The nonlinear evolution of free-stream vortical disturbances entrained in the entrance region of a channel is investigated using asymptotic and numerical methods, building on the linear framework developed by Ricco & Alvarenga (2021 J. Fluid Mech., vol. 927, A18). The focus is on low-frequency disturbances that induce streamwise-elongated structures at Reynolds numbers for which the entrance flow is locally stable according to classical linear stability theory. The perturbation flow along the channel entrance is generated by free-stream vortical disturbances located at the channel inlet. These disturbances are symmetric or antisymmetric with respect to the centreplane and their amplitude is sufficiently intense to provoke nonlinear interactions within the channel. The formation and evolution of the perturbation flow are described by the nonlinear unsteady boundary-region equations. Combined with physically realistic initial conditions, the resulting initial-boundary-value problems are solved numerically using a streamwise integration method. A parametric study is conducted to elucidate how the nonlinear channel flow is influenced by the Reynolds number and the inlet-disturbance properties, i.e. the amplitude and the streamwise, wall-normal and spanwise wavelengths. Nonlinearity is found to stabilise the intense algebraic growth and to drive the formation of elongated channel-entrance structures that span the entire cross-section. These structures, characterised by low- and high-speed regions and streamwise vortices, meander along the streamwise direction and persist even when the base flow is fully developed. They exhibit a half-turn rotational symmetry with respect to the vortex centres. These properties emerge downstream regardless of the symmetry of the initial perturbation flow, provided nonlinear interactions are sufficiently intense. The occurrence of travelling waves is detected sufficiently downstream, and their similarity to those found in the fully developed region by other researchers is discussed. Our results show good agreement with theoretical predictions, numerical results and experimental measurements for both the mean flow and the perturbation flow.

Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent, capturing the shear layer. The Oldroyd-B model discretised with Chebyshev polynomials is employed, and energy budget analysis is used to interpret underlying mechanisms. At low Weber numbers, the jet evolves axisymmetrically and the instability is governed by interfacial gas-pressure fluctuations; as the Weber number increases, the growing inertia drives a transition of the predominant mode from axisymmetric to helical. At weak elasticity, the instability is also primarily governed by gas-pressure fluctuations. As elasticity increases, the predominant mode transitions from axisymmetric to helical. This transition is accompanied by a migration of disturbance structures from the interface toward the jet interior and an enhanced coupling between velocity perturbation and the basic flow. These trends reveal a new predominant instability mechanism – the elasticity-enhanced shear-driven instability – which is distinct from capillary or Kelvin–Helmholtz instabilities in Newtonian jets. A $\textit{We}$–$El$ phase diagram delineates the boundary between predominant modes and experimental results obtained in a flow-focusing configuration validate the theoretical predictions. Compared with temporal stability results, the spatial framework – by directly resolving the convective downstream amplification of disturbances – achieves quantitative agreement with experiments and highlights the superiority of spatial instability analysis in capturing the dynamics of strongly convective, non-parallel jet flows. These findings provide mechanistic insight into viscoelastic jet instabilities and offer guidance for applications involving droplet and fibre formation in co-flow systems.

Camassa et al. (J. Fluid Mech. 745, 2014, 682–715) demonstrated excellent agreement between the theoretical predictions using the longwave equation and experimental observations for the absolute instability-induced plug formation in the gravity-driven flow of a liquid coating the inner surface of a tube. A similar flow of airway surface liquid (ASL) exists in the proximal airways, driven by the turbulent airflow in addition to gravity. Motivated by the conclusions of previous studies, we probe for the existence of absolute instability in the proximal airways in the present study to determine plug formation and subsequent airway closure by considering ASL elasticity, cylindrical flow geometry and the effect of inhaled air temperature. To accomplish this, we derive a longwave evolution equation, which is then used to obtain the dispersion relation. In contradistinction to the distal airways, the analysis predicts the absence of absolute instability-induced airway closure in the proximal airways for a healthy lung. However, an increased ASL thickness and/or elasticity due to excessive secretion of mucus and mucins in a diseased lung could lead to airway closure due to ASL plugs. Furthermore, inhaling colder air (than body temperature) enhances the absolute instability region, and the opposite is true for inhaling warmer air (than body temperature). For lungs with increased ASL thickness (due to diseases), plug formation is aggravated by colder air inhalation, thus demonstrating that inhaling colder (warmer) air is detrimental (beneficial) for diseased lungs. The predictions of the present analysis are in agreement with clinical observations.

