This study investigates the aerodynamic noise control mechanisms of a forced rotating circular cylinder at a subcritical Reynolds number ($Re = 4.7 \times 10^4$) using large-eddy simulation coupled with the Ffowcs Williams–Hawkings acoustic analogy, validated by wind tunnel experiments. Five representative rotation ratios, $\alpha =0$, $0.5$, $1$, $2$ and $4$, are analysed to relate wall-pressure fluctuations and wake organisation to the radiated noise. At $\alpha =0.5$, the natural shedding tone separates into two components, $St_{01}\approx 0.18$ and $St_{02}\approx 0.23$. Their three-dimensional (3-D) structures exhibit spanwise phase dislocation and reduced coherence, explaining the decrease in tonal radiation despite locally enhanced wall-pressure fluctuations. Coherent shedding partially recovers at $\alpha =1$, whereas $\alpha =2$ gives the strongest tonal-noise reduction among the investigated cases, accompanied by weakened wake fluctuations, spanwise coherence and wall–wake correlation. At $\alpha =4$, the classical Kármán mode is suppressed and localised near-wall helical structures are associated with a broadband elevation near $St\approx 0.1$. The results show that rotation controls noise through changes in both unsteady-loading amplitude and 3-D source organisation.

Model-based active flow control requires predictive models that are accurate, stable and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through reduced-order models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then learn a time-stepping predictor for the dynamics in the latent space. Here, we study how the choice of the spatial encoder affects the predictability of the resulting latent coordinates for wake flows under control inputs. Using two actuated two-dimensional wake configurations, a simplified truck wake and the fluidic pinball, we compare proper orthogonal decomposition (POD) against nonlinear convolutional autoencoders (CAEs) and two types of variational autoencoders for compression, and evaluate several temporal predictors based on long short-term memory networks. The CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce a latent dynamics that is more irregular and with broadband spectral content. As a consequence, long-horizon forecasts degrade faster and show a higher probability of catastrophic divergence than POD-based models. The POD yields smoother latent trajectories that are easier to learn and extrapolate, leading to more reliable predictions beyond the short-term regime. These results reveal a clear trade-off between compactness and forecast accuracy, and suggest that the stability of the latent dynamics prediction can outweigh maximal compression. This is particularly relevant for control strategies rooted in forecasts of the dynamics, such as model predictive control and reinforcement learning. The findings provide practical guidance for designing actuation-aware, hardware-feasible predictive ROMs for real-time flow control.

We demonstrate that enhanced inter-scale energy transfer – a defining hallmark of turbulence – can be actively induced in Navier–Stokes flows even at Reynolds numbers of order unity. By reinterpreting the spectral energy flux as mechanical work resulting from the alignment between turbulent stress and large-scale rate of strain tensors, we show that, by actively enforcing geometric alignment between these tensors and amplifying the perturbation-induced stress, the flow exhibits scale-to-scale energy flux magnitudes comparable to those reported in the weakly turbulent regime of two-dimensional flows, even in the absence of dominant inertia. This study indicates that the mechanisms underpinning spectral energy flux are not exclusive to high-Reynolds-number turbulence but can extend into regimes previously deemed dynamically trivial. Our result also reveals a generic mechanism for directly accessing the same stress–strain-rate energy-flux pathway that underlies classical turbulence, but without the need for inertial dominance.

