that the compression fan can compress the turbulent boundary layer without separation, while the focused swept shock wave drives the whole turbulent boundary layer to separate. The flat plate turbulent boundary layer beside the fin is mainly rolled into the separation vortex. The focused swept shock wave adjusts the separation zone to be quasi-conical, suggesting that the quasi-conical separation is the nature of the flowfield in which a turbulent boundary layer interacts with a swept shock wave. The isentropic compression part of the curved fin can prevent the secondary separation of the planar swept shock wave/turbulent boundary layer interaction by changing the attachment process. Based on the focus point of the compression wave fan, the equivalent apex of the curved fin is proposed. The area and intensity of the separation vortex induced by the curved fin are nearly linear as those in the planar fin interaction flowfield. However, the area of the separation vortex induced by the curved fin is larger. The intensity growth of the vortex caused by the curved fin is slower than that of the planar fin.

A family of adverse pressure gradient turbulent boundary layers with upstream favourable pressure gradients

A flat-plate turbulent boundary layer (TBL) is experimentally subjected to a family of 22 favourable–adverse pressure gradients (FAPGs) using a ceiling panel of variable convex curvature. We define FAPGs as a sequence of streamwise pressure gradients in the order of favourable followed by adverse, similar in sequence to the pressure gradients over the suction side of an airfoil. For the strongest pressure gradient case, the acceleration parameter, $K$ , varied spatially from $6 \times 10^{-6}$ to $- 4.8 \times 10^{-6}$ . The adverse pressure gradient (APG) region of this configuration is studied using particle image velocimetry in the streamwise–wall-normal plane. The statistics of the APG TBL show that the upstream favourable pressure gradient (FPG) exerts a strong and lasting downstream influence, and that the rapid spatial changes in the pressure gradients imposed cause an internal boundary layer to grow within the TBL for 15 of the cases studied. The internal layer typically occupies 20 $\%$ of the boundary layer thickness and dominates the boundary layer response, containing the peak turbulent production, peak strength and population of vortices, and most of the spectral energy content of the flow. The outer layer, on the other hand, develops in the APG region without considerable changes to the state dictated by the upstream FPG. These trends are in contrast to APG TBLs that originate from a zero pressure gradient region, where the outer/wake region is known to dominate TBL response. The observed changes are quantified across the family of FAPGs imposed.

Turbulent boundary layer control with DBD plasma actuators

The flat-plate turbulent boundary layer at Re τ = 1140 is manipulated using a spanwise array of bidirectional dielectric barrier discharge (DBD) plasma actuators. Based on the features of no moving mechanical parts in the DBD plasma control technology and hot-wire anemometer velocity measurements, a novel convenient method of local drag reduction (DR) measurement is proposed by measuring the single-point velocity within the linear region of the viscous sublayer. We analyze the premise of using the method, and the maximum effective measurement range of −73.1% < DR < 42.2% is obtained according to the experimental environment in this work. The local drag decreases downstream of the center of two adjacent upper electrodes and increases downstream of the upper electrodes. The magnitude of the local DR increases with increasing voltage and decreases as it moves away from the actuators. For the spanwise position in between, the streamwise distribution of the local DR is very dependent on the voltage. The variable-interval time-average detection results reveal that all bursting intensities are reduced compared to the baseline, and the amount of reduction is comparable to the absolute values of the local DR. Compared with previous results, we infer that the control mechanism is that many meandering streaks are combined together into single stabilized streaks.

