In the past, various flow control methods have been used to enhance the growth rate of the supersonic mixing layer (SML), yet suppression strategies remain underexplored. The flow fields of the free SML (FSML) and the SML controlled by the micro vortex generator (MVG) array (CSML) were obtained via flow visualisation and large-eddy simulations, which show that the CSML’s growth rate is substantially lower. The $Q$-criterion analysis confirms that under MVG control, the dominant vortical structures in the initial stage of SML transition from spanwise to streamwise vortices. Circulation analysis shows that streamwise circulation $\varGamma _x$ and transverse circulation $\varGamma _y$ are significantly enhanced in the CSML, thereby facilitating energy redistribution. Dynamic mode decomposition reveals that the first two dominant modes of the FSML exhibit spanwise periodic structures. However, the dominant modes exhibit ‘comb-like’ patterns in the initial stage of the CSML, while the spanwise vortices regain dominance further downstream. The interaction between streamwise and spanwise vortices dominates the spatial growth of the CSML, which is in contrast to the sole dominance of Kelvin–Helmholtz vortices in the FSML. By suppressing the Reynolds normal stress $\langle {v'v'} \rangle$ and restructuring the turbulent kinetic energy (TKE) transport process, MVGs enhance the central amplitudes of TKE transport terms, and narrow their spanwise distribution width. Therefore, the diffusion of TKE towards the high- and low-speed flows is inhibited, thereby reducing the SML’s growth rate. This study offers a viable approach and insights for applications that require inhibiting the SML’s growth rate.

The onset and control of unsteadiness in an idealised porous medium are investigated using global stability and sensitivity analysis. The flow is modelled by a periodic representative elementary volume composed of tandem-arranged circular cylinders, and the Hopf bifurcation is characterised over a broad porosity range ($0.45 \leqslant \phi \leqslant {0.95}$). The neutral stability curve exhibits an approximately linear dependence on $\phi$, indicating that porosity serves as an effective predictor for the transition threshold. In the vicinity of instability onset, several eigenmode families emerge, clarifying the organisation of the competing branches. Energy budget analysis further shows that perturbation production is dominated by the lift-up mechanism. In addition, adjoint-based sensitivity analysis near criticality identifies where a localised steady forcing produces the largest drift of the leading global mode. The result highlights the throat of the main passage as the region of strongest receptivity, offering a clear target and an efficient tool for designing flow-control strategies.

Self-excited thermoacoustic oscillations remain a key obstacle to low-emission combustion, especially in time-aperiodic regimes where quasiperiodic and chaotic dynamics hinder conventional controller design. We experimentally demonstrate data-driven suppression of such aperiodic thermoacoustic oscillations in a flame-driven Rijke tube using genetic programming (GP). In closed-loop form, the GP-discovered control laws are static nonlinear feedback maps that generate, in real time, actuation commands from a sensor signal. Performance is evaluated by a cost function that penalises both the thermoacoustic amplitude (state cost) and the actuation effort (input cost), enabling efficiency comparisons. We benchmark GP closed-loop control (GCC) against GP open-loop control and conventional open-loop harmonic forcing. In the quasiperiodic regime, all three strategies achieve nearly $90\,\%$ amplitude reduction, but the closed-loop strategy is the most efficient. The low-amplitude controlled state is dominated by a preferred (high-gain) mode of the open-flame describing function, and can persist even after control deactivation, indicating basin-of-attraction switching. In the chaotic regime, GCC again outperforms both open-loop strategies, achieving the largest thermoacoustic amplitude reduction with minimal actuation effort. Synchronisation analysis reveals phase trapping, drifting and locking between pressure and heat-release-rate fluctuations, while the 0–1 test and complexity–entropy diagnostics reveal that the GP-suppressed state retains measurable signatures of deterministic chaos. Overall, this study shows that GP control can provide an efficient model-free tool for suppressing aperiodic thermoacoustic oscillations by autonomously exploiting high-receptivity flame pathways with state-dependent actuation.

