A transition control methodology using hybrid laminar flow control (HLFC) for drag reduction for civil transport aircraft is described. An HLFC concept with a single suction chamber with varying porosity can be integrated into the leading-edge wing structure, with the wing ice protection system and high lift system. The resultant structural system is less complex than the multi-chamber concept, and with weight saving.

A turbulent type of pressure distribution has been applied to a civil transport retrofit HLFC wing design resulted with a higher aerodynamic performance than a favourable gradient type of pressure distribution. A turbulent type of pressure distribution also has the potential of being able to retain the performance of a conventional aircraft in the case of suction system failure.

An analysis of wind tunnel transition data with linear stability analysis method is described. Detailed measurements of the tunnel environment and fluctuations within the boundary layer are required to provide a better understanding of the physics of transition and data for non-linear methods.

A wind tunnel testing capability developed for measuring the effect of small features on transition in natural laminar flow could be extended to HLFC to investigate the effect of suction on the disturbances due to various degree of surface imperfections. A high Reynolds number wind tunnel simulation technique using surface suction to thin the turbulent boundary layer has been demonstrated theoretically and experimentally for a turbulent flow wing design. A theoretical investigation has shown that this technique could be extended to an aircraft with a HLFC wing design.

Turbulence-induced friction is a significant contributor to energy consumption in the fluid-transport and piping industries. Here, we describe a passive approach to suppress turbulence and reduce friction: we show that a local increase in streamwise flow curvature, combined with changing a circular cross-section to an oval, relaminarises turbulent flow in curved pipes. We exemplify this effect in a $180^{\circ }$ bend at ${\textit{Re}}_D=10\,000$ and $20\,000$ (based on bulk velocity $U_B$ and pipe diameter $D$), well above the limit for sustained turbulence in straight pipes and the linear stability limit in $180^{\circ }$ bends. Curvature inhibits streamwise Reynolds stresses, and cross-sectional modifications weaken the unstable secondary flow, together disrupting the near-wall regeneration cycle and collapsing turbulence. Simulations and experiments confirm that these geometric modifications suppress turbulence and reduce pressure loss by 53 % and 36 % compared with the baseline $180^{\circ }$ bend and a fully developed straight pipe of equal length, respectively. The results establish a passive, mechanism-based route to relaminarisation in curved pipes with implications for energy-efficient control in other wall-bounded flows with curvature.

Spanwise wall oscillation (SWO) of turbulent boundary layers (TBLs) is investigated via direct numerical simulations (DNS) over an extended actuation region (momentum Reynolds number $344\lt Re_\theta \lt 2340$) with oscillation periods up to $T_{\textit{sc}}^+=600$, scaled by the uncontrolled friction velocity $u_{\tau 0}$ at the onset of SWO (i.e. $ \textit{Re}_\theta =344$). For low periods ($T_{\textit{sc}}^+\lt 200$), drag reduction ($ \textit{DR} $) decreases with increasing $ \textit{Re}_\theta$, consistent with conventional inner-scaled control strategies targeting near-wall turbulence. In sharp contrast, for large periods ($T_{\textit{sc}}^+\gt 200$), $ \textit{DR} $ increases with $ \textit{Re}_\theta$. For example, at $T_{\textit{sc}}^+=600$, $ \textit{DR} $ rises from 1.3 % at $ \textit{Re}_\theta =713$ to 7.0 % at $ \textit{Re}_\theta =2340$. This unexpected growth is partly explained by the streamwise evolution of the effective oscillation parameter: as a TBL develops, $u_{\tau 0}$ decreases downstream, reducing the local-scaled period $T^+$ and thereby enhancing suppression of near-wall turbulence. Interestingly, if the results are compared at approximately fixed $T^+$, then $ \textit{DR} $ for $T^+\gt 350$ still exhibits a weak positive dependence on $ \textit{Re}_\theta$, consistent with recent experiments by Marusic et al. (2021, Nat. Commun., vol. 12, 5805). We further develop a new analytical relationship that links $ \textit{DR} $ to the upward shift of mean velocity in the wake region. Unlike previous formulations, the relationship avoids logarithmic-region fitting and does not rely on an invariant Kármán constant under SWO, while maintaining good agreement with DNS data. Flow diagnostics – including Reynolds stresses, skin-friction decomposition, and energy spectra – demonstrate that the observed variation of $ \textit{DR} $ with Reynolds number ($ \textit{Re}$) arises from period-dependent modulation of near-wall turbulence. Overall, these findings challenge the conventional view that $ \textit{DR} $ inevitably deteriorates with $ \textit{Re}$, and demonstrate that out-scaled actuation can instead enhance $ \textit{DR} $ performance – offering new physical insights for high-$ \textit{Re}$ control strategies.