Wall-Modeled Large-Eddy Simulation with Second-Order-Accurate Upwind Scheme

In aircraft aerodynamic design, it is essential for certification by analysis to estimate aircraft aerodynamic characteristics with high fidelity across the full flight envelope using computational fluid dynamics. Improving accuracy of the simulation of unsteady flows such as transonic buffet is one of the problems. Wall-modeled large-eddy simulation (WMLES) is expected to improve the accuracy. In this study, three quantitative requirements for the matching points, where LES feeds the wall model with flow variables, are proposed to ensure the accuracy of the WMLES with a second-order-accurate upwind scheme that is often used for engineering codes. These requirements are related to 1) matching point height, 2) the number of cells below the matching point, and 3) grid resolution at the matching point. The proposed requirements are assessed on a flat-plate turbulent boundary layer and a shock/turbulent boundary-layer interaction flow. As a result, it is clarified that all of the requirements are necessary to ensure the accuracy in terms of mean velocity, Reynolds stresses, and skin friction.

Analysis of a higher-order vorticity confinement scheme in flux correction form

This article presents a detailed comparison of the classical source-term formulation of higher-order Vorticity Confinement with a flux-correction version, through an application to a series of well-documented cases. Both formulations and their numerical implementation are presented first. Then the methods are applied to the simple case of the long-time advection of an inviscid and isentropic vortex. A shock-vortex interaction case is also computed to demonstrate the compatibility of the method with the shock-capturing properties of the baseline scheme. Both methods are finally applied to a ZDES mode 3 (Wall-Modelled LES) simulation of a zero-pressure-gradient flat-plate turbulent boundary layer, showing a better preservation of smaller-scale vortical structures with respect to standard higher-order numerical schemes. Furthermore, the flux-correction form of Vorticity Confinement significantly improves the prediction of skin friction with respect to both the baseline scheme and the classical source-term formulation, thus showing that the flux-correction form of confinement is essential for a reliable prediction of this quantity.

On the turbulent boundary layer over a flat plate at moderate Reynolds numbers

Two separate experimental campaigns of a spatially developing turbulent boundary layer under approximately zero-pressure-gradient at moderate Reynolds numbers (1700&amp;lt;Reθ&amp;lt;3400) are conducted with stereoscopic Particle Image Velocimetry (PIV) and one component Hot Wire Anemometry. This range of Reynolds numbers is found to be of particular interest for turbulent boundary layer control investigations. The motivations behind this work rely on the lack of recent studies that provide a rigorous experimental database on a flat plate turbulent boundary layer, openly available online. This is critical as, in most of the cases, the modification of the statistics resulting from turbulent boundary layer control strategies are compared with a smooth baseline reference. The statistics of the velocity fields, obtained with the two techniques, show a good match with the direct numerical simulation in literature results. We focused on the skin friction evaluation by means of Clauser's chart technique. The near wall turbulence activity and the associated coherent structures are investigated by means of the Variable Interval Time Averaging technique using the hot wire signal. The influence of the acquisition and algorithm parameters as well as the effect of the Reynolds number are reported. The logarithmic and outer structures are investigated by applying the Uniform Momentum Zones technique to the PIV dataset. The hierarchical distribution of the uniform momentum zones as a function of the wall distance as well as their variation with the Reynolds number confirm the validity of the attached eddy model even at the moderate Reynolds numbers of the current investigation.

Vortex evolution of flow past the near-wall circular cylinder immersed in a flat-plate turbulent boundary layer