The dynamic response of a zero-pressure-gradient turbulent boundary layer (TBL) to a large-scale perturbation in the outer region was investigated experimentally. The baseline TBL had a moderate Reynolds number such that there were no naturally occurring energetic large-scale structures (LSS) present. An active plasma-based actuator was then placed in the outer region of the TBL to introduce a periodic, spanwise-uniform, synthetic LSS. Thus this novel actuation scheme provides a new tool by which to experimentally examine an idealised case of outer–inner layer interaction within the TBL. The TBL response to this synthetic LSS was investigated using a combination of planar particle image velocimetry and spanwise offset hot-wires, over a large streamwise extent downstream of the actuator device. Phase-locked analysis was implemented to isolate and measure the streamwise development of the imposed synthetic LSS and resulting phase-dependent changes in turbulence amplitudes throughout the TBL. A strong correlation was observed between large-scale motions near the wall, which were found to be linearly superimposed from the outer-region synthetic LSS, and a periodic modulation of the turbulence amplitude. Further, this periodic modulation was found to be linked to phase-dependent changes in both the production and transport of turbulence driven by the induced streamwise and wall-normal large-scale motions. The phase speed of these induced large-scale motions, coupled with intermittent changes to spanwise coherence near the wall, also revealed a clear, but transient, effect of the outer-region synthetic LSS on the near-wall cycle dynamics. Overall, these results serve to characterise the influences, and limitations, of idealised outer–inner interactions on global TBL dynamics, and highlight considerations for the design and optimisation of future flow control techniques.

We present a phase-based framework for reducing the pressure fluctuations within a spanwise-periodic supersonic turbulent cavity flow with an incoming free-stream Mach number of 1.4 and a depth-based Reynolds number of $10^4$. Open cavity flows exhibit large fluctuations due to the feedback between the shear-layer instabilities and the acoustic field. The dominant flow physics includes the formation, convection and impingement of large-scale spanwise-oriented vortical structures into the aft wall. We implement a phase-reduction approach to identify the flow response about this time-varying convective process by defining a phase variable using dynamic mode decomposition. Three-dimensional impulse perturbations with various spanwise actuation wavenumbers, $\beta$, are introduced from the cavity leading edge to characterise the phase advancement or delay of convection. We perform open-loop flow control through unsteady blowing using actuation frequencies slightly different from the vortex-convection frequency to disrupt the feedback loop. After designing a phase-sensitivity-based actuation waveform optimised for quick flow modification, we investigate the speed of fluctuation reduction and compare it with a sinusoidal waveform actuation. At a spanwise actuation wavenumber of $\beta =2\pi$, both perform similarly, achieving a 46 % reduction of pressure fluctuations within five convective times. At $\beta =\pi$, the phase-sensitivity-based actuation performs better by achieving a 40 % reduction compared with the 30 % with a sinusoidal waveform within six convective times. The present method explicitly targets the temporal dynamics to achieve rapid suppression within a few convective times. This study shows the potential of phase-based analysis for timing-based (event-based) flow control and rapid flow modification of unsteady turbulent flows.

This study investigates the application of deep reinforcement learning (DRL) for active flow control in a three-dimensional NACA0012 wing section with periodic spanwise boundary conditions at low Reynolds number ($ \textit{Re}_c=1000$) and high angle of attack ($\text{AoA}=20^\circ$), where the flow exhibits massive separation, strong vortex shedding and a chaotic three-dimensional wake. The baseline configuration is validated against previous numerical studies, showing the accuracy of the computational set-up. Two DRL control policies are trained with different reward functions, leading to fundamentally different control strategies. The DRL set-up uses a multi-agent reinforcement learning framework to coordinate distributed actuators along the wing span. In the first case study, when the reward prioritises drag reduction, agents delay the leading-edge separation and stabilise the wake, reducing drag by $21.1\,\%$ and lift fluctuations by $54.1\,\%$ while maintaining baseline lift. In the second case, when the reward targets lift enhancement instead, agents synchronise actuations with vortex shedding, forming leading-edge instabilities that increase lift by $42.3\,\%$, albeit at the cost of higher fluctuations and slightly increased drag. A comparison with classical open-loop control further demonstrates that DRL autonomously determines physically meaningful and interpretable strategies consistent with established mechanisms in the literature. To the best of the authors’ knowledge, this is the first study in which a fully three-dimensional computational fluid dynamics simulation has been employed to train a DRL model for active flow control in wings, suggesting promising directions for extending DRL-based strategies to higher Reynolds numbers and more complex wing configurations where prior physical knowledge may be limited.