Clustering techniques provide a powerful framework for analysing complex flow dynamics while reducing computational costs in large-scale simulations. In this work, we propose a clustering-based approach using vector quantisation principal component analysis (VQPCA) to identify structural sensitivity zones, i.e. regions where the flow is most receptive to perturbations. To the authors’ knowledge, this is the first application of VQPCA to a fluid dynamics problem for identifying flow patterns and dynamically relevant regions. As a fully data-driven technique, it does not rely on adjoint methods and depends exclusively on direct simulation data. This method extracts dominant flow features by partitioning the flow field into regions characterised by their intrinsic dynamics. Its validity is assessed by analysing the wake behind a circular cylinder, where the identified regions show strong similarity with previously established structural sensitivity zones. Robustness is further evaluated under different operating conditions for this configuration. The approach is then applied to the interaction of two planar synthetic jets to investigate more complex flow dynamics and illustrate how the identified regions can guide flow control strategies. These results highlight the potential of clustering-based methods as practical tools for analysing complex flows and identifying regions where small perturbations can strongly influence global dynamics.

This study investigates the interaction between shock waves and hydrogen–oxygen cylindrical flames both experimentally and numerically. Experiments are conducted in a newly designed chemically reactive shock tube, where high-speed schlieren imaging captures the detailed flame propagation, deformation and wave dynamics. Following incident shock, flame evolution is primarily dominated by hydrodynamic instability: its upstream interface first flattens, then undergoes phase inversion and subsequently develops into a slender spike. The estimated Darrieus–Landau growth rate is more than an order of magnitude smaller than the Richtmyer–Meshkov instability (RMI)-induced growth rate, confirming that intrinsic flame instabilities play a negligible role and that early-stage evolution is governed predominantly by RMI. However, following reshock, combustion dominates flame evolution, with the upstream interface exhibiting turbulent-like combustion, promoting faster growth of flame length, width and area. High-fidelity simulations employing the Kéromnès mechanism are performed under identical experimental conditions, along with corresponding inert cases for comparison. Pronounced discrepancies are observed: locally, spike roll-up existing in inert cases is largely suppressed in reactive cases; globally, heat release-induced volume expansion drives rapid growth of flame length, width and area. It is found that combustion detaches vortex sheets from the flame interface, suppressing small-scale roll-up and producing abundant disordered small-scale vortical structures within the flame. Shock compression (increasing pressure and temperature) and flame deformation (increasing surface area) significantly enhance heat release, with each mechanism dominating at different stages. Two Damköhler numbers are introduced to characterize the competition between hydrodynamics and chemistry: the flow Damköhler number $\textit{Da}_{\!f} \gg 1$ initially confirms a hydrodynamically dominated regime following the incident shock and decreases progressively as combustion–flow coupling strengthens after reshock; the diffusion Damköhler number $\textit{Da}_d \ll 1$ throughout indicates that combustion remains reaction-kinetic-controlled. Both postshock and post-reshock thermodynamic states lie well within the non-explosive region, confirming that reshock-induced turbulent-like combustion is driven by combustion–flow coupling rather than homogeneous chain-branching explosion.

Active control of transition induced by an isolated sharp-edged roughness element in a supersonic boundary layer is investigated via direct numerical simulation and biglobal stability analysis. The blowing/suction strips and distributed blowing/suction configurations are employed for transition control, respectively. A parametric study of control amplitudes for the blowing/suction strip reveals that multiple distinct mechanisms govern the control efficacy. Specifically, small-amplitude blowing suppresses sharp-edged roughness-induced transition, while large-amplitude blowing promotes it. Analysis via the flow-freezing technique discloses an intrinsic competition mechanism: the blowing strip suppresses the wake mode while simultaneously inducing very-low-frequency unsteadiness related to the horseshoe vortices on both sides of the roughness. Conversely, suction strip control exhibits the opposite behaviour: low amplitudes sharply promote transition, while high amplitudes effectively delay it. Dynamic mode decomposition indicates that the small-amplitude suction strip will excite an ultra-low-frequency unstable mode, and the transition is driven by non-modal growth rather than the wake mode. To mitigate the limitations of strip-based control, we propose three distributed blowing/suction configurations that can significantly reduce the growth rates of both sinuous and varicose modes, thereby delaying the transition more effectively. To investigate the underlying control mechanisms, the linearised vorticity transport equation is derived. This framework enables quantitative analysis of sinuous and varicose mode growth mechanisms from a vortex dynamics perspective, elucidating the growth-promoting interactions among different vorticity components within wake modes and accounting for their enhanced growth rates relative to the Tollmien–Schlichting waves. Based on perturbed vorticity transport equations, it is revealed that the key mode stabilisation mechanism is mainly associated with marked suppression of the tilting terms for wall-normal perturbation vorticity and the production term for the spanwise perturbation vorticity for strip control. However, the proposed distributed blowing/suction configurations not only suppress the spanwise perturbation vorticity generation but also totally inhibit the wall-normal perturbation vorticity production term, leading to effective transition delay.