In a previous study, we have proposed a mechanism for simultaneous reduction of drag and lift by half-rotation at moderately low Reynolds numbers. The axis of rotation ($z$) is perpendicular to both the drag ($x$) and lift ($y$) directions, i.e. the rotation is transverse to the incoming flow direction. Under laminar flow conditions, force-element analysis indicates that a partially rotating sphere can significantly reduce both drag and lift with suppression of vortex shedding. This study extends investigation of the same mechanism of half-rotating a sphere to the turbulence regime at a Reynolds number $Re = 1 \times 10^4$. Similar to the laminar case, half-rotation of the sphere introduces a significant negative velocity drag term, which effectively counteracts the rapid increase in the volume- and surface-vorticity drag terms. Numerical simulations with delayed detached eddy simulation, aided by direct numerical simulation, show that the drag coefficient decreases monotonically with increasing the non-dimensional rotational speed $\alpha$, even becoming negative at $\alpha =10$, while the lift and side-force coefficients remain small for all $\alpha$. However, in contrast to laminar conditions, the turbulent regime is characterised by an earlier onset of shear-layer instabilities, which accelerates the transition of the wake into a fully turbulent state. The relative importance of volume- and surface-vorticity contributions to the drag and lift is the most outstanding difference between the laminar and turbulent flows. In turbulent flow, simultaneous reduction of drag and lift is more pronounced as the contributions of volume- and surface-vorticity lift terms almost cancel each other exactly. These mechanisms and characteristics are systematically compared with those observed in the flow around a fully rotating sphere at the same Reynolds number in terms of vorticity structures, force elements, pressure distributions as well as surface-vorticity distributions.

This study examines how wavy orientation and undulation-induced geometric variations regulate vortex formation, wake transitions and aerodynamic performance in sinusoidally wavy cylinders. Using three-dimensional (3-D) simulations at a Reynolds number Re = 100, we analyse the transition from two-dimensional (2-D) to 3-D wakes across varying spanwise wavelengths and undulation configurations. A novel framework is introduced for classifying vortex structures, analyisng centreline trajectories and decomposing vortex structures, revealing how geometric variations induce distinct 3-D vortical structures. At short wavelengths, vortices originate from bluff regions and diminish in a continuous manner, stabilising the wake. At longer wavelengths, phase-dependent vortex onset leads to localised interactions, disrupting wake coherence and delaying stabilisation. A key discovery is the role of transverse recirculating flow in wake stabilisation, which induces reverse impingement, redirects fluid and weakens spanwise vortex coherence. Additionally, wavy orientation strongly influences vortex evolution and dislocation, altering vortex trajectories and wake stability. To further clarify these wake transitions, a classification framework is introduced, defining distinct phases such as vortex stretching, break-up and re-symmetrisation. The relationship between force characteristics and wake stabilisation is also established, with wavy orientation and undulation geometry regulating the transition from quasi-2-D spanwise vortical flow to 3-D spiral flow. A critical wavelength is identified where drag and lift fluctuations are minimised, with elliptical-section undulations achieving superior aerodynamic performance through enhanced vortex synchronisation. These findings provide new insights into vortex control strategies, with applications in bio-inspired propulsion, passive flow control and energy-efficient aerodynamic designs across engineering and industrial fields.

Travelling wave control is a promising technique for reducing turbulent skin friction by suppressing turbulence in boundary layers. This study presents experimental observations of the streamwise evolution of turbulence over a travelling wavy wall. Particle image velocimetry measurements were performed at multiple downstream locations. The travelling wave was generated by oscillating a rubber sheet to attain properties that are known to achieve drag reduction. The results reveal a two-stage process where the drag-reduction mechanism qualitatively changes in the streamwise direction. In the upstream region (up to approximately two wavelengths from the start of control), turbulent fluctuations are rapidly reduced, however, being limited to the near-wall region. Further downstream, the suppression effect diffuses in the wall-normal direction, leading to a modification on the edge of the boundary layer. The diffusion process of the turbulence-suppression effect is consistently interpreted within the framework of an internal boundary layer, whose development follows a power law. Two-point correlation analysis indicates that the wave crests initially disrupt the near-wall streaky structures, and subsequently reorganise into a characteristic state with a shorter streamwise coherence length downstream. While fully developed states have been studied previously, this work presents the streamwise development of turbulence suppression within a finite length, informing the design of practical drag-reduction devices.