An experimental investigation is conducted in a wind tunnel on a NACA0012 airfoil with a partially flexible polydimethylsiloxane membrane leeward surface extended from 16.7 % to 83.3 % of the chord length. Aerodynamic forces, membrane deformation and the surrounding flow field are measured simultaneously. The results show that membrane vibration effectively reduces the extent of the recirculation zone, thereby improving aerodynamic performance. Specifically, the stall angle is delayed by $3^\circ$, and the maximum lift coefficient is increased by 12.4 % compared with that of the rigid airfoil. Novel insights into the flow–structure interaction are established from both spatial and temporal perspectives. Spatially, comparisons across angles of attack reveal that membrane vibrations driven by strong pressure fluctuations near the trailing edge can propagate upstream, accompanied by modifications in the distribution of turbulent kinetic energy and enhanced flow mixing. Temporally, a detailed analysis of the strongly periodic membrane motion and unsteady flow structures near stall further demonstrates that the membrane dynamics is tightly coupled with the evolution of the leading-edge vortex. This coupling is associated with the modulation of coherent flow structures through periodic absorption and release of mechanical energy. Overall, the flexible membrane can provide effective flow control by reorganising the spatio-temporal distribution of energy within the flow via flow–structure interaction, without external energy input. The findings provide insights into potential low-energy flow-control strategies.

This study employs synthetic jet actuation (SJA) to control large-scale flow separation on the suction side of a NACA0015 aerofoil at a Reynolds number of 2.1 $\times$ $10^5$ and an angle of $18^\circ$. The underlying control mechanism is investigated using large-eddy simulations to resolve the dynamics of jet-induced coherent structures associated with the low-frequency actuation. During the periodic blowing and suction cycle, two distinct types of spanwise coherent vortices are identified: blowing-induced vortices (BIVs) and suction-induced vortices (SIVs), which differ significantly in spatial distribution and energy content. As these vortices are convected downstream at speeds comparable to the free-stream velocity, BIVs exhibit a significantly slower rate of energy decay, whereas SIVs dissipate rapidly, particularly near the trailing edge. Triple decomposition analysis shows that energy addition is primarily associated with the coherent velocity components. Notably, BIVs exhibit a stronger entrainment capacity, enhancing momentum exchange between the separated shear layer and outer flow via coherent Reynolds shear stresses. This intensified exchange facilitates the outward transport of low-momentum fluid, effectively enhancing aerodynamic performance and delaying flow separation. Furthermore, spectral proper orthogonal decomposition reveals distinct energy peaks centred at the actuation frequency and its harmonics. Among the two vortex types, BIVs contribute most of the coherent spectral energy, highlighting their critical role in the overall effectiveness of the flow control. These findings elucidate the flow organisation and modulation mechanisms associated with low-frequency SJA under deep-stall conditions, and provide a physical interpretation of the observed reorganisation of the separated flow.

Stall flutter is suppressed on a NACA0012 airfoil at a low Reynolds number (Re $=$ 1000–5000) through a counter-intuitive strategy: targeted enhancement of the second leading-edge vortex (sLEV) via phase-optimised surface morphing, in contrast to the conventional paradigm of suppressing vortices. Two distinct flow topologies are identified: (I) boundary-layer-eruption-induced leading-edge vortex (LEV) shedding at large amplitudes ($A_\alpha$ ≥ 10°), accompanied by sLEV formation, and (II) bluff-body-type shedding at small amplitudes ($A_\alpha$ ≤ 5°) without sLEV. A new circulation scaling is introduced to identify topology I, which drives severe structural oscillations. Flow-structure analysis reveals a novel sLEV–trailing-edge vortex (TEV) interaction mechanism that mitigates stall flutter: strengthening sLEV triggers a chain effect that weakens the TEV, elevates the aerodynamic moment trough and disrupts the feedback loop sustaining the oscillation. An energy-based map is constructed to characterise the boundary of stall flutter across control parameters and to enable rapid prediction of control performance. By combining the clustering-based vortex-induced load partitioning method with this energy framework, an optimal phase indicator is established: actuation synchronised with the peak sLEV-induced moment consistently yields near-optimal control performance, providing a direct quantitative link between pre-control flow features and optimal control parameters. A phase-locked-loop strategy further demonstrates that surface morphing with an amplitude an order of magnitude smaller than the characteristic LEV scale can nonetheless achieve complete suppression of stall flutter within the topology I regime. These findings not only demonstrate the efficacy of surface morphing control but also offer new physical insight into stall flutter dynamics and their precision control via targeted vortex interactions.