The linear stability of a viscoelastic liquid film containing insoluble surfactant on a horizontal quasi-periodic oscillating plane for disturbances with arbitrary wavenumbers is investigated. The combined effects of viscoelasticity and quasi-periodic oscillation on the instability mechanism in the presence of surfactant are described with the Floquet theory. For long-wavelength instability, the solution in the limit of long-wave perturbations is obtained by the asymptotic expansion method. The results indicate that, in the absence of gravity, the stability of the oscillating film is determined by the competition between viscoelastic and surfactant effects. In the presence of gravity, the U-shaped neutral curves with separation bandwidth appear. Due to the existence of viscoelasticity, the effects of different frequency ratios and amplitude ratios on the U-shaped neutral curve in the high-frequency region are significantly different from the results under Newtonian fluids. Furthermore, whether gravity exists or not, the viscoelastic effect exhibits a dual effect of initially destabilising, subsequently stabilising and finally destabilising again in the high-frequency oscillating liquid film. The finite-wavelength instability is solved numerically based on the Chebyshev spectral collocation method. The study demonstrates that viscoelasticity results in a non-monotonic trend in the critical Reynolds number of finite-wavelength modes. In the high-frequency region, a bifurcation phenomenon appears due to competition between different standing-wave modes. Increasing the viscoelastic parameter, frequency ratio or amplitude ratio significantly destabilises the flow under high-frequency oscillations.

The stability of a horizontally oscillating liquid film under sidewall confinement is investigated through a bi-global Floquet analysis. The classical two-dimensional oscillating liquid film is extended to a three-dimensional configuration with oscillating sidewalls. This framework resolves the high-dimensional eigenvalue problem arising from the spatio-temporal coupling in this three-dimensional system. For long-wave instabilities, a semi-analytical asymptotic approach is adapted to capture the growth rates efficiently, while the arbitrary-wavelength instabilities are solved via Chebyshev spectral collocation methods. The asymptotic and numerical results reveal that the sidewalls suppress both long-wave and finite-wavelength instabilities by contracting the unstable frequency range and elevating the critical Reynolds numbers. Besides, two distinct instability modes are identified: a long-wave mode dominated by surface shear stress, and a finite-wavelength mode driven by Reynolds stress. Energy budget analysis confirms that sidewalls stabilise the flow by dampening energy production. This work provides fundamental insights into controlling oscillating film instabilities through geometric confinement.

In this study, experimental deep reinforcement learning (DRL) control of aerofoil flow separation is conducted at a chord-based Reynolds number of ${\textit{Re}}_c=1.5\times 10^5$. A dielectric barrier discharge plasma actuator mounted at the leading edge and a hotwire placed in the separated shear layer act as the flow disturber and the state monitor, respectively. The closed-loop control law is parameterised by a radial basis function network and executed in real time on a field-programmable gate array at 1 kHz. With the aid of a deep deterministic policy gradient algorithm, a satisfying closed-loop control strategy can be derived in less than one minute, and the resulting lift coefficient increment (21 %) is similar to that achieved by the best open-loop control. For stable and effective DRL control, the sensor should be placed at the position with strongest velocity fluctuation, and both time delay and cashing period should be accounted in the reward design. Incorporating historical sensor measurements are beneficial to DRL control, and the optimal history length is approximately equal to the ratio of the local Taylor microscale to the control period. The final control law sought by DRL dictates that strong plasma actuation should only be applied when the flow separation region contracts to a minimum. Statistically, control benefits can be ascribed to both the increase of average reward at each cluster and the elevation of occurrence probabilities of high-reward clusters. Physically, suppression of the aerofoil flow separation is attributed to the excitation of large-scale shear layer vortices, which promotes the momentum exchange between the free stream and the reverse flow.