This paper examines how in-plane contraction/relaxation waves applied to the walls affect a two-dimensional laminar flow in a channel. Of primary interest is how the application of such waves alters the pressure gradient required to drive a prescribed flow rate. It is shown that the waves generate a pumping effect that acts in the direction opposite to wave propagation. Depending on the exact configuration at hand, this pumping can enhance or reduce the pressure losses in the flow. Waves that propagate against the flow always reduce the pressure losses, while waves that propagate with the flow can only reduce the losses if they are sufficiently slower than the flow. It is demonstrated that a significant increase in pressure losses can be achieved when the properties of the waves align with the natural frequencies of the flow. Finally, it is shown that the pumping effect generates propulsion if one of the walls is allowed to move.

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.

The description of riblets and other drag-reducing devices has long used the concept of longitudinal and transverse protrusion heights, both as a means to predict the drag reduction itself and as equivalent boundary conditions to simplify numerical simulations by transferring the effect of riblets onto a flat virtual boundary. The limitation of this idea is that it stems from a first-order approximation in the riblet-size parameter $s^+$, and as a consequence it cannot predict other than a linear dependence of drag reduction upon $s^+$; in other words, the initial slope of the drag-reduction curve. Here the concept is extended to a full asymptotic expansion using matched asymptotics, which consistently provides higher-order protrusion coefficients and higher-order equivalent boundary conditions on a virtual flat surface. While the majority of this expansion, though nonlinear in $s^+$, remains linear in velocity, and therefore we shall not directly address the shape of the drag-reduction curve, this procedure will also allow us to explore the way nonlinearities of the Navier–Stokes equations first enter the $s^+$ expansion, with somewhat surprising negative results.

Slow viscous flow around a fixed body generates a shape-dependent drag. We explore the drag-minimising shapes of bodies centred between two parallel plates in two-dimensional viscous flow. The channel width introduces a length scale so that the optimal profile is area-dependent. We solve the shape optimisation problem numerically over a wide range of areas. We also compute the optimal elliptical shapes and this identifies how these shapes should be slightly altered to reduce the drag with reductions of up to $3.8\,\%$ attained at high areas. More broadly, we derive two properties of general optimal shapes within the confined flow: the magnitude of the surface vorticity is approximately (but not exactly) constant and the noses have sharp angles that are independent of area. For relatively small bodies, the optimal shape becomes identical to that in an unconfined geometry, but the drag is qualitatively different owing to the influence of confinement; within a channel, it is proportional to the inverse of the logarithm of the body area. At relatively large areas, the optimal body becomes long and its surface is approximately parallel to the channel boundaries, except in the vicinity of the noses. Using a lubrication approximation, we recast the optimisation problem as an Euler–Lagrange equation that is solved to determine the drag-minimising shape, finding that the drag is proportional to the body area in this regime.

The effect of a smooth surface hump on laminar–turbulent transition over a swept wing is investigated using direct numerical simulation (DNS), and results are compared with wind tunnel measurements. When the amplitude of incoming crossflow (CF) perturbation is relatively low, transition in the reference (without hump) case occurs near $53\,\%$ chord, triggered by the breakdown of type I secondary instability. Under the same conditions, no transition is observed in the hump case within the DNS domain, which extends to $69\,\%$ chord. The analysis reveals a reversal in the CF velocity component downstream of the hump’s apex. Within this region, the structure and orientation of CF perturbations are linearly altered, particularly near the wall. These perturbations gradually recover their original state further downstream. During this recovery phase, the lift-up mechanism is weakened, reducing linear production, which stabilises the stationary CF perturbations and weakens spanwise gradients. Consequently, the neutral point of high-frequency secondary CF instability modes shifts downstream relative to the reference case, leading to laminar–turbulent transition delay in the presence of the surface hump. In contrast, when the amplitude of the incoming CF perturbation is relatively high, a pair of stationary counter-rotating vortices forms downstream of the hump. These vortices locally deform the boundary layer and generate regions of elevated spanwise shear. The growth of secondary instabilities in these high-shear regions leads to a rapid advancement of transition towards the hump, in agreement with experimental observations.