Blended-wing-body (BWB) aircraft with distributed propulsion offers significant potential for aerodynamic efficiency. However, this tightly integrated configuration inherently operates under boundary layer ingestion (BLI) conditions. The ingested thick fuselage boundary layer, coupled with the strong aerodynamic interactions between the S-shaped intake and wing, generates adverse pressure gradients at the inlet alongside low total pressure recovery coefficients and high outlet distortion. This study investigates integrated flow control under high-altitude flight conditions using a BWB aerofoil integrated with a semi-embedded S-shaped intake model, incorporating energy analysis. During cruise, strong adverse pressure gradients between the wing shock wave and intake cause distinct lip separation, resulting in a low total pressure recovery coefficient and high distortion. Distributed dual-row suction generates secondary flow generates distributed secondary flow near the separation point with equivalent energy consumption. This enhances fuselage boundary layer mixing, reduces near-wall adverse pressure gradients and improves the total pressure recovery coefficient. The integration of internal jet control synergistically augments the benefits of external wing suction via distinct spatial mechanisms: central jets replenish core flow kinetic energy to suppress separation and improve the total pressure recovery coefficient, while side jets enhance mixing between separation zones and mainstream flow, mitigating secondary swirl losses and substantially reducing distortion at the aerodynamic interface plane (AIP). Energy analysis confirms that a modest energy input (equivalent to 7.4% of the mainstream kinetic energy) yields a significant increase in intake thrust, while simultaneously reducing total pressure and swirl distortion.

We perform causal analysis on the low-dimensional Galerkin model for shear flow developed by Moehlis et al. (New J. Phys., vol. 6, 2004, 56). Our method integrates both equation-based analysis and the proposed Galerkin-based Granger causality (GGC) to investigate the effect of the nonlinear terms on the dynamics. Two types of quadratic interactions are identified: a fully triadic interaction and a modulated two-mode coupling. The propagation of these interactions through the nonlinear dynamics leads to a directed cause-and-effect network. Furthermore, the relative importance of each mode amplitude on the dynamics of the target mode is quantified. This analysis provides a deeper understanding of the nonlinear dynamics and distills control opportunities. To demonstrate the applicability of the proposed GGC to realistic flows where Galerkin projection is impractical, a turbulent lid-driven cavity flow is further studied. We foresee applications of the proposed causal analysis framework as valuable tools for Galerkin modelling – guiding investigations of modal causality, prediction uncertainty, model-order reduction and control design.

This study experimentally investigates the aerodynamic drag reduction capabilities of distributed micro-roughness (DMR) coatings on a streamlined model, utilising the 1-m magnetic suspension and balance system (MSBS) at Tohoku University. Previous direct numerical simulations indicated that DMR can mitigate turbulent-energy growth by suppressing Tollmien–Schlichting waves and influencing the breakdown of streamwise vortices. The present work provides the first experimental validation of these effects using an interference-free MSBS, which is essential for accurate measurement in the laminar and transitional regimes. A streamlined model was tested with two rows of artificial tripping tape to induce transition; the DMR height was approximately 1 % of the local boundary layer thickness, significantly smaller than typical roughness elements. Direct aerodynamic drag measurements using the MSBS revealed a substantial reduction of up to 43.6 % within the transitional flow regime. Crucially, integrated analysis using wall-resolved large eddy simulations (LES) and dynamic oil-flow visualisation confirmed that this benefit does not mainly originate from the suppression of flow separation. The LES drag decomposition established that the total pressure-drag budget is subordinate to skin friction, a finding complemented by oil-flow observations, which revealed qualitatively similar flow patterns regardless of the surface condition. Consequently, the observed drag reduction is primarily ascribed to friction drag reduction achieved through the modification of the boundary layer state. These findings provide compelling experimental evidence for the efficacy of DMR and offer valuable insights for optimising surface designs for passive flow control.