We propose a novel flow-control strategy to suppress low-frequency unsteadiness in shock wave–turbulent boundary layer interactions. Our analysis reveals that the breathing motion of the separation bubble is governed by the leading two-dimensional global mode through a modal resonance mechanism, with its growth rate primarily concentrated in a narrow region near the shock foot. By introducing a micro-bump at this critical location, we achieve targeted stabilisation of the global mode, resulting in a substantial attenuation of the low-frequency breathing motion. Consequently, the turbulent kinetic energy and wall-pressure fluctuations associated with the breathing motion are reduced by 85 % and 70 %, respectively. This study demonstrates an effective and precise approach for controlling low-frequency unsteadiness in shock-induced separation, while minimally disturbing the flow.

The absolute and convective instability properties of a parallel shear flow in a stratified fluid, confined between two parallel rigid plates is considered. The flow is assumed to be two-dimensional, inviscid and incompressible, and is modelled using both a discontinuous two-layer stratification profile and a continuous stratification profile. Significantly, it is found that asymmetrically confining the flow by the two plates, and asymmetrically positioning the density interface such that it does not occur at the centre of the shear layer, both lead to a destabilisation of the flow for a range of flow parameter values, with an absolute instability occurring for an increased parameter range. We identify parameter regimes for asymmetric confinement where the destabilising effect is strong enough to generate an absolutely unstable co-flow shear layer; this contrasts with the unconfined case for which only absolutely unstable counterflow shear layers exist. In the semi-confined case (i.e. asymmetric confinement by one plate) it is found that the most unstable scenario occurs when the plate is placed in the faster/lighter stream. The robustness of the results found for a discontinuous density interface are confirmed using a continuous density profile. These results give valuable new insight into a class of flows such as coaxial injectors for high-speed fluid atomisation.

We present a linear stability analysis of plane Poiseuille flow of an Oldroyd-B fluid confined between rigid, isotropic porous layers at the upper and lower boundaries. The study aims to investigate the interplay between elasticity, inertia and wall permeability on the onset of flow instability. The system is characterized by four dimensionless parameters: the Reynolds number ($ \textit{Re}$), Weissenberg number ($ \textit{Wi}$), permeability parameter ($\alpha$) and solvent viscosity ratio ($\beta$), with porosity held fixed at $\epsilon = 0.6$. We focus on the low-permeability regime, where inertial effects within the porous layers are negligible. The governing equations are formulated using a modified Darcy–Brinkman–Oldroyd-B model, following the framework of Tan & Masuoka (2005 Phys. Fluids, vol. 17, p. 023101), and are coupled across the fluid–porous interfaces using appropriate interfacial conditions. The formulation recovers the classical results for impermeable viscoelastic channels and Newtonian flows with porous surfaces in the appropriate limits. At low $ \textit{Wi}$, the dominant mode resembles a viscoelastic Tollmien–Schlichting instability, but porous boundaries significantly alter the spectrum, introducing concentric eigenvalue rings and modal shifts. At higher $ \textit{Wi}$, an elastic wall mode emerges near the interfaces and dominates at low $ \textit{Re}$. The critical Reynolds number $ \textit{Re}_{\textit{cr}}$ depends on $ \textit{Wi}$ and $\beta$, with a secondary instability branch appearing at large $ \textit{Wi}$. For highly permeable walls ($\alpha =50$), $ \textit{Re}_{\textit{cr}}$ varies in a non-uniform trend with $\beta$, in contrast to impermeable cases.

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.

Shock–boundary-layer interactions on hypersonic cone-step flows exhibit a range of intrinsic unsteady behaviours, from shear-layer oscillations to large-scale pulsations. This work investigates the unsteadiness in a cone-step geometry at Mach 6 under quiet-flow conditions at different free-stream Reynolds numbers using time-resolved schlieren imaging and spectral proper orthogonal decomposition. Experimental results are compared with high-fidelity axisymmetric and three-dimensional simulations. Results demonstrate regime transition in the parameter space, across the unsteadiness boundary, all the way from shear-layer breakdown to shock system oscillations and ultimately to large-amplitude pulsations. The dominant mode in the experiments and the simulations corresponds to a Strouhal number St $\approx 0.17$ for small oscillations reducing to St $ \approx 0.13$ for large pulsations. A detailed description of the unsteady shock dynamics and an analysis of the nonlinear limit cycle is presented.

