A nonlinear Harmonic Navier-Stokes (HNS) framework is introduced for simulating instabilities in laminar spanwise-invariant shear layers, featuring sharp and smooth wall surface protuberances. While such cases play a critical role in the process of laminar-to-turbulent transition, classical stability theory analyses such as parabolized or local stability methods fail to provide (accurate) results, due to their underlying assumptions. The generalized incompressible Navier-Stokes (NS) equations are expanded in perturbed form, using a spanwise and temporal Fourier ansatz for flow perturbations. The resulting equations are discretized using spectral collocation in the wall-normal direction and finite-difference methods in the streamwise direction. The equations are then solved using a direct sparse-matrix solver. The nonlinear mode interaction terms are converged iteratively. The solution implementation makes use of a generalized domain transformation to account for geometrical smooth surface features, such as humps. No-slip conditions can be embedded in the interior domain to account for the presence of sharp surface features such as forward- or backward-facing steps. Common difficulties with Navier-Stokes solvers, such as the treatment of the outflow boundary and convergence of nonlinear terms, are considered in detail. The performance of the developed solver is evaluated against several cases of representative boundary layer instability growth, including linear and nonlinear growth of Tollmien-Schlichting waves in a Blasius boundary layer and stationary crossflow instabilities in a swept flat-plate boundary layer. The latter problem is also treated in the presence of a geometrical smooth hump and a sharp forward-facing step at the wall. HNS simulation results, such as perturbation amplitudes, growth rates, and shape functions, are compared to benchmark flow stability analysis methods such as Parabolized Stability Equations (PSE), Adaptive Harmonic Linearized Navier-Stokes (AHLNS), or Direct Numerical Simulations (DNS). Good agreement is observed in all cases. The HNS solver is subjected to a grid convergence study and a simple performance benchmark, namely memory usage and computational cost. The computational cost is found to be considerably lower than high-fidelity DNS at comparable grid resolutions.@en

Achieving and maintaining laminar flow on large swept lifting surfaces of subsonic aircraft poses a considerable challenge.

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This work focuses on the suppression of Tollmien-Schlichting (TS) waves in a two-dimensional laminar boundary layer using optimized unsteady suction and blowing jets as an Active Flow Control (AFC) method. The suppression of TS waves via this AFC system is enabled through two artificial intelligence-based optimization methodologies: Single-Step Deep Reinforcement Learning (SDRL) and Particle Swarm Optimization (PSO). The primary aim of this research is to assess the performance of these methods in optimizing the AFC parameters with respect to convergence rate, computational efficiency, and ability to find an optimum control state. The findings demonstrate the success of both methods in finding appropriate control parameters resulting in TS wave attenuation by up to 40 dB in the maximum convective instability amplitude for the linear and nonlinear stages of development. The comparative study in this paper presents the effectiveness of the SDRL algorithm in optimizing the AFC system for TS waves’ suppression and demonstrates that it can outperform PSO in terms of convergence rate and computational efficiency alongside a better performance in finding an improved optimum for linear control cases. However, the advantage of the SDRL-based controller over the PSO-based one diminishes in multi-frequency nonlinear control cases where the controller is located downstream and attempting to control highly amplified multi-modal TS waves.@en