The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a linear arbitrary Lagrangian–Eulerian method to solve the fluid–structure linear problem as well as a forced problem where a harmonic motion of the bodies is imposed. We then propose a low computational-cost impedance-based criterion to predict the instability thresholds. A global stability analysis of the fluid–structure system is then performed for a tandem of cylinders and the instability thresholds obtained are found to be in perfect agreement with the predictions of the impedance-based criterion. An extensive parametric study is then performed for a tandem of cylinders and the effects of mass, damping and spacing between the bodies are investigated. Finally we also apply the impedance-based method to a three-body system to show its validity to a higher number of bodies.

A comprehensive set of experiments were performed to document the separated flow over a three-dimensional (3-D) bump with the purpose of generating a benchmark experimental database useful in validating computational fluid dynamics flow simulations and improving model development. The emphasis of this manuscript is on the 3-D topographical and topological features of the separated flow that forms downstream of the bump and its sensitivity to upstream flow conditions. The bump model geometry was designed to provide well-defined and repeatable smooth-body flow separation conditions that were suitable for both experiments and simulations. The bump had a Gaussian streamwise profile with a constant maximum height equal to 8.5 % of its width over the central 60 % of its span. The remaining 40 % were outboard spanwise portions that gradually taper to zero using an error function profile to minimize tunnel sidewall boundary layer interaction effects. The model was immersed in a canonical turbulent boundary layer that was developed on a suspended flat plate in the Notre Dame Mach 0.6 closed-circuit wind tunnel. To document the effect of the incoming boundary layer thickness on the flow separation, the bump model could be located at two streamwise positions. The measurements of the flow separation region included fluorescent surface flow visualization, wall shear stress using oil-film interferometry, mean and dynamic surface pressure, hot-wire anemometry and planar and stereoscopic particle image velocimetry. It is shown that the surface flow separation topology is characterized by the `owl-face pattern of the first kind’. This flow topology consists of four singular points – two saddle points at the bump centrespan and two foci located at a spanwise-symmetric position. It is shown that the spanwise separation of the twin foci increases with Reynolds number indicating a corresponding increase in the spanwise extent of the flow separation. The two surface foci represent the footprint of vortices that lift off the ramp surface and form an arch vortex time-mean off-surface flow topology aft of the bump.

The stability of the interface in a core–annular flow (CAF) of two immiscible Newtonian fluids with contrasting densities has been investigated, emphasising the role of strong circumferential rotation for the first time. The aim of the investigation is to give insight into the physical mechanisms underlying interfacial disruption. We examine the combined effects of gravity, interfacial tension, axial and azimuthal shear stresses, and centrifugal force on interface stability. The Rayleigh–Taylor instability, induced by gravity, appears as a spiral mode with a azimuthal wavenumber of one. As gravitational effects decrease, the most unstable mode number increases sharply before decreasing with increasing rotation. This non-monotonic behaviour is attributed to the interplay between azimuthal shear and centrifugal acceleration. We demonstrate that this velocity ratio fundamentally governs the onset of spiral modes by varying the ratio of the axial velocities of the core and annular fluids. Higher Reynolds numbers in the annular phase promote the emergence of higher-order spiral modes concomitant with amplified azimuthal shear at the interface. In a parametric study of the gap between the core and pipe wall, we identified a suppressive effect of reduced annular thickness on the growth of higher azimuthal wavenumbers. An energy budget analysis further delineated distinct mechanisms underpinning each instability regime and clarified transitions between them. These findings extend our understanding of interfacial stability in swirling CAFs and provide a predictive framework to control spiral-mode selection.

