The T-shaped mixer is widely used in fundamental studies of chemical engineering. Its transitional regime is well understood, whereas the turbulent dynamics has received scarce attention so far. Here, we perform direct numerical simulations of the turbulent regime for Reynolds numbers up to $\textit{Re}=2000$ at Schmidt number $\textit{Sc}=1$. Our analysis reveals two distinct stages along the mixing channel prior to relaxation toward duct flow. Near the junction, a jet-like flow forms and exhibits the approximately self-similar behaviour of transitional planar jets. Subsequently, a decay region characterised by power-law decay of turbulent kinetic energy, dissipation and scalar variance emerges. For the velocity field, the observed exponents are consistent with those of decaying turbulence in bounded domains, whereas the scalar-variance exponent is consistent with that of unbounded turbulence. We argue that this apparent discrepancy is a consequence of the mixing process progressing from the centre of the channel toward the sidewalls in the decay region, while turbulence already fills the channel cross-section entirely at the end of the jet region.The time-averaged mixing state presents error-function profiles of the scalar in the transverse direction, similar to the laminar cases, and is quantified here through a streamwise evolving effective diffusion coefficient.

Cavitation bubbles collapsing near capillary exits can generate fast microjets that penetrate into the channel and promote fluid exchange. Here, we combine high-speed imaging and axisymmetric compressible volume-of-fluid simulations to study laser-induced cavitation bubbles near the exit of a long capillary. By varying the stand-off distance $\gamma$, the normalised inner radius $R_i^*$ and the normalised outer radius $R_o^*$, we identify two distinct jetting mechanisms. Regular jets are driven primarily by the vertical collapse of the bubble surface distal to the capillary, whereas wave-driven jets arise from the propagation and convergence of an interfacial wave initiated at the proximal bubble surface, causing distal-surface splitting and strong local pressure amplification. Wave-driven jets occur for sufficiently small stand-off distances and outer radii, with formation velocities typically above $500\,\mathrm{m\,s}^{-1}$ and reaching up to $2000\,\mathrm{m\,s}^{-1}$ in the simulations. Regular jets dominate at larger stand-off distances or larger outer radii, where interfacial-wave effects weaken. The outer radius $R_o^*$ governs the jetting regime by controlling interfacial-wave formation, propagation and convergence, while the inner radius $R_i^*$ mainly affects the later jet dynamics, including the impact location and vapour-jet penetration into the capillary. Compared with the needle jet generated by a bubble collapsing near a smooth rigid wall at nearly zero stand-off distance, the wave-driven jet here occurs over a much wider parameter range and its velocity and size can be tuned geometrically. These results establish a physical framework for cavitation-driven jetting near capillary boundaries and suggest strategies for controlling confined microjets in microfluidics and biomedical applications.

Microorganisms swimming are typically explored in low-Reynolds-number environments where fluid inertia is negligible. However, in complex fluids such as lyotropic liquid crystal polymers (LCPs), the interplay between fluid inertia and anisotropy may lead to distinctive dynamical features. This study combines asymptotic analysis and direct numerical simulations to investigate the role of fluid inertia in undulatory locomotion through a lyotropic LCP using a classical model of Taylor’s swimming sheet. In isotropic LCPs, we suggest that the behaviours of swimmers are similar to those observed in Oldroyd-B viscoelastic fluids. Fluid inertia enhances the swimming speed and mechanical efficiency at finite Reynolds numbers. By contrast, in nematic LCPs, we reveal that the swimming speed and efficiency monotonically decrease with Reynolds numbers for parallel and perpendicular swimming, showing Newtonian-like behaviours. We demonstrate that the phase transition of the LCPs significantly alters their mechanical responses.