This work explores the dynamic response of a turbulent boundary layer to large-scale reactive opposition control, at a friction Reynolds number of Reτ≈2240. A surface-mounted hot-film is employed as the input sensor, capturing large-scale fluctuations in the wall-shear stress, and actuation is performed with a single on/off wall-normal blowing jet positioned 2.4δ downstream of the input sensor, operating with an exit velocity of vj=0.4U∞. Our study builds upon the work of Abbassi et al. [Int. J. Heat Fluid Flow 67, 30 (2017)0142727X10.1016/j.ijheatfluidflow.2017.05.003] and includes a control-calibration experiment and a performance assessment using PIV- and PTV-based flow field analyses. With the control-off calibration-experiment conducted a priori, a transfer kernel is identified so that the velocity fluctuations that are to-be-controlled can be estimated. The controller targets large-scale high-speed zones in an "opposing"mode and low-speed zones in a "reinforcing"mode. A desynchronized mode was tested for reference and consisted of a statistically similar control mode, but without synchronization to the incoming velocity fluctuations. An energy-attenuation of about 40 % is observed for the opposing control mode in the frequency band corresponding to the passage of large-scale motions. This proves the effectiveness of the control in targeting large-scale motions: an energy-intensification of roughly 45% occurs for the reinforcing control mode instead, while no change in energy, within the wall-normal range targeted, appears with the desynchronized control mode. Moreover, direct measures of the skin-friction drag are inferred from PTV data. Results indicate that the opposing control logic yields the lowest wall-shear stress (3% lower than the desynchronized control, and 10% lower than the uncontrolled flow). Finally, a FIK-decomposition of the skin-friction coefficient revealed that the off-the-wall turbulence follows a consistent trend with the PTV-based wall-shear stress measurements, although biased by an increased shear in the wake of the boundary layer given the formation of a plume due to the jet-in-crossflow actuation.

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One of the most critical technological challenges embedded in the electrification of future aircraft revolves around the thermal management of batteries and fuel cells. An innovative idea involves using the aircraft’s aerodynamic surfaces to dissipate the extra heat, thereby reducing the impact that traditional thermal management systems (e.g. ram air heat exchanger) have on the overall aerodynamic efficiency of the aircraft. However, the limited experimental research addressing the influence of a heated surface on the stability and transition of the crossflow instability (CFI) hinders the assessment of the aerodynamic impact of this technology for future aircraft, where swept wings are ubiquitous. Thus, the objective of this work is to experimentally study the effect of a heated wall on the stability and final breakdown of CF vortices. To do so, experiments are conducted on a 45◦ swept flat plate wind tunnel model, where the surface temperature is increased by means of a surface-embedded electrical heater, yielding a mean wall-temperature ratio of T _w/T _∞ = 1.055. Overall, the experimental (i.e. HWA) and numerical (i.e. CLST) results show that wall heating leads to significant destabilization of the stationary CFI. Interestingly, a spectral analysis of the HWA signal reveals substantial amplification of the traveling CF mode under wall-heating conditions, which in turn appears significantly more destabilized than the stationary CF mode. Additionally, inspection of the high-frequency content in the HWA measurements indicates premature breakdown of the CF vortices and advancement of the laminar-turbulent transition by Δ _x/c _x = 6.3% with wall heating. The results presented in this work render a first insight into the impact of a non-adiabatic wall on the development of the crossflow instability and subsequent breakdown to turbulence.

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A new experimental facility named Swept Transition Experimental Platform (STEP) has been designed and built for detailed studies of crossflow instability and its interaction with surface irregularities and varying wall temperature conditions. The STEP is designed for use in the anechoic low-turbulence wind tunnel facility at the Delft University of Technology (TU Delft). The new facility consists of a swept flat-plate model with a movable leading edge capable of precisely translating to create forward/backward-facing step irregularities. In addition, the plate’s wall temperature can be adjusted to study the potential of thermal laminar flow control. An adjustable pressure body provides the favorable pressure distribution required to enhance the development of crossflow instability. Static pressure measurements are conducted to characterize the nominal pressure distribution. In addition, detailed hot-wire measurements and theoretical stability calculations reveal that the combination of discrete roughness elements, pressure distribution, and experimental facility allows for a detailed study of the development of crossflow instability in the linear and non-linear growth regime. Consequently, the STEP enables further fundamental research on laminar flow control at TU Delft.@en

A novel mechanism is identified, through which a spanwise-invariant surface feature (a two-dimensional forward-facing step) significantly stabilizes the stationary crossflow instability of a three-dimensional boundary layer. The mechanism is termed here as reverse lift-up effect, inasmuch as it acts reversely to the classic lift-up effect; that is, kinetic energy of an already-existing shear-flow instability is transferred to the underlying laminar flow through the action of cross-stream perturbations. To characterize corresponding energy-transfer mechanisms, a theoretical framework is presented, which is applicable to generic three-dimensional flows and surface features of arbitrary shape with one invariant spatial direction. The identification of a passive geometry-induced effect responsible for dampening stationary crossflow vortices is a promising finding for laminar flow control applications.