A joint experimental–computational investigation was conducted to examine the aerodynamic behaviour of a partially closed cavity model in Mach-6 flow. The model, consisting of a flat plate with a rectangular cavity and a forward-facing hinged door, resulted in a strong 500 Hz fluctuation with a 7.5$^\circ$ door and 25 mm cavity depth. The experiments revealed a recirculation bubble present upstream of the cavity region. The fluctuations, detected by surface pressure sensors on the upper surface, upstream cavity wall and cavity floor, were caused by oscillations of the separation bubble along the streamwise axis. Notably, this phenomenon is not explained by established empirical models for cavity flows, such as the Rossiter mechanism or closed-box acoustic resonance. To further elucidate the flow physics, detached eddy simulations (DESs) of the flow were conducted, providing a detailed understanding of the complex flow phenomena. The DES results complemented the experimental data, offering insights into the unsteady flow behaviour and the mechanisms driving the pressure fluctuations. Additional experiments and simulations were conducted for other door angles to simulate different stages of opening. The strong pressure fluctuations at approximately 500 Hz were only experimentally observed for door angles between 5.0$^\circ$ and 7.5$^\circ$ but were absent at much smaller and larger angles. Additionally, several cavity depths were tested, which demonstrated that a shallower cavity delayed the onset of fluctuations until a higher free-stream Reynolds number was reached. The combination of experimental and numerical results provides valuable initial data on the aerodynamic performance of a hypersonic forward-facing door over a cavity.

This paper examines two-dimensional liquid curtains ejected from a narrow horizontal outlet at an angle to the vertical. Curtains are characterised by the Froude number ${\textit{Fr}}=U/ ( gH ) ^{1/2}$, Reynolds number ${\textit{Re}}=UH/\nu$ and Weber number ${\textit{We}}=\rho U^{2}H/\sigma$, where $U$ is the ejection velocity, $g$ the gravity, $H$ the outlet’s half-width, $\nu$ the kinematic viscosity and $\sigma$ the surface tension. It is assumed that ${\textit{Fr}}\gg 1$ (so that the radius of the curtain’s curvature due to gravity exceeds $H$), ${\textit{Re}}\ll 1$ (viscosity is strong) and ${\textit{We}}\sim 1$ (surface tension is on par with inertia). It is shown that steady oblique curtains exist only subject to a constraint of the form ${\textit{We}}\gt f({\textit{Fr}}^{2}{\textit{Re}})$, which is more restrictive than the previously known constraint ${\textit{We}}\gt 1$. Thus, sufficiently strong viscosity and/or surface tension eliminate the steady regime and make the curtain evolve – typically, rotate around the outlet, eventually producing the teapot effect.

The classical Prats problem of flow instability in a horizontal porous channel saturated by a fluid subject to a buoyancy force is reconsidered. In the original formulation, the driving buoyancy force results from thermal diffusion. This study, however, substitutes thermal diffusion with mass diffusion. Furthermore, the usual scheme of mass diffusion is extended to comprehend also the anomalous phenomena of superdiffusion and subdiffusion. Such phenomena are modelled via a time-dependent mass diffusivity which yields a significant change in the formulation of the stability eigenvalue problem. In particular, the ordinary differential equations governing the time evolution of the perturbations acting on the base throughflow become non-autonomous. This makes a significant difference in the discussion of the conditions leading to instability, with a marked effect of the anomaly in the mass diffusion process. The transition from convective to absolute instability for subdiffusion processes is also addressed.