Neural network observers (NNOs) are proposed for online estimation of fluid flows, addressing a key challenge in flow control: obtaining flow states online from a limited set of sparse and noisy sensor data. For this task, we propose a generalisation of the classical Luenberger observer. In the present framework, the estimation loop is composed of subsystems modelled as neural networks (NNs). By combining flow information from selected probes and a neural network surrogate model (NNSM) of the flow system, we train NNOs capable of fusing information to provide the best estimation of the states, that can in turn be fed back to a neural network controller (NNC). The NNO capabilities are demonstrated for three nonlinear dynamical systems. First, a variation of the Kuramoto–Sivashinsky (KS) equation with control inputs is studied, where variables are sparsely probed. We show that the NNO is able to track states even when probes are contaminated with random noise or with sensors at insufficient sample rates to match the control time step. Then, a confined cylinder flow is investigated, where velocity signals along the cylinder wake are estimated by using a small set of wall pressure sensors. In both the KS and cylinder problems, we show that the estimated states can be used to enable closed-loop control, taking advantage of stabilising NNCs. Finally, we present a legacy dataset of a turbulent boundary layer experiment, where convolutional NNs are employed to implement the models required for the estimation loop. We show that, by combining low-resolution noise-corrupted sensor data with an imperfect NNSM, it is possible to produce more accurate and robust estimates. Our approach presents better robustness to noise when compared with direct reconstructions via super-resolution NNs and predictions from graph NNs and Fourier neural operators.

Fluidic propulsion based on bladeless fan technology has shown strong potential to generate sufficient thrust for lightweight commuter aircraft. Bladeless fans work by entraining and directing ambient air, a feature that can be harnessed not only for thrust generation but also to augment lift. This research investigates the integration of bladeless fans over aircraft wings through both two-dimensional and three-dimensional computational simulations, supplemented by wind tunnel experiments. Multiple configurations were examined – varying fan height, spanwise and chordwise placement, orientation and the number of fan units – and compared against the aerodynamic performance of a baseline wing. The results demonstrate that leading-edge fan placement outperforms trailing-edge configurations, particularly in the post-stall regime. For 2D cases, a maximum of 71% lift increment in the post-stall region with 25% increase in the stall angle was observed. Additionally, the bladeless fans effectively reshape the flow field over the wing, increasing lift at the cost of higher drag relative to the baseline. For 2D cases, a 50% increase in zero lift drag was observed; however, 39% reduction was also observed in post-stall region. Among all configurations, the triple-bladeless-fanjet arrangement delivered the best performance, with further gains observed when a positive incidence angle was applied to the fans. An increase of 45% in lift coefficient was observed for triple fan configuration. These computational findings were validated through wind tunnel tests on a propeller-driven aircraft model, where the bladeless fan-equipped version exhibited superior aerodynamic performance compared to the baseline.

A benchmark road vehicle geometry – the square-back Windsor body with wheels and at zero yaw angle – is simulated using high-fidelity wall-resolved large eddy simulation. Passive control for drag reduction, in the form of optimisation of its rear roof extension, is performed. The rear roof extension is parameterised by its taper penetration distance, angle of incidence and length. This optimisation process uses Gaussian process-based surrogate modelling combined with Bayesian optimisation (Kriging), guided by an expected improvement criterion. The optimisation converged in six iterations (60 simulations), achieving a $6.5\,\%$ drag reduction. Six distinct drag-reduction mechanisms were identified: diffuser-induced pressure recovery, base-size reduction, vertical wake balance modification, separation effects, recirculation region core relocation and spanwise re-symmetrisation. Rather than isolating individual mechanisms, the study reveals how they interact when multiple geometric parameters are varied concurrently, providing a system-level picture that yields practical design rules. The optimal configuration was found at a roof extension angle of incidence corresponding to the onset of separation, with taper penetration distance and extension length at their maximum values within the analysed domain. These findings establish a robust framework for aerodynamic optimisation and reinforce the effectiveness of Bayesian optimisation in Computational Fluid Dynamics-based design. In this way, the work bridges fundamental wake studies with applied design practice, showing how coupled wake–geometry interactions can be harnessed for improved aerodynamic performance.