Active flow control often exploits disturbance amplification mechanisms to achieve desired flow properties. Recently, theoretical predictions of optimal control based on stability analysis have gained traction. However, these methods are limited in their ability to predict nonlinear control strategies, such as burst-mode actuation for separated flows, which involve intermittent and high-amplitude forcing. To address this limitation, we developed a nonlinear optimal forcing analysis based on optimal perturbation theory. This method is specifically designed to capture non-harmonic forcing patterns and the nonlinear temporal evolution of the disturbance field. We applied this method to the two-dimensional high-subsonic, low-Reynolds number flow around a NACA0012 airfoil to reattach the separated flow and investigate the onset mechanism of low-frequency oscillation. The analysis identified an optimal temporal forcing pattern characterized by damped oscillation. This forcing exploits flow amplification mechanisms over the separation bubbles, promoting the formation of spanwise vortices in the shear layer. When implemented as a periodic forcing concentrated at the separated point, these vortices were stably generated, resulting in a significant lift increase via momentum exchange. A key finding is that the application of this optimal forcing induced long-term changes in the flow field, driven by the transient emergence of low-frequency oscillations. Furthermore, we explored the intermittent application of this forcing and found that an appropriate duty cycle can enhance the lift coefficient while reducing energy consumption.

The transition between dripping and jetting regimes of capillary jets is crucial for applications such as ink-jet printing and drug release. A liquid jet emitting from a nozzle usually exhibits a non-uniform initial velocity profile, influencing the transition between regimes, with the role of velocity relaxation remaining largely unexplored. Here we investigate the dripping–jetting transition of a capillary jet with velocity relaxation through a combination of experiments and stability analysis. Experimental measurements show that velocity relaxation consistently lowers the critical transition Weber number, ${\textit{We}}_c$, contradicting predictions from the classic local spatio-temporal stability theory. To resolve this discrepancy, we developed a global stability model accounting for the velocity relaxation to calculate ${\textit{We}}_c$ at different Reynolds numbers (${\textit{Re}}$). Our model provides accurate predictions for jets both with and without velocity relaxation and reveals that the key to the discrepancy lies primarily in the non-parallel effects of jet disturbances caused by velocity relaxation. The velocity relaxation process upstream facilitates the non-uniformity and non-parallelism of the global disturbances and leads to stronger radial–axial coupling in the disturbance field at a higher ${\textit{Re}}$, showing a global dynamics beyond the ability of local analysis. Formulas of ${\textit{We}}_c$ for both Poiseuille- and uniform-velocity jets are proposed based on the results of global stability analysis. These findings elucidate the dynamics of the global instability for dripping–jetting transition under the influence of velocity relaxation and provide guidance for the precise control of jet behaviours in practical applications.

The linear instability of liquid film with insoluble surfactants on a quasiperiodic oscillating plane for disturbances with arbitrary wavenumbers is investigated. The combined effects of insoluble surfactants and quasiperiodic oscillation on the instability are described using Floquet theory. For long-wavelength instability, the solution in the limit of long wave perturbations is obtained by the asymptotic expansion method. The results show that a new stable region emerges in the low-frequency domain of the neutral stability curve in the absence of gravity. As the imposed frequency increases, this newly formed stable region is progressively absorbed into a broader stable zone. The U-shaped neutral curves with separation bandwidth appear in the presence of gravity, and the presence of the surfactants will decrease the unstable frequency bandwidth and increase the critical Reynolds number. The finite-wavelength instability is solved numerically based on the Chebyshev spectral collocation method. Both travelling-wave and standing-wave modes are found due to the existence of surface surfactants. As the surfactant concentration increases, the finite-wavelength instability region expands significantly, and the intersection point marking the transition from travelling waves to standing waves shifts progressively towards lower frequencies. The physical mechanisms underlying perturbation growth are further elucidated through an energy budget analysis. Energy budget analysis demonstrates that long-wavelength instability is dominated mainly by surface shear stress, whereas finite-wavelength instability is primarily governed by the combined effects of Reynolds stress and surface shear stress.