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves. Nevertheless, research on depth-induced NED has been predominantly confined to unidirectional irregular waves, while the role of directionality remains largely unexplored. The scarce studies on multidirectional waves mainly rely on numerical simulations and have yielded conflicting results. In this work, we report on an experimental investigation of wave directionality on the depth-induced non-equilibrium wave statistics. High-order statistical moments, skewness and kurtosis, are used as proxies for the non-equilibrium wave response. Our results indicate that the directional spreading has a minor effect on decreasing the maximum values of these statistical moments. In contrast, the incidence direction plays a significant role in the non-equilibrium wave response, which is attributed to the effective bottom slope.

This study examines the transition to turbulence downstream of fluttering and non-fluttering bioprosthetic aortic valves using global linear stability theory. During systole, increasing inflow velocities result in temporally evolving flow profiles downstream of the valve which are highly influenced by the leaflet kinematics. These profiles are time averaged at the sinotubular junction over successive windows and used as boundary conditions to obtain base flows for stability analysis. Three-dimensional global modes are computed for one design of each valve type across multiple time windows, revealing several unstable modes whose frequencies and growth rates increase over time. Notably, the non-fluttering valve exhibits higher growth rates than the fluttering valve. The resulting eigenspectra show that, for each case, the most unstable eigenvalues align along two distinct parabolic branches in the complex plane. For each valve case, the modes within each branch are found to have similar group velocities, suggesting that the unstable modes along a branch constitute a coherent structure. Motivated by this, a transient growth analysis is conducted to identify the optimal initial perturbations that maximise energy gain for a given time horizon. When superimposed onto the base flow, these perturbations generate vortical structures that closely resemble those observed in fully coupled nonlinear fluid–structure interaction simulations for a similar time scale as the one used to obtain the optimal perturbations. These results suggest that the optimal perturbations may initiate the shear-layer instabilities responsible for transition to turbulence, providing valuable insight into the underlying mechanisms in the flow fields downstream of bioprosthetic valve designs.

Linear and weakly nonlinear stability analyses are carried out to understand the influence of anisotropic slip on the instability and transition characteristics of pressure-driven parallel flow in the fluid overlying a porous medium. The slip is induced on the upper plate dominating in the streamwise direction. The investigation is made by imposing Navier slip on the classical model considered by Aleria et al. (SIAM J. App. Math., vol. 84, 2024, pp. 433–463). For finite-amplitude disturbances, a weakly nonlinear stability analysis based on the cubic-Landau theory is exploited. The bifurcation phenomena are investigated as a function of slip length at the critical instability point (CIP) and as a function of Reynolds number away from the CIP. The linear stability analysis shows that Squire’s theorem does not hold for anisotropic slip, and the mode of instability along the neutral curve is sensitive to slip length. Along the instability boundary, slip stabilises (destabilises) the porous mode (odd-fluid mode), whereas in the even-fluid mode, slip can have either a stabilising or destabilising effect. When the porous mode or odd-fluid mode dominates the flow instability, only the supercritical bifurcation exists at and away from the CIP. For each value of the depth ratio, there exists a finite interval of slip parameter in which the three-dimensional disturbances are least stable and the critical mode of instability is the even-fluid mode. Both the subcritical and supercritical bifurcations are possible for the even-fluid mode of instability and the supercritical bifurcation at the CIP always shifts to a subcritical bifurcation away from the CIP. The nonlinear kinetic energy analysis reveals that modifications in energy due to gradient production and viscous dissipation are mainly responsible for inducing the subcritical instability. The role of spanwise slip, Darcy number, porosity and Beavers–Joseph coefficient is also investigated. The results demonstrates a stabilising (destabilising) impact of spanwise slip (porosity and Beavers–Joseph coefficient), and instability as well as bifurcation characteristics is a function of ${\sqrt {\textit{Da}}}/{\hat{d}}$, rather than individual Darcy number ($Da$) and depth ratio ($\hat{d}$). Overall, this study finds a significant relationship among the critical modes of instability, dimension of the least stable disturbances, bifurcation phenomena and skin-friction coefficient. The present results also witness good experimental support for the stability of flow in the fluid overlying a porous medium and slippery flow in a single-fluid layer configuration.