We investigate the influence of shear-thinning and viscoelasticity on turbulent drag reduction in lubricated channel flow – a configuration where a thin lubricating layer of non-Newtonian fluid facilitates the transport of a primary Newtonian fluid. Direct numerical simulations are performed in a channel flow driven by a constant mean pressure gradient at a reference shear Reynolds number $\textit{Re}_\tau = 300$. The interface between the two fluid layers is characterised by Weber number $\textit{We} = 0.5$. The fluids are assumed to have matched densities. In addition to a single-phase reference case, we analyse four configurations: a Newtonian lubrication layer, a shear-thinning Carreau fluid layer, a shear-thinning and viscoelastic FENE-P fluid layer, and a purely viscoelastic FENE-CR fluid layer. Consistent with previous findings (Roccon et al. 2019, J. Fluid Mech., vol. 863, R1), surface tension is found to induce significant drag reduction across all cases. Surprisingly, variations in the lubricating layer viscosity do not yield noticeable drag-reducing effects: the Carreau fluid, despite its lower apparent viscosity, behaves similarly to the Newtonian case. In contrast, viscoelastic effects lead to a further reduction in drag, with both the FENE-P and FENE-CR fluids demonstrating enhanced drag-reducing capabilities.

We present a combined experimental and theoretical exploration of three-layer, horizontal core–annular pipe flow, in which two fluids are separated by a deformable elastic solid. In the experiments, an elastic solid created by an in situ chemical reaction maintains the separation of the core and annular fluids. Corrugations of the elastic interface are observed, and stable pipelining, where the elastic shell created separating the two fluids remains intact, is successfully demonstrated even when the core fluid is buoyant. The theoretical model combines lubrication theory for the fluids with standard shell theory for the elastic solid. The model is used to predict the buckling states resulting from radial compression of the shell, and to explore the sedimentation of a buoyant core. The self-sculpting of the shell by buckling cannot by itself generate hydrodynamic lift owing to symmetry in the direction of flow. Instead, we demonstrate that hydrodynamic lift can be achieved by other elastohydrodynamic effects, when that symmetry becomes broken during the bending of the shell.

Experimental deep reinforcement learning (DRL) control of a turbulent boundary layer is conducted for the first time at $Re_\tau$ = 1196, with the aim of friction-drag reduction. Two hot films, an impinging plasma jet actuator array and two wall hot wires act as the state detector, flow disturber and reward evaluator, respectively. The control law parametrised by a radial basis function network is executed in real time on a field programmable gate array and optimised using a classical value-based algorithm (deep Q-network). Results show that DRL control requires only 30 s to train a closed-loop control law with satisfactory drag-reduction performance. Compared with open-loop control where only fine-tuned periodical forcing can reduce the friction drag, the experimental efficiency is improved significantly. Proper setting of the hyper-parameters is crucial in DRL. Particularly, the reward time delay and control frequency need to match the convection time scale and the characteristic frequency of the turbulent boundary layer. The optimal DRL control setting achieves 6.7 % relative drag reduction, almost three times that of the best open-loop control (2.3 %). Physically, plasma actuation induces alternating low-speed and high-speed zones that confine the sidewise motion of turbulent streaks. The final control law optimised by DRL can be simplified as a threshold control, firing the plasma actuator after perceiving a streak burst event and a long-lasting high-speed zone. Control benefits are attributed to the increase in the occurrence probability of high-reward states and the elevation of mean reward at different clusters.

This study experimentally investigates passive drag reduction on a sphere using azimuthally spaced surface protrusions under subcritical Reynolds numbers, focusing on the effects of the protrusion number at fixed surface coverage. The proposed surface modification strategy, termed partial protrusions, maintains a constant total protruded area while varying the number of protrusions $N$, thereby adjusting their azimuthal spacing. The objective is to determine whether such configurations can outperform the conventional full protrusion, in which protrusions continuously surround the azimuthal direction, and to elucidate the flow mechanisms behind any observed enhancement. Drag and flow field measurements reveal that increasing $N$ significantly improves aerodynamic performance. When $N$ exceeds a certain threshold, the partial-protrusion configuration achieves a greater drag reduction than the full-protrusion case, despite using only half the surface coverage. For low $N$, asymmetric pressure distributions across the protruded and smoothed sides induce unsteady separation delay, leading to shear-layer oscillations and elevated turbulent kinetic energy. As $N$ increases, the azimuthal spacing between protrusions decreases, promoting stable interaction between the two sides and leading to separation delay farther downstream than in the full-protrusion case, along with suppression of flow unsteadiness. These results demonstrate that a well-designed partial-protrusion configuration can outperform the full-protrusion configuration in drag reduction and unsteadiness control, offering new insights into effective passive flow control strategies for bluff body flows.