A low-density jet is known to exhibit global self-excited axisymmetric oscillations at a discrete natural frequency. This global mode manifests as large-scale periodic vortex ring structures in the near field. We experimentally investigate the effectiveness of axial and transverse forcing in controlling such global vortical structures. We apply acoustic forcing at a frequency ($f_{\!f}$) around the natural global frequency of the jet ($f_n$) leading up to and beyond lock-in. Using time-resolved stereoscopic particle image velocimetry, we find that the jet synchronises to $f_{\!f}$ when forced sufficiently strongly. When forced purely axially, the jet exhibits in-phase roll-up of the shear layers, producing axisymmetric vortex ring structures. When forced purely transversely, the jet exhibits anti-phase roll-up of the shear layers, producing tilted vortex ring structures. We find that the former produces relatively strong oscillations, while the latter produces oscillations that are even weaker than those of the unforced case due to asynchronous quenching. We show that the transverse forcing breaks the jet axisymmetry by altering the topology of the coherent structures in the near field, leading to global instability suppression. We also find that the wavelength of the applied forcing has a notable influence on the evolution of vortical structures, thereby modifying the forced response of the jet. The efficacy of transverse forcing and the influence of the forcing wavelength in suppressing the global mode of a self-excited low-density jet present new possibilities for the open-loop control of a variety of globally unstable flows.

In this paper, we perform a Floquet-based linear stability analysis of the centrifugal parametric resonance phenomenon in a Taylor–Couette system subjected to a time-quasiperiodic forcing where both the inner and outer cylinders are oscillating with the same amplitude and different angular velocities given respectively by $\varOmega _0 \cos (\omega _1t)$ and $\varOmega _0 \cos (\omega _2t)$. In this context, the frequencies $\omega _1$ and $\omega _2$ are incommensurate, where the ratio $\omega _2/\omega _1$ is irrational. Taking into account non-axisymmetric disturbances, a new set of partial differential equations is derived and solved using the spectral method along with the Runge–Kutta numerical scheme. The obtained results in this framework show that this forcing triggers new and numerous reversing and non-reversing Taylor vortex flows arising via either synchronous or period-doubling bifurcations. A rich and complex dynamics is found owing to strong mode competition between these modes that alters significantly the topology of the marginal stability curves. The latter exhibit a multitude of small and condensed parabolas, giving rise to several codimension-two bifurcation points, discontinuities and cusp points in the stability diagrams. Furthermore, a proper tuning of the frequency ratio leads to a significant control of both the instability threshold and the axisymmetric nature of the primary bifurcation. Moreover, using a local quasi-steady analysis when the cylinders are slowly oscillating, intermittent instabilities are detected, characterised by spike-like behaviour in the stability diagrams with several successive growths, dampings and periods of quietness. In this limit case, the inner cylinder drive becomes the responsible forcing of the Taylor vortices’ formation where the calculated critical instability parameters correspond to those of the inner oscillating cylinder case with fixed outer cylinder. The potentially unstable regions between the cylinders are determined on the basis of the Rayleigh discriminant, where an excellent agreement with the linear stability analysis results is pointed out.

Smooth surface features were recently found to stabilise stationary cross-flow instability (CFI) of swept-wing boundary layers, thus holding potential for passive laminar flow control. Notably, the effect of surface features on the transition location exhibited a significant dependence on the CFI amplitude. In this work, numerical solutions of the harmonic Navier–Stokes (HNS) equations are used to explore the impact of a smooth surface hump on the linear and nonlinear development of stationary CFI under various perturbation amplitudes. Linear simulations identify regions of successive inhibited and enhanced perturbation growth. Despite the recovery of the base flow and perturbation kinetic energy to the reference (i.e. no-hump) state, significantly reduced perturbation growth is observed. The distorted perturbation profile due to the interaction with the hump is postulated to be responsible for this. Increasing the perturbation amplitude results in a response of the flow that is qualitatively similar to the linear case, albeit with increasing local destabilisation of new fundamental (i.e. primary wavelength) structures and higher-order harmonics near the wall. An energy budget analysis reveals that the growth of the fundamental incoming CFI is inhibited through the reduced effectiveness of the lift-up mechanism downstream of the hump. This is preceded by a spatial perturbation shape deformation, governed by (spanwise) transport terms. The results suggest that stabilisation of incoming stationary CFI via smooth surface humps is most effective at low incoming perturbation amplitudes. At higher perturbation amplitudes, newly formed near-wall structures, pre-conditioned by the incoming CFI, overtake the incoming CFI and could anticipate the transition process.