Research in the last decades has shown a strong interaction between near-wall turbulence and outer-layer large-scale motions in turbulent wall-bounded flows. In this paper, we propose a spatiotemporal multivariate approach based on state-of-the art methods of signal processing and a significantly enlarged data base to provide insight into the inner-outer interaction via superposition, bursts, and amplitude modulation. Spatially resolved, two-dimensional velocity fields within the viscous sublayer and the log layer are used to study spatial interactions. The temporal information provides insight into the temporal evolution of these features. In contrast to traditional studies, a noise-assisted multivariate empirical mode decomposition is applied to determine the involved scales. In this method, all velocity components of one time instant are simultaneously decomposed, which preserves intercomponent relations in the modal representations. In addition, the noise assistance ensures a temporal coherence of the resulting modes. Intermode comparisons, and thus the inner-outer interaction analysis, significantly benefit from this mode alignment by more precise findings, which is verified by comparisons with the univariate empirical mode decomposition results. The analysis reveals a considerable time-dependent behavior of the interaction phenomena with respect to the inner-outer correlation and the associated inclination angle. Regarding the superposition and the sweeps, the temporal variations are strongly linked to the rates of high-speed large scales to total large-scale fluctuations. The comparison to findings from purely temporal signals demonstrates distinct differences.

The alteration of the near-wall flow field of a turbulent boundary layer flow subjected to spanwise travelling transversal surface waves at a friction Reynolds number $Re_\tau \approx 1525$ is investigated. The results of a spatial noise-assisted multivariate empirical mode decomposition reveal that this flow control method periodically induces near-wall large-scale bursts while simultaneously lowering the energetic content of small-scale features. The increasing occurrence of intense large-scale ejections in the near-wall region is of particular importance for reducing the wall-shear stress since these ejections balance large-scale sweeps originating from the outer layer. Thus, they corrupt the outer-layer impact on the near-wall dynamics and, consequently, the overall fluctuation intensity at the wall is attenuated. This disturbed top-down momentum exchange is highlighted by an inner–outer interaction analysis, which further reveals an increased bottom-up communication provoked by the large-scale ejections. Moreover, it is shown that the periodic secondary flow field induced by the actuation interferes with the quasi-streamwise vortices in the near-wall region. The velocity gradients of the secondary flow field deform the vortices’ cross-section into an elliptic shape, which yields an unstable vortex state resulting in vortex disintegration. In combination with the effect of the large-scale ejections, the reduced number of quasi-streamwise vortices compared with the undisturbed boundary layer flow results in a decreased wall-normal momentum exchange and the widening and weakening of near-wall streaks. This yields a reduced fluctuation intensity in the near-wall region that lowers the overall wall-shear stress level.

The structure of turbulent wall-bounded flows is comprised by a complete spectrum of scales. Studies showed that the large-scale structures of the outer layer influence near-wall small-scale structures by several mechanisms, namely, superposition, amplitude and frequency modulation, and distortions by sweeps and ejections. Most analyses focus on one specific aspect of these phenomena, which means that the full interaction scenario is not comprehensively analyzed. In this paper, a method is presented which targets the combined effect of superposition, amplitude modulation, and distortions on the near-wall dynamics. It is validated against synthetic signals to provide a reliable tool for further analysis including the scale separation technique and the detection and elimination of large-scale influences. For the sake of clarity, the proposed method is applied to one-dimensional signals. Besides synthetic data, one-dimensional time-dependent streamwise velocity fluctuations of a near-wall and an outer-layer location extracted from a three-dimensional direct numerical simulation of a turbulent channel flow at ${\text{Re}}_{\tau }\approx 1000$ are analyzed. The paper shows that scale separation by the empirical mode decomposition approach and by conventional spectral filtering yields similar conclusions about the interaction mechanisms. However, the empirical mode decomposition is advantageous since it does not require any a priori knowledge about the analyzed flow and, thus, preprocessing and error sources are reduced. Furthermore, an approach for the investigation of the amplitude modulation is presented. Compared to existing techniques, it is superior in revealing this phenomenon due to a preceding removal of the influences of superposition and distortions and a different approach to determine the near-wall modulation. The near-wall and the outer-layer large-scale amplitudes are determined from the analytical large-scale signals, which are obtained by the Hilbert transform. Unlike conventional methods, this approach reveals the existence of a significant amplitude modulation across the channel half-height.

An extended experimental method is presented in which the micro-pillar shear-stress sensor (MPS ${}^3$ ) and high-speed stereo particle-image velocimetry measurements are simultaneously performed in turbulent channel flow to conduct concurrent time-resolved measurements of the two-dimensional wall-shear stress (WSS) distribution and the velocity field in the outer flow. The extended experimental setup, which involves a modified MPS ${}^3$ measurement setup and data evaluation compared to the standard method, is presented and used to investigate the footprint of the outer, large-scale motions (LSM) onto the near-wall small-scale motions. The measurements were performed in a fully developed, turbulent channel flow at a friction Reynolds number $R{e}_{\tau }=969$ . A separation between large and small scales of the velocity fluctuations and the WSS fluctuations was performed by two-dimensional empirical mode decomposition. A subsequent cross-correlation analysis between the large-scale velocity fluctuations and the large-scale WSS fluctuations shows that the streamwise inclination angle between the LSM in the outer layer and the large-scale footprint imposed onto the near-wall dynamics has a mean value of ${\overline{\Theta }}_x={16.53}^{\circ }$ , which is consistent with the literature relying on direct numerical simulations and hot-wire anemometry data. When also considering the spatial shift in the spanwise direction, the mean inclination angle reduces to ${\overline{\Theta }}_{xz}={13.92}^{\circ }$ .