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.

Jet vortex generators (JVGs) are a promising technique for controlling laminar separation in low-Reynolds-number aerofoils, such as those used in micro air vehicles (MAVs). While previous studies have demonstrated their aerodynamic benefits, the three-dimensional structure of the vortices they generate and their interaction with the boundary layer remain poorly characterised experimentally. In this study, volumetric velocity measurements are performed using the double-pulse Shake-the-Box (STB) technique on an SD7003 aerofoil equipped with skewed and pitched JVGs. Experiments are conducted at Reynolds numbers of 30 000 and 80 000, for angles of attack of 8$^{\circ}$, 10$^{\circ}$ and 14$^{\circ}$. The results provide the first experimental visualisation of the full three-dimensional vortex topology induced by JVGs, revealing asymmetric streamwise vortices that penetrate the separated shear layer and re-energise the near-wall region. In pre-stall conditions, the JVGs reshape the laminar separation bubble into a thinner and more stable structure, reducing its sensitivity to angle of attack. In stall conditions, they induce partial or full flow reattachment, delaying large-scale separation. The evolution of characteristic bubble parameters and the chordwise distribution of the shape factor $H = \delta ^{\ast }/\theta$, where $\delta ^{\ast }$ is the displacement thickness and $\theta$ is the momentum thickness, show a consistent trend of enhanced boundary-layer recovery. These findings offer new insight into the physical mechanisms underlying active separation control at low Reynolds numbers and establish a framework for evaluating vortex-based control strategies using volumetric diagnostics.

One-degree-of-freedom flow-induced vibration (FIV) and energy harvesting through FIV of an elastically mounted circular cylinder with mechanically coupled rotation were investigated numerically for low Reynolds number 100, mass ratio 8 and a wide range of reduced velocities. The aims of this study are to investigate the effect of the flow direction angle $\beta$ on the vibration and energy harvesting through FIV. Two types of lock-in are found: vortex-induced vibration (VIV) and galloping. The response amplitude increases with the increase of $\beta$ in both regimes. Both VIV response and galloping regimes are found for $\beta$ = 45° to $\beta$ = 90°. For $\beta$ = −90° to $\beta$ = 0°, only VIV response regimes are found. The fluid force and fluid torque play different roles in exciting/damping the vibration. In the high-amplitude gallop regime, the fluid force excites the vibration, and the torque damps the vibration. Energy harvesting at flow direction angle 90° is investigated as this flow direction has the maximum galloping amplitude. The energy harvesting is achieved by a linear electric damping coefficient in the numerical model. The maximum harvestable power in the galloping regime is significantly greater than that in the VIV regime, and it increases with the increase of the reduced velocity. When the reduced velocity is 20, the harvested power is over 20 times that in the VIV regime, and can further increase if reduced velocity further increases. The maximum efficiency over all simulated parameters is 0.424, occurring when the reduced velocity is 20, and electric damping factor is 0.04.

This paper presents experimental studies on a novel active high-frequency coaxial injector system designed for enhanced flow mixing and control at extreme flow velocity conditions. The flow dynamics and mixing characteristics of the system operating at 15kHz were captured using planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques and compared against its steady and baseline modes. In pulsed mode, this active injection system delivers a pulsed supersonic actuation air jet at the inner core of the coaxial nozzle that provides large mean and fluctuating velocity profiles in the shear layers of an acetone-seeded fluid stream injected surrounding the core through an annular nozzle. The instantaneous velocity, vorticity and acetone concentration fields of the injector are discussed. The high-frequency streamwise vortices and shockwaves tailored to the mean flow significantly enhanced supersonic flow mixing between the fluids compared to a classical steady coaxial configuration operating at the same input pressure. The paper analyses the dynamic and diffusion characteristics of this active coaxial injection system, which may have potential for supersonic mixing applications.

We address the Reynolds number dependence of the turbulent skin-friction drag reduction induced by streamwise-travelling waves of spanwise wall oscillations. The study relies on direct numerical simulations of drag-reduced flows in a plane open channel at friction Reynolds numbers in the range $1000 \leqslant Re_\tau \leqslant 6000$, which is the widest range considered so far in simulations with spanwise forcing. Our results corroborate the validity of the predictive model proposed by Gatti & Quadrio (J. Fluid Mech. vol. 802, 2016, pp. 553–558): regardless of the control parameters, the drag reduction decreases monotonically with $Re$ at a rate that depends on the drag reduction itself and on the skin-friction of the uncontrolled flow. We do not find evidence in support of the results of Marusic et al. (Nat. Commun. vol. 12, no. 1, 2021, pp. 5805), which instead report by experiments an increase of the drag reduction with $Re$ in turbulent boundary layers, for control parameters that target low-frequency, outer-scaled motions. Possible explanations for this discrepancy are provided, including obvious differences between open channel flows and boundary layers, and possible limitations of laboratory experiments.

We develop an optimal resolvent-based estimator and controller to predict and attenuate unsteady vortex-shedding fluctuations in the laminar wake of a NACA 0012 airfoil at an angle of attack of 6.5°, chord-based Reynolds number of 5000 and Mach number of 0.3. The resolvent-based estimation and control framework offers several advantages over standard methods. Under equivalent assumptions, the resolvent-based estimator and controller reproduce the Kalman filter and LQG controller, respectively, but at substantially lower computational cost using either an operator-based or data-driven implementation. Unlike these methods, the resolvent-based approach can naturally accommodate forcing terms (nonlinear terms from Navier–Stokes) with coloured-in-time statistics, significantly improving estimation accuracy and control efficacy. Causality is optimally enforced using a Wiener–Hopf formalism. We integrate these tools into a high-performance-computing-ready compressible flow solver and demonstrate their effectiveness for estimating and controlling velocity fluctuations in the wake of the airfoil immersed in clean and noisy free streams, the latter of which prevents the flow from falling into a periodic limit cycle. Using four shear–stress sensors on the surface of the airfoil, the resolvent-based estimator predicts a series of downstream targets with approximately $3\,\%$ and $30\,\%$ error for the clean and noisy free stream conditions, respectively. For the latter case, using four actuators on the airfoil surface, the resolvent-based controller reduces the turbulent kinetic energy in the wake by $98\,\%$.

This paper presents an experimental and analytical investigation into the use of trailing edge slits for the reduction of aerofoil trailing edge noise. The noise reduction mechanism is shown to be fundamentally different from conventional trailing edge serrations, relying on destructive interference from highly compact and coherent sources generated at either ends of the slit. This novel approach is the first to exploit the coherence intrinsic to the boundary layer turbulence. Furthermore, the study demonstrates that trailing edge slits not only achieve superior noise reductions compared with sawtooth serrations of the same amplitude at certain conditions, but also offer frequency-tuning capability for noise reduction. Noise reduction is driven by the destructive interference between acoustic sources at the root and tip of the slit, which radiate with a phase difference determined by the difference in times taken for the boundary layer flow to convect between the root and tip. Maximum noise reductions occur at frequencies where the phase difference between these sources is $180^\circ$. The paper also presents a detailed parametric study into the variation in noise reductions due to the slit length, slit wavelength and slit root width. Additionally, a simple two-source analytic model is proposed to explain the observed results. Wind tunnel measurements of the unsteady flow field around the trailing edge slits are also presented, providing insights into the underlying flow physics.