Energy transfer across scales is fundamental in fluid dynamics, linking large-scale flow motions to small-scale turbulent structures in engineering and natural environments. Triadic interactions among three wave components form complex networks across scales, challenging understanding and model reduction. We introduce triadic orthogonal decomposition (TOD), a method that identifies coherent flow structures optimally capturing spectral momentum transfer, quantifies their coupling and energy exchange in an energy-budget bispectrum and reveals the regions where they interact. Triadic orthogonal decomposition distinguishes three components – a momentum recipient, donor and catalyst – and recovers laws governing pairwise, six-triad and global triad conservation. We apply TOD to three examples: the classical cylinder wake, experimental wind turbine wake data and a direct numerical simulation of isotropic turbulence. Energy transfer can be spatially distributed but vanish upon integration or spatially localised but facilitate net interscale exchange, so a complete characterisation of nonlinearity requires examination of both integral and local transfers. In the cylinder wake, we link backscatter of energy from high to low frequencies to a compact attenuation region downstream of the cylinder. In the turbine wake, we confirm the known association between energy amplification and decay and vortex tilting, but observe more complex secondary mechanisms in suboptimal modes. For isotropic turbulence, we derive and confirm inertial-range frequency scaling for convective–recipient covariances, then demonstrate self-similar energy transfer at each rank.

This study offers the first comprehensive analysis of convective onset in a uniformly internally heated, rotating porous sphere. By incorporating the Coriolis force into Darcy’s law, we formulate the linear stability problem using a vector potential expansion combined with spherical harmonic decomposition. The resulting equations are solved numerically via a spectral method based on Worland polynomials. In the absence of rotation, the most unstable mode corresponds to a spherical harmonic degree $l = 2$, with a critical Rayleigh number of 91.95. When rotation is introduced, the Coriolis force further stabilises the flow, causing the critical Rayleigh number to increase monotonically with the Taylor number. Notably, the system consistently favours an azimuthal wavenumber $m = 2$ across nearly the entire parameter range. This behaviour contrasts sharply with rotating fluid convection, where the preferred wavenumber increases indefinitely with the rotation rate. This fundamental difference arises from the disruption of the quasi-geostrophic balance by the strong Darcy resistance, leading to the failure of the Proudman–Taylor theorem. Under strong rotation, the system exhibits power-law scaling and develops an Ekman-like boundary layer localised near the polar axis, which channels global heat and mass transport. These findings provide novel theoretical insights into the thermal structure and evolution of early evolutionary bodies, such as rapidly rotating planetesimals or undifferentiated asteroids with high permeability, and lay the groundwork for future nonlinear studies of rotating porous convection.

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.

We systematically investigate the multiplicity of flow states in centrifugal convection in water at about $40\,^\circ$C with Prandtl number $Pr = 4.3$ in a vertically aligned annulus in which the inner radius, the gap between the cylinders and the height all coincide (6 cm). This leaves two independent control parameters: the thermal driving, quantified by the Rayleigh number ${\textit{Ra}}$, and the rotation strength, expressed by the Froude number ${\textit{Fr}}$. We explore the range $2\times 10^{5} \le {{\textit{Ra}}} \le 10^{7}$ for ${{\textit{Fr}}} = 10$ and $100$ with direct numerical simulations (DNS). The states are characterised by the number of convection rolls in the mid-height cross-section. We show that the final state sensitively depends on the initial condition, leading to pronounced multistability and substantial variations in heat and momentum transport, while the range of attainable states is strongly restricted. We derive a theoretical estimate of the admissible roll numbers based on the Poincaré–Friedrichs inequality and demonstrate quantitative agreement with the DNS. We further show that, for larger ${\textit{Ra}}$, the range of possible states shrinks systematically due to an elliptical instability, providing a predictive framework for the selection and disappearance of coherent roll states in centrifugal convection.