As a step towards realising a skin-friction drag reduction technique that scales favourably with Reynolds number, the impact of a synthetic jet on a turbulent boundary layer was explored through a study combining wind-tunnel measurements and large eddy simulations. The jet was ejected in the wall-normal direction through a rectangular slot whose spanwise dimension matched that of dominant large-scale structures in the logarithmic region to target structures of that size and smaller simultaneously. Local skin-friction reduction was observed at both $x/\delta =2$ and $x/\delta =5$ downstream of the orifice centreline, where $\delta$ is the boundary-layer thickness. At $x/\delta =2$, the skin-friction reduction was observed to be due to the synthetic-jet velocity deficit intersecting the wall. At $x/\delta =5$, evidence from the simulations and wind-tunnel measurements suggests that a weakening of wall-coherent velocity scales is primarily responsible for the skin-friction reduction. Local skin-friction reduction which scales favourably with Reynolds number may be achievable with the synthetic jet employed in this study. However, there are many technical hurdles to overcome to achieve net skin-friction drag reduction over the entire region of influence. For instance, regions of skin-friction increase were observed close to the orifice ($x/\delta \lt 2$) and downstream of the orifice edge due to the induced motion of synthetic-jet vortical structures. Additionally, a recirculation region was seen to form during expulsion, which has implications for pressure drag on non-planar surfaces.

An experimental study is performed to control flow separation from a two-dimensional curved ramp using a spanwise pulsed blowing slit jet placed near the separation point of the baseline flow. The momentum-thickness-based Reynolds number $ \textit{Re}_{\theta}$ is 5700. Four control parameters are investigated, including the velocity ratio $\overline{U_{J,c}^{*}}$, duty cycle dc, dimensionless excitation frequency $f_{e}^{{*}}$ and jet blowing angle $\alpha$. The control mechanisms are found to differ from small to large jet angle. Empirical scaling analysis for $\alpha \leq 55^{\circ}$ unveils that $\Delta \overline{C_{p,e}}=f_{1}(\overline{U_{J,c}^{*}}, { d}c, f_{e}^{*}, \alpha , Re_{\theta })$ may be reduced to $\Delta \overline{C_{p,e}}/\varPi (\tau )=f_{2}(\xi )$, where $f_{1}$ and $f_{2}$ are different functions, $\Delta \overline{C_{p,e}}$ is the variation in the pressure coefficient at the end of the ramp under control, $\varPi (\tau )$ is a function of dimensionless duration $\tau$ at which the jet is closed within one excitation period, $\Delta \overline{C_{p,e}}/\varPi (\tau )$ represents the control efficiency, and $\xi$ is a scaling factor that is physically the energy ratio per unit area of the blowing jet to the mainstream. This scaling law is also found to be valid for steady jet control. Several interesting inferences can be made from this scaling law, which provides important insight into the physics of flow separation control.

Asymptotic flow states with limiting drag modification are explored via direct numerical simulations in a moderate-curvature viscoelastic Taylor–Couette flow of the FENE-P fluid. We show that asymptotic drag modification (ADM) states are achieved at different solvent-to-total viscosity ratios ($\beta$) by gradually increasing the Weissenberg number from 10 to 150. As $\beta$ decreases from 0.99 to 0.90, for the first time, a continuous transition pathway is realised from the maximum drag reduction to the maximum drag enhancement, revealing a complete phase diagram of the ADM states. This transition originates from the competition between Reynolds stress reduction and polymer stress development, namely, a mechanistic change in angular momentum transport. Reduced $\beta$ has been found to effectively enhance elastic instability, suppressing large-scale Taylor vortices while promoting the formation of small-scale elastic Görtler vortices. The enhancement and in turn dominance of small-scale structures result in stronger incoherent transport, facilitating efficient mixing and substantial polymer stress development that ultimately drives the AMD state transition. Further analysis of the scale-decomposed transport equation of turbulent kinetic energy reveals an inverse energy cascade in the gap centre, which is attributed to the polymer-induced energy redistribution: polymers extract more energy from large scales than they can dissipate, with the excess energy redirected to smaller scales. However, the energy accumulating at smaller scales cannot be dissipated immediately and is consequently transferred back to larger scales via nonlinear interactions, thereby unravelling a novel polymer-mediated cycle for the reverse energy cascade. Overall, this study unravels the challenging puzzle of the existence of distinct dynamically connected ADM states and paves the way for coordinated experimental, simulation and theoretical studies of transition pathways to desired ADM states.