We investigate the control effects of spanwise heterogeneous roughness on shock-wave/turbulent boundary-layer interactions (STBLIs) using wall-resolved large-eddy simulations. The roughness extends over the entire computational domain and consists of streamwise-aligned sinusoidal ridges alternating with flat valleys. The baseline case is a Mach 2.0 impinging STBLI flow with a 40$^\circ$ impinging-shock angle, for which we consider incoming turbulent boundary layers at two friction Reynolds numbers, $Re_\tau \approx$ 350 and 1200. Multiple roughness configurations are analysed, which maintain consistent geometric characteristics under either inner or outer scaling. The results show that the rough-wall configurations introduce a moderate increase in mean drag, while substantially modifying the dynamics of the interaction. The wall-pressure fluctuations near the separation-shock foot consist of two components: low-frequency fluctuations associated with large-scale shock excursions and high-frequency fluctuations linked to amplified turbulence. We find that both spectral components can be significantly attenuated by the investigated wall roughness. At low Reynolds number, the attenuation of low- and high-frequency components contributes comparably to the overall reduction. At high Reynolds number, an overall stronger reduction of the pressure fluctuation peak is observed and is mainly attributed to the effective suppression of the low-frequency component. Cross-correlation analyses support downstream mechanisms for the low-frequency dynamics in the current strong interaction regime, where large-scale shock excursions are mainly driven by the breathing of the reverse-flow bubble. Large-scale Görtler-like vortices are identified around the reattachment location in all cases. They appear largely unaffected by roughness geometry and contribute to the flow dynamics over a wide range of frequencies.

The present study experimentally investigates the onset of ventilation of surface-piercing hydrofoils. Under steady-state conditions, the depth-based Froude number $\textit{Fr}$ and the angle of attack $\alpha$ define regions in which distinct flow regimes are either locally or globally stable. To map the boundary between these stability regions, the parameter space $(\alpha , \textit{Fr})$ was systematically surveyed by increasing $\alpha$ until the onset of ventilation while maintaining a constant $\textit{Fr}$. Two simplified model hydrofoils were examined: a semi-ogive with a blunt trailing edge and a modified NACA 0010-34. Tests were conducted in a towing tank under quasi-steady-state conditions for aspect ratios of $1.0$ and $1.5$, and for $\textit{Fr}$ ranging from $0.5$ to $2.5$. Ventilation occurred spontaneously for all test conditions as $\alpha$ increased. Three distinct trigger mechanisms were identified: nose, tail and base ventilation. Nose ventilation is prevalent at $\textit{Fr} \lt 1.0$ and $\textit{Fr} \lt 1.25$ for aspect ratios of $1.0$ and $1.5$, respectively, and is associated with an increase in the inception angle of attack. Tail ventilation becomes prevalent at higher $\textit{Fr}$, and the inception angle of attack exhibits a negative trend. Base ventilation was only observed for the semi-ogive profile, but it did not lead to the development of a stable ventilated cavity. Notably, the measurements indicate that the boundary between bistable and globally stable regions is not uniform and extends to significantly higher $\alpha$ than previously estimated. A revised stability map is proposed to reconcile previously published and current data, demonstrating how two alternative paths to a steady-state condition can lead to different flow regimes.