Upon radial liquid sheet expansion, a bounding rim forms, with a thickness and stability governed, in part, by the liquid influx from the unsteady connected sheet. We examine how the thickness and fragmentation of such a radially expanding rim change upon its severance from its sheet, absent of liquid influx. To do so, we design an experiment enabling the study of rims pre- and post-severance by vaporising the thin neck connecting the rim. No vaporisation occurs of the bulk rim itself. We confirm that the severed rim follows a ballistic motion, with a radial velocity inherited from the sheet at severance time. We identify that the severed rim undergoes fragmentation in two types of junctions: the base of inherited, pre-severance, ligaments and the junction between nascent rim corrugations, with no significant distinction between the two associated time scales. The number of ligaments and fragments formed is captured well by the theoretical prediction of rim corrugation and ligament wavenumbers established for unsteady expanding sheets upon droplet impact on surfaces of comparable size to the droplet. Our findings are robust to changes in impacting laser energy and initial droplet size. Finally, we report and analyse the re-formation of the rim on the expanding sheet and propose a prediction for its characteristic corrugation time scale. Our findings highlight the fundamental mechanisms governing interfacial destabilisation of connected fluid-fed expanding rims that become severed, thereby clarifying destabilisation of freely radially expanding toroidal fluid structures absent of fluid influx.

This study investigates the low-frequency dynamics of a turbulent separation bubble (TSB) forming over a backward-facing ramp, with a focus on large-scale coherent structures associated with the so-called `breathing motion’. Using time-resolved particle image velocimetry (PIV) in both streamwise and spanwise planes, we examine the role of sidewall confinement, an aspect largely overlooked in previous research. Spectral proper orthogonal decomposition (SPOD) of the streamwise velocity field reveals a dominant low-rank mode at low Strouhal numbers ($St \lt 0.05$), consistent with prior observations of TSB breathing. Strikingly, the spanwise-oriented PIV data uncover a previously unreported standing-wave pattern, characterised by discrete spanwise wavenumbers and nodal/antinodal structures, suggesting the presence of spanwise resonance. To explain these observations, we construct a resolvent-based model that imposes free-slip conditions at the sidewall locations by superposing left- and right-travelling three-dimensional modes. The model accurately reproduces the spanwise structure and frequency content of the measured SPOD modes, demonstrating that sidewall reflections lead to the formation of standing-wave-like patterns. Global stability analysis reveals a zero-frequency eigenmode originating from a centrifugal instability, giving rise to the observed low-frequency breathing. Downstream, the associated coherent structures are further amplified through non-modal lift-up mechanisms. Our findings highlight the critical influence of spanwise boundary conditions on the selection and structure of low-frequency modes in TSBs. This has direct implications for both experimental and numerical studies relying on spanwise-periodic boundary conditions and offers a low-order framework for predicting sidewall-induced modal dynamics in separated flows.

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 generation and growth of wind waves are re-examined using linear viscous shear flow instability theory by solving the coupled in-air and in-water Orr–Sommerfeld equations. To enable comparison with the available laboratory observations, model simulations are performed for a wide range of wavelengths spanning the gravity–capillary and gravity wave regimes typical of such experiments. The sensitivity of the results to key modelling assumptions is investigated, including the friction velocity, the surface drift velocity at the air–water interface as well as the shapes of velocity profiles in air and in water, which are modelled using the mixing-length approach. Airflows both over an initially smooth surface and over a surface modified by the emergence of fast-growing short ripples, and thus effectively rough, are considered. A detailed energy budget analysis, based on eigenfunctions of the coupled Orr–Sommerfeld equations across different wavelengths, provides further insight into the mechanisms governing energy transfer from wind to water waves under diverse flow conditions.