The modulation of drag through dispersed phases in wall turbulence has been a longstanding focus. This study examines the effects of particle Stokes number ($\textit{St}$) and Froude number ($\textit{Fr}$) on drag modulation in turbulent Taylor–Couette (TC) flow, using a two-way coupled Eulerian–Lagrangian approach with Reynolds number ${\textit{Re}}_i = r_i \omega _i d/\nu$ fixed at 3500. Here, $\textit{St}$ characterises particle inertia relative to the flow time scale, while $\textit{Fr}$ describes the balance between gravitational settling and inertial forces in the flow. For light particles (small $\textit{St}$), drag reduction is observed in the TC system, exhibiting a non-monotonic dependence on $\textit{Fr}$. Specifically, drag reduction initially increases and then decreases with stronger influence of gravitational settling (characterised by inverse of $\textit{Fr}$), indicating the presence of an optimal $\textit{Fr}$ for maximum drag reduction. For heavy particles, a similar non-monotonic trend can also be observed, but significant drag enhancement results at large $\textit{Fr}^{-1}$. We further elucidate the role of settling particles in modulating the flow structure in TC flow by decomposing the advective flux into contributions from coherent Taylor vortices and background turbulent fluctuations. At moderate effects of particle inertia and gravitational settling, particles suppress the coherence of Taylor vortices which markedly reduces angular velocity transport and thus leads to drag reduction. However, with increasing influence of particle inertia and gravitational settling, the flow undergoes abrupt change. Rapidly settling particles disrupt the Taylor vortices, shifting the bulk flow from a vortex-dominated regime to one characterised by particle-induced turbulence. With the dominance of particle-induced turbulence, velocity plumes – initially transported by small-scale Görtler vortices near the cylinder wall and large-scale Taylor vortices in the bulk region – are instead carried into the bulk by turbulent fluctuations driven by the settling particles. As a result, angular velocity transport is enhanced, leading to enhanced drag. These findings offer new insights for tailoring drag in industrial applications involving dispersed phases in wall-bounded turbulent flows.

Linear-stability modelling suggests that all sufficiently large riblets promote maximally growing spanwise rollers (García-Mayoral & Jiménez 2011 J. Fluid Mech. vol. 678, 317–347), yet direct numerical simulations (DNS) have shown that this is not the case (Endrikat et al. 2021 J. Fluid Mech. vol. 913, A37) some riblet shapes do not form spanwise rollers at all. Thus, the drag-reduction breakdown across all riblet shapes cannot be solely attributed to maximally growing spanwise rollers, prompting a reappraisal of the modelling. In this paper, comparing DNS data with riblet-resolving linear-stability predictions shows that the spanwise rollers are actually marginal modes, not maximally growing instabilities. This riblet-resolved linear analysis also predicts that not all riblet shapes promote spanwise rollers, in agreement with DNS, and unlike earlier linear-stability modelling, which relied on a one-dimensional (1-D) mean flow and on an over-simplified effective wall-admittance boundary condition. These riblet-resolved calculations further inform how to capture the effect of the riblet shape in a 1D model. Once captured, predictions with an effective boundary condition match riblet-resolved results, but still do not indicate what features of the riblet geometry promote the roller instability. Thus, the wall admittance is measured near the riblet crests, in both the riblet-resolved linear analysis and DNS, to show that the in-groove dynamics is dominated by a balance between the overlying pressure and unsteady inertia, and not viscous diffusion, as previously assumed. This pressure–unsteady-inertia balance sets the linear scaling of the wall admittance with riblet size, as observed in DNS, and is a key factor in setting the streamwise wavelength of the spanwise rollers. Furthermore, modelling this pressure–unsteady-inertia balance in the wall admittance reveals the role of riblet slenderness in promoting spanwise rollers, which provides the missing link in previous correlations between the riblet geometry and the presence or lack of rollers.