In many electrochemical systems, variations in fluid density due to salinity gradients are unavoidable, leading to solutally driven Rayleigh–Bénard convection (RBC). In this study, we perform direct numerical simulations and theoretical analyses of two-dimensional solutal convection near perfectly cation-selective membranes by incorporating buoyancy and electrostatic forces into the Navier–Stokes and Poisson–Nernst–Planck equations. When electroconvection (EC) is negligible, we observe a flow reversal of large-scale circulation (LSC) in salt-driven RBC within a square-cavity electrochemical system, triggered by the periodic reconfiguration of corner vortices. Furthermore, we found that the competition between RBC and EC determines the dominant flow pattern. The buoyancy-driven convection and the LSC are suppressed at sufficiently strong EC flow, leading to a transition from buoyancy-driven flow to electrically driven flow. Consequently, the flow structures into a pair of EC vortices, driven by strong electric field forces within the extended space charge layer. Using Grossmann–Lohse theory, we derive a critical scaling law that describes the flow pattern selection, governed by the combined effects of the Rayleigh number, voltage difference and hydrodynamic coupling coefficient. Our work presents a novel approach to controlling flow patterns, distinct from existing strategies in thermally driven RBC.

We integrate a discrete vortex method (DVM) with complex network analysis to strategise dynamic stall mitigation over aerofoils with active flow control. The objective is to inform the actuator placement and the timing to introduce control inputs during the highly transient process of dynamic stall. To this end, we treat a massively separated flow as a network of discrete vortical elements and quantify the interactions among the vortical nodes by tracking the spread of displacement perturbations between each pair of vortical elements using a DVM. This allows us to perform network broadcast mode analysis to identify an optimal set of discrete vortices, the critical timing and the direction to seed perturbations as control inputs. Motivated by the objective of dynamic stall mitigation, the optimality is defined as maximising the reduction of total circulation of the free vortices generated from the leading edge over a prescribed time horizon. We demonstrate the use of the analysis on a two-dimensional flow over a flat plate aerofoil and a three-dimensional turbulent flow over an SD$7003$ aerofoil. The results from the network analysis reveal that the optimal timing for introducing disturbances occurs slightly after the onset of flow separation, before the shear layer rolls up and forms the core of the dynamic stall vortex. The broadcast modes also show that the vortical nodes along the shear layer are optimal for introducing disturbances, hence providing guidance to actuator placement. Leveraging these insights, we perform nonlinear simulations of controlled flows by introducing flow actuation that targets the shear layer slightly after the separation onset. We observe that the network-guided control results in a $21 \,\%$ and $14\,\%$ reduction in peak lift for flows over the flat plate and SD$7003$ aerofoil, respectively. A corresponding decrease in vorticity injection from the aerofoil surface under the influence of control is observed from simulations, which aligns with the objective of the network broadcast analysis. The study highlights the potential of integrating the DVMs with the network analysis to design an effective active flow control strategy for unsteady aerodynamics.

The electrohydrodynamic force of a surface dielectric barrier discharge (SDBD) has been well-developed for flow control applications during recent decades. In the present paper, a geometrical modification of the SDBD plasma actuator has been applied to induce a vectorised normal flow at the trailing edge of a NACA0015 aerofoil. The pitot-tube velocity measurements of the normal jet along its propagation direction revealed formation of vortices at the centre of the electrode distance played a role in flow control authority of the jet. The aerodynamic operation of the double-SDBD structure as a virtual flap was assessed versus a single counter-flow jet of a floating structure at pre- and post-stall angles of attack at low Reynolds numbers. It was found that at small angles of attack, the steady counter-flow gives the most effectiveness of lift enhancement in low velocity, whereas in the higher velocity the unsteady one results in more efficacy. The efficiency of both steady and unsteady normal jets increased considerably at high angles such that a lift coefficient improvement of 38% was achieved at $\alpha = 14^\circ $. In the higher velocity, the plasma induced vertical flow acts like a Gurney flap, causing lift increase at high angles by affecting the vortical structures at the trailing edge. Evaluating the obtained results recommended employment of the induced normal flow as a virtual flap at high angles of attack in the unsteady actuation mode.