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This work examines the control of cross-flow instabilities (CFIs) and laminar–turbulent transition on a swept wing, through the plasma-based base flow modification (BFM) technique. The effect of experimentally derived plasma body forces on the steady boundary layer base flow is explored through numerical simulations. Linear stability theory is subsequently used to predict the net BFM effect on CFIs. Based on these preliminary predictions, experiments are conducted in a low-turbulence wind tunnel where a spanwise-invariant plasma actuator is installed near the wing leading edge and operated at constant input voltage and frequency. Various flow parameters governing the plasma-based BFM technique are investigated, namely the Reynolds number, angle of attack and wavelength of excited stationary CFI modes. Stationary and travelling CFIs are quantified by planar particle image velocimetry while the transition topology and location are recorded by infrared thermography. The results confirm the stabilising effect of BFM on the swept-wing boundary layer. However, the plasma-based BFM is found to render the boundary layer more susceptible to travelling CFIs. In the presence of both net BFM effect and intrinsic plasma unsteady perturbations, the plasma-based BFM technique achieves transition delay with specific combinations of Reynolds number, angle of attack and wavelength of excited stationary CFI modes. The present findings provide insights into the fundamental principles of operating plasma actuators within the context of BFM control.@en

This study reports the first time-resolved particle image velocimetry characterization of a planar two-phase mixing layer flow, whose velocity field is measured simultaneously in gas and liquid streams. Two parallel air and water flows meet downstream of a splitter plate, giving rise to an initially spanwise invariant configuration. The aim is to elucidate further the mechanisms leading to the flow breakup in gas-assisted atomization. The complete experimental characterization of the velocity field represents a database that could be used in data-driven reduced-order models to investigate the global behaviour of the flow system. After the analysis of a selected reference case, a parametric study of the flow behaviour is performed by varying the liquid and gas Reynolds numbers, and as a consequence also the gas-to-liquid dynamic pressure ratio , shedding light on both time-averaged (mean) and unsteady velocity fields. In the reference case, it is shown that the mean flow exhibits a wake region just downstream of the splitter plate, followed by the development of a mixing layer. By increasing both and, the streamwise extent of the wake decreases and eventually vanishes, the flow resulting in a pure mixing layer regime. The spectral analysis of the normal-to-flow velocity fluctuations outlines different flow regimes by variation of the governing parameters, giving more insights into the global characteristics of the flow field. As a major result, it is found that at high and values, the velocity fluctuations are characterized by low-frequency temporal oscillations synchronized in several locations within the flow field, which suggest the presence of a global mode of instability. The proper orthogonal decomposition of velocity fluctuations, performed in both gas and liquid phases, reveals finally that the synchronized oscillations are associated with a low-frequency dominant flapping mode of the gas-liquid interface. Higher-order modes correspond to interfacial wave structures travelling with the so-called Dimotakis velocity. For lower gas Reynolds numbers, the leading modes describe higher frequency fingers shedding at the interface.

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The influence of a wall-embedded Helmholtz resonator on the development and stability of Tollmien-Schlichting (TS) waves is investigated numerically and experimentally for a range of frequencies extending from below to above resonance. Interactions are found to be limited in the near-wall region and toward the trailing edge of the resonator orifice while at the same time being linear nature. The dynamic response of the flow-excited resonator is shown to have a fixed phase relation with respect to the TS-waves, indicating that only amplification of the latter can be achieved. The same resonant behavior is maintained regardless of whether the resonator is flow-excited or acoustically excited. Thus, it is suggested that pressure perturbations propagate perpendicularly and acoustically within the resonator throat and cavity. The amplification observed in the vicinity of the resonator displays features typical of TS-wave scattering; however, it is confirmed that this is not solely the result of mean flow distortion due to the geometry and recirculation region. Instead, the results indicate that the phenomenology is a consequence of the combination of scattering, localized non-modal growth, and wall-forcing in the wall-normal direction due to resonance.