The vortex evolutions and the turbulent characteristics in flow past the near-wall circular cylinder immersed in a flat-plate turbulent boundary layer are investigated with particle image velocimetry (PIV), with the objective of clarifying the interaction between the turbulent boundary layer flow and the near-wall cylinder wake. The Reynolds number based on the cylinder diameter D is 1.0×103, and three gap ratios (i.e., G/D=0.5, 1 and 2) are chosen for comparison at δ/D=6.7 where G is the gap size and δ is turbulent boundary layer thickness without the presence of cylinder. The proper orthogonal decomposition (POD) analysis is used to obtain phase-averaged flow fields, combining with the vortex identification method λci, which can capture effectively the evolution process of vortex. For three gap ratios, the cylinder is placed at the logarithmic-law layer of incoming flow, and the Karman-vortex sheets can be generated from the curling of the cylinder shear layers. At G/D=0.5 and G/D=1, the secondary vortex can be formed periodically in the wall due to the induction of the lower wake vortex. The vortex evolutions and turbulent characteristics are significantly affected by incoming turbulent boundary layer flow. The swirling strength of the wake vortices shed from the cylinder is enhanced with increasing G/D, and the swirling strength of the upper wake vortex is slightly bigger than that of the lower wake vortex due to velocity differences of incoming flow. The variation of the Strouhal number (St) is dependent on the gap ratio, and there is nearly 10.4% increase from St=0.211 at G/D=2 to St=0.233 at G/D=0.5, which is caused by the combined effects of the deflected gap flow and the velocity gradient. At large gap ratios, especially at G/D=2, the upstream high-velocity fluids interact with the cylinder wake, leading to strong velocity fluctuations behind the cylinder, and the magnitudes of production and turbulent diffusion in turbulent kinetic energy are increased, which also enhances turbulent transports behind the cylinder.

Turbulence characteristics of the ship air-wake with two different topside arrangements and inflow conditions

We investigate the effect of the Atmospheric Boundary Layer (ABL) and vessel topside arrangement on ship air-wake flow. The investigation is performed by comparing experimental results with two inflow conditions: a simulated ABL and a smooth-wall flat-plate turbulent boundary layer; and two simplified ship models: Simplified Frigate Ship model 2 (SFS2) and NATO-Generic Destroyer (NATO-GD). Particle Image Velocimetry (PIV) and point measurements over the landing deck center-line show that the ABL inflow increases the flow fluctuations but reduces the length of the wake. Furthermore, we observed an enhancement of turbulence energy on the ship landing deck when the ABL is simulated. The data also show that the topside arrangement, especially at the hangar elevation upstream of the landing deck, plays an essential role in the air-wake over the ship center line. There are significant differences in the flow re-circulation regions, turbulence structure and energy content. Based on a turbulence structure and energy spectrum analysis, we highlight regions with a possible increased safety risk for both models. Over the SFS2 center line, regions with an increased safety risk are located directly above the landing deck. Meanwhile, on the NATO-GD center line, these regions are located above the hangar elevation.

Properties of the compressibility and transport motion in wall-bounded turbulent flows at Mach 8

The compressibility effect and transport motion in highspeed turbulent boundary layer (TBL) is a fundamental problem because they dominate the average and statistical characteristics. Using the statistical methods and flow visualization technology, flat-plate TBLs at [Formula: see text] with high- and low-wall temperatures, [Formula: see text] and 1.9, are investigated based on the direct numerical simulation (DNS) datasets. Compared with previous studies, this study considers relative higher Mach number and strong cold wall temperature condition at the same time. First, the turbulent Mach number and turbulent intensity show that the compressibility effects are enhanced by the cooling process. Second, the high-order statistical moments and structure parameters confirm cold wall that causes stronger compressibility and the corresponding increased intensities of local streamwise and wall-normal transport motions. Finally, for uncovering the relationship between the compressibility effect and turbulent transport, more in-depth visualization analyses of velocity streaks are performed. It is found that ‘knot-like’ structures are generated when cooling the wall, and they lead to stronger intermittent, which results in the rapid increase of local compressibility effect and the wall-normal transport motion. Our research sheds light on providing a theoretical basis for further understanding the compressibility effects of TBL at high Mach number.

Turbulence Measurement of Two Velocity Components in a Boundary Layer by a Two Parallel Hot-Wire Anemometer

A novel hot-wire technique consisting of two parallel hot-wires is proposed. The gap between the two parallel wires is filled with an adhesive, which can be expected to improve the sensitivity to the flow angle at high velocity regions. In the present study, measurement accuracy of the two component velocity fluctuations is appraised experimentally in a flat-plate turbulent boundary layer. As a result, it was verified that the present probe can reproduce not only the DNS database but also the measurements obtained by the standard I- and X-type hot-wire probes. In addition, the proposed probe can be brought closer to the wall than the X-type one. However, it is observed that the turbulent intensity measurements in the streamwise direction are slightly reduced, and the power spectrum of the streamwise velocity fluctuations is attenuated accordingly in a high-frequency range. Thus, fluid-dynamical and thermal effects of the adhesive need to be investigated in more detail in the future.