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This work presents the first experimental characterization of the flow field in the vicinity of periodically spaced discrete roughness elements (DRE) in a swept wing boundary layer. The time-averaged velocity fields are acquired in a volumetric domain by high-resolution dual-pulse tomographic particle tracking velocimetry. Investigation of the stationary flow topology indicates that the near-element flow region is dominated by high- and low-speed streaks. The boundary layer spectral content is inferred by spatial fast Fourier transform (FFT) analysis of the spanwise velocity signal, characterizing the chordwise behaviour of individual disturbance modes. The two signature features of transient growth, namely algebraic growth and exponential decay, are identified in the chordwise evolution of the disturbance energy associated with higher harmonics of the primary stationary mode. A transient decay process is instead identified in the near-wake region just aft of each DRE, similar to the wake relaxation effect previously observed in two-dimensional boundary layer flows. The transient decay regime is found to condition the onset and initial amplitude of modal crossflow instabilities. Within the critical DRE amplitude range (i.e. affecting boundary layer transition without causing flow tripping) the transient disturbances are strongly receptive to the spanwise spacing and diameter of the elements, which drive the modal energy distribution within the spatial spectra. In the super-critical amplitude forcing (i.e. causing flow tripping) the near-element stationary flow topology is dominated by the development of a high-speed and strongly fluctuating region closely aligned with the DRE wake. Therefore, elevated shears and unsteady disturbances affect the near-element flow development. Combined with the harmonic modes transient growth these instabilities initiate a laminar streak structure breakdown and a bypass transition process.

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This investigation explores the utility of Alternating Current, Dielectric Barrier Discharge (AC-DBD) plasma actuators for producing three-dimensional disturbances of a desired spanwise wavelength via superposition. The technique utilizes two pairs of exposed and covered electrodes on a single dielectric layer arranged in streamwise succession. Two-dimensional forcing is achieved through operation of the upstream, spanwise uniform electrode pair, while three-dimensional forcing at a prescribed spanwise wavelength is attained by operating both electrode pairs simultaneously, with the downstream actuator spanwise modulating the upstream, two-dimensional output. The ability to produce disturbances of different spanwise wavelengths but with equal streamwise wavelength, frequency and total momentum is established through a combined characterization effort that considers quiescent and in-flow conditions. A demonstration of the technique in an exemplary wall-bounded shear flow, a laminar separation bubble, is provided, revealing spanwise wavelength dependent disturbance growth in the flow that could be exploited for performance gains in future flow control endeavours. Graphical abstract: [Figure not available: see fulltext.]

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A novel method for control of convective boundary layer instabilities using metamaterial concepts is investigated. Attenuation of Tollmien-Schlichting (TS) waves with surface-embedded one-dimensional phononic crystals (PCs) is theoretically and numerically modeled, capitalizing on the inherent frequency band stop of PCs. The PC is tuned to the targeted TS wave characteristics through the use of analytical models derived from transfer matrix and interface response theories, verified using a finite elements analysis. The interaction between TS waves and a single PC is investigated using coupled two-dimensional fluid structure interaction simulations in the frequency domain. It is shown that TS waves are either amplified or attenuated depending on whether the PC free-face surface displacement and unsteady perturbation pressure at the wall are in-phase or out-of-phase, respectively. The perturbation pressure acts solely as the driver for the mechanical oscillation of the PC. The emerging hydrodynamic coupling between TS waves and the PC is found to be governed by a combination of the Orr mechanism and wall-normal velocity linear superposition near the wall. Finally, a metasurface comprised of an array of streamwise-distributed PCs is evaluated, resulting in an amplitude growth delay of 11.3% of the TS wavelength along the metasurface extent.

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The Parabolized Stability Equations (PSE), Adaptive Harmonic Linearized Navier-Stokes (AHLNS) and Harmonic Navier-Stokes (HNS) solvers are used to analyze the linear and nonlinear stability of swept-wing boundary layers under the influence of smooth wall deformations of varying size and geometry. Special attention is given to the validity of the slowly varying flow assumption of PSE via a comparison with AHLNS and HNS results. The surface deformations analyzed in this work are found to affect the development of the primary stationary crossflow instability mode as well as higher harmonics. Analysis of the locally most amplified mode reveals successive modulation of the growth rate in the vicinity of the surface deformation. This process was found to be largely governed by linear terms and driven by the base flow modification due to the deformed wall. Similarly, the base flow modification causes higher harmonics to experience a significant destabilization. This is followed by stabilization as nonlinear interactions become dominant. The PSE methodology proved capable of predicting the stability response for small wall deformations with only minor amplitude discrepancies compared to HNS results. The main difference was found to occur in the wall-normal velocity profiles of the mean flow distortion mode. The deviations of the PSE results compared to harmonic stability methods increased as the protuberance was made steeper. Moreover, the PSE framework was not able to converge for all cases nonlinearly.@en

The wake-mixing layer flow developing past a splitter plate separating two parallel gas and liquid co-flowing currents is experimentally investigated in this work. Time-resolved particle image velocimetry (TR-PIV) measurements of the two-phase velocity field are simultaneously performed in gas and liquid streams, shedding light on both mean (time-averaged) and unsteady features of the flow configuration. A selected reference case is first analyzed, revealing the presence of a wake region within the flow field, right behind the splitter plate. By progressively moving downstream along the streamwise G direction, a pure mixing layer region is retrieved. The effect of two governing flow parameters, namely the gas Reynolds number '46 and the gasliquid dynamic pressure ratio ", is then investigated, focusing first on the mean flow topology. It is found that the streamwise extension of the wake GF is a monotonic decreasing function of '46, and it vanishes for the highest '46 value considered, the two-phase flow resulting in a pure mixing layer regime. The flow unsteady development is then characterized by means of the spectral analysis of normal-to-flow (i.e. along H direction) velocity fluctuating quantities E0 ¹C°, performed in both gas and liquid flows. As major results, it is found that frequency spectra are characterized by a high frequency content in the low '46 configuration, the peak frequency depending on the streamwise location G. On the other hand, by progressively increasing '46 the peak frequency shifts to lower values, and it becomes independent on the specific spatial location by increasing ". It is found that, at high '46 and " values, velocity fluctuations are characterized by low frequency temporal oscillations synchronized over a large spatial extent of the flow field. The different regimes outlined by variation of the flow governing parameters are found to be consistent with convective/absolute instability behaviors highlighted by spatiotemporal linear stability analyses of the flow recently presented in literature.

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The present work details the steady and unsteady flow topology in the vicinity of an array of periodically spaced super-critical (i.e. causing flow tripping) discrete roughness elements (DRE) applied in a swept wing boundary layer. The stationary flow field is acquired by means of high-magnification dual-pulse tomographic particle tracking velocimetry (3D-PTV), while the unsteady instabilities are investigated through high-resolution hot wire anemometry (HWA). The 3D-PTV time-averaged velocity fields, indicate that the near-element flow region is dominated by the alternation of high- and low-speed streaks. A high-speed region substitutes the wake development shortly downstream of the DRE location, due to the high-speed streaks merging. This initiates a region of strong unsteady fluctuations that expands in the spanwise and wall-normal directions, ultimately leading to the boundary layer transition to turbulence. The spectral content of the stationary flow structures is investigated through a spanwise spatial Fourier transform. The extracted spectra and instability amplitudes, indicate the presence of non-modal mechanisms in the near-element stationary wake region. Nonetheless, the temporal spectral analysis of the HWA velocity signal, identifies the presence of strongly tonal shedding mechanisms initiating and the unsteady instabilities the element vicinity. Their rapid downstream growth and evolution retains a fundamental role in the transitional process. @en

This work presents the first reported experimental characterization of the flow field in the direct vicinity of discrete roughness elements (DRE), in a swept wing boundary layer. High magnification tomographic Particle Tracking Velocimetry (3D-PTV) measurements are used to acquire time-averaged velocity and standard deviation fields in a 3D volume directly aft of the DRE elements. The collected data detail the near-element flow topology, providing information on the developing wake and emerging flow structures, their organization and amplitude evolution. A transient growth behaviour is identified in the element wake, while onset and growth of crossflow instabilities is observed further downstream. As such, the near element flow is confirmed to be a fundamental part of the receptivity process, contributing in setting the initial amplitudes for the crossflow instability evolution.