A universal velocity profile for turbulent wall flows including adverse pressure gradient boundary layers

A recently developed mixing length model of the turbulent shear stress in pipe flow is used to solve the streamwise momentum equation for fully developed channel flow. The solution for the velocity profile takes the form of an integral that is uniformly valid from the wall to the channel centreline at all Reynolds numbers from zero to infinity. The universal velocity profile accurately approximates channel flow direct numerical simulation (DNS) data taken from several sources. The universal velocity profile also provides a remarkably accurate fit to simulated and experimental flat plate turbulent boundary layer data including zero and adverse pressure gradient data. The mixing length model has five free parameters that are selected through an optimization process to provide an accurate fit to data in the range $R_\tau = 550$ to $R_\tau = 17\,207$ . Because the velocity profile is directly related to the Reynolds shear stress, certain statistical properties of the flow can be studied such as turbulent kinetic energy production. The examples presented here include numerically simulated channel flow data from $R_\tau = 550$ to $R_\tau =8016$ , zero pressure gradient (ZPG) boundary layer simulations from $R_\tau =1343$ to $R_\tau = 2571$ , zero pressure gradient turbulent boundary layer experimental data between $R_\tau = 2109$ and $R_\tau = 17\,207$ , and adverse pressure gradient boundary layer data in the range $R_\tau = 912$ to $R_\tau = 3587$ . An important finding is that the model parameters that characterize the near-wall flow do not depend on the pressure gradient. It is suggested that the new velocity profile provides a useful replacement for the classical wall-wake formulation.

Thermochemical non-equilibrium effects on hypersonic shock wave/turbulent boundary-layer interaction

The research on shock wave/turbulent boundary-layer interactions is mainly limited to calorically perfect gases; little has been reported on the thermochemical non-equilibrium (real gas) effect. This effect is prominent at conditions of high Mach and Reynolds numbers. In this work, a household parallel solver for hypersonic thermochemical non-equilibrium flows with a Reynolds-averaged Navier–Stokes turbulence model is developed in which the coupling of turbulence with vibration and chemistry occurs under a gradient-law assumption. The thermal non-equilibrium is based on Park's two-temperature model, and the chemical non-equilibrium is based on Gupta's 11-species model. The method proposed in this paper is first validated using experimental data, including cases of a laminar cylinder flow at a high-enthalpy condition, a supersonic flat-plate turbulent boundary layer flow, a hypersonic transition flow, and a hypersonic compression corner flow at a low-enthalpy condition. This approach is then applied to assess the hypersonic flow characteristics past the 34° compression corner at a flight height of 30 km. Results show that the joint effects of turbulence and thermochemical non-equilibrium have a significant impact on the flow field organization, wall data, and separation length of the shock wave/boundary-layer interaction. Furthermore, the mechanism of the neck region accompanied by maximum heat flux, wall pressure and skin friction in both laminar and turbulent cases is well-interpreted. This study can be used as a reference tool for the aerodynamic design of future hypersonic vehicles accounting for multi-physics effects.

Error estimation of a homogenized streamwise periodic boundary layer

This work concerns the simulation of a homogenized streamwise periodic boundary layer which reduces the computational cost of direct numerical simulations of incompressible flat plate turbulent boundary layers. It expands upon the understanding of how the transpiration velocity changes dependent on whether a blending function is used to account for inner and outer self-similar scaling effects. With this rescaling correction, lower Reynolds number effects on the transpiration velocity are captured by the homogenized streamwise periodic boundary layer simulation.

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.