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Two different plasma actuation strategies for producing near-wall flow oscillations, namely the burst-modulation and beat-frequency mode, are characterized with planar particle image velocimetry in quiescent air. Both concepts are anticipated to work as non-mechanical surrogates of oscillating walls aimed at turbulent flow drag reduction, with the added benefit of no moving parts, as the fluid is purely manipulated by plasma-generated body forces. The current work builds upon established flow-control and proof-of-concept demonstrators, as such, delivering an in-depth characterization of cause and impact of the plasma-induced flow oscillations. Various operational parameter combinations (oscillation frequency, duty cycle and input body force) are investigated. A universal performance diagram that is valid for plasma-based oscillations, independent of the actuation concept is derived. Results show that selected combinations of body force application methods suffice to reproduce oscillating wall dynamics from experimental data. Accordingly, the outcomes of this work can be exploited to create enhanced actuation models for numerical simulations of plasma-induced flow oscillations, by considering the body force as a function of the oscillation phase. Furthermore, as an advantage over physically displaced walls, the exerted body force appears not to be hampered by resonances and therefore remains constant independent of the oscillation frequency. Hence, the effects of individual parameter changes on the plasma actuator performance and fluid response as well as strategies to avoid undesired effects can be determined.

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Experiments have been conducted on a swept wing model in a low-turbulence wind tunnel at chord Reynolds number of to investigate the unsteady interaction of a forward-facing step (FFS) with incoming stationary crossflow (CF) vortices. The impact of varying the FFS height on the development and growth of primary and secondary CF disturbances and the ensuing laminar-turbulent transition is quantified through detailed hot-wire anemometry and infrared thermography measurements. The presence of the FFS results in either a critical (i.e. moderate transition advancement) or a supercritical behaviour (i.e. transition advancing abruptly to the FFS location). The arrival of the forced stationary CF vortices at the step is accompanied by their amplification. Unsteady analysis for the critical cases indicates temporal velocity fluctuations following closely the development of the baseline configuration (i.e. agreeing with the development of secondary instabilities). Consequently, laminar breakdown originates from the outer side of the upwelling region of the CF vortices. In contrast, for the supercritical FFS, the laminar breakdown unexpectedly originates from the inner side of the upwelling region. Evidence points to an unsteady mechanism possibly supported by locally enhanced spanwise-modulated shears and the recirculation region downstream of the FFS edge. This mechanism appears to govern the abrupt tripping of the flow in supercritical step cases. The findings in this work provide insight into the unsteady FFS-CF vortex interaction, which is pivotal to understanding the influence of an FFS on the laminar-turbulent boundary-layer transition in swept aerodynamic surfaces.

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In the present work, planar and tomographic PIV are used to investigate how the organisation of wall turbulence is altered when actuators are operated with the objective of reducing the skin friction drag. When the wall is mechanically oscillated in the spanwise direction, high-resolution planar PIV enable the direct measurement of wall shear and a 15% reduction of skin friction is observed. The use of tomographic PIV enables access to the three dimensional organisation of low- and high-speed streaks, along with ejection events and associated hairpin vortices. These observations help forming a conceptual model of the salient drag reduction mechanism, whereby hairpin auto-generation is inhibited through a tilting action at the tail of low-speed streaks. The second part of the study documents an effort to surrogate the mechanical oscillation by means of a densely distributed array of AC-DBD plasma actuators. The latter are first characterised in quiescent flow, where the induced velocity distribution is obtained and compared to the solution of the classical second Stokes problem that models the mechanical oscillation. The induced peak of spanwise velocity is found to surpass the velocity of the oscillating wall. However, the wall jet height develops further away from the wall. More importantly, the spatially inhomogeneous distribution of the unsteady body force produces an unwanted lattice of starting streamwise vortices. The latter are deemed to be detrimental for the purpose of drag reduction, compared to the orderly and homogeneous sideways motion induced by mechanical wall motion. The application of the AC-DBD actuator currently leads to a pronounced momentum deficit in the logarithmic region and increases skin friction. Finally, further research directions are anticipated, that potentially circumvent the formation of streamwise vortices by means of AC-DBD actuators operating in steady regime. @en