The shear flow induced by a jetting cavitation bubble within grooved structures is systematically investigated using a three-dimensional compressible volume-of-fluid (VoF) solver combined with ultra-high-speed photography of one million frames per second (fps). The structured surface comprises twenty parallel micro-channels, and local mesh refinement down to $0.1\ {\unicode[Arial]{x03BC}}\text{m}$ near the groove bottom resolves the linear tangential velocity profile within the boundary layer. The simulations accurately reproduce experimental observations for two representative configurations, namely bubbles initiated above the groove and above the protrusion. In general, a microjet formed from the distal bubble surface impacts the lower bubble interface and subsequently spreads both along and across the groove channel, generating strong shear flow. Spatio-temporal wall-stress distributions indicate that the maximum shear stress occurs near the instant of jet impact, while the subsequent evolution is further modulated by daughter-bubble fragmentation and re-expansion. For a bubble initiated above the groove, the microjet produces a single impact, whereas for a bubble initiated above the protrusion, the jet becomes oblique: it first strikes the protrusion, spreads into the trapped bubble inside the groove and finally pierces the lower bubble surface at an angle. The influences of three geometric parameters, namely the horizontal offset $d^*$, vertical stand-off distance $h^*$ and groove width $w^*$, are systematically examined, revealing their coupled effects on bubble deformation, jet orientation, fragmentation and the vortex dynamics. A peak wall-shear stress of approximately $150\,\text{kPa}$ is obtained under specific geometric conditions due to rapid jet spreading and flow refocusing within the groove. These results provide fundamental insight into the three-dimensional, unsteady wall-shear generation produced by jetting cavitation bubbles interacting with micro-structured surfaces.

The interaction of a moving shock wave with a localised constriction in a straight conduit is studied using large-eddy simulations, validated against time-resolved schlieren imaging and wall-pressure measurements from shock-tube experiments. The blockage ratio (0.35–0.75) and the normalised constriction length (0.25–2) are varied independently for two limiting geometric families, an abrupt rectangular constriction and a smoothly contoured sinusoidal constriction, at incident Mach numbers of 1.4 and 1.8. The start-up process within the constriction develops over time scales one to two orders of magnitude longer than the shock passage time, and in the sinusoidal family it follows two distinct pathways: shock-induced separation of an attached transonic flow in longer constrictions and acceleration of a separated jet in shorter ones. Despite these differences, the late-time reflected and transmitted shock strengths depend primarily on the blockage ratio, with constriction length and contour acting as secondary modifiers. We attribute this regularity to choking at an effective sonic area, and show that this condition supplies the closure required to predict both reflected and transmitted asymptotic shock-wave strengths, recovering reduced-order models developed here as limiting forms. The contraction coefficients required by this closure follow from the constriction geometry and the local flow analysis, without fitting. The predictions agree with the simulations to within approximately 1 % for the reflected shock and a few per cent for the transmitted shock. A reflection-corrected geometrical shock-dynamics formulation, closed by the same condition, reproduces the approach of the transmitted shock front to this asymptote for the smooth contours.

The presence of sidewalls in turbulent duct flows leads to the emergence of secondary flow structures in the form of counter-rotating streamwise vortices near the corners (Prandtl’s secondary flow of the second kind). This work develops reduced-order Galerkin projection models that can predict the emergence and structure of these turbulent mean secondary flows in a square duct geometry, without requiring any prior knowledge of the turbulent statistics. The models are obtained by projecting the Navier–Stokes equations onto eigenmodes of the linearised system, with the resulting systems of ordinary differential equations simulated with the addition of zero-mean forcing. We show that most models obtained using leading streamwise-constant eigenmodes predict the correct shape and direction of the secondary mean, with the minimal such model requiring only two modes. In these models, the secondary mean contribution arises due to the non-zero average coefficient of an eigenmode that possesses all of the symmetry properties expected of a secondary mean. The models are sufficiently simple such that the relationship between this mean coefficient and the joint second moment of other mode coefficients can be computed analytically. We confirm that running streamwise-constant direct numerical simulations (DNS) with the same forcing structure as used in the reduced-order models produces similar secondary flow structures. We additionally demonstrate that our models produce qualitatively similar Reynolds stress distributions to fully resolved DNS, with improved agreement as model dimension increases.

This paper is concerned with the stability of time-harmonic plane internal gravity–inertial waves in an unbounded, uniformly stratified, rotating fluid under the Boussinesq and $f$-plane approximations. The focus is on how the often-used ‘local’ analysis of short-scale instabilities, which is based on the WKB approximation, relates to the formal (‘global’) stability treatment using Floquet theory, and on whether any important physics is lost as a result of this approximation. By recasting the stability equations in Lagrangian coordinates following particle paths in the basic wave and introducing normal modes, it is demonstrated rigorously that in the limit of large disturbance wavenumber ($k\rightarrow \infty$), such ‘Lagrangian’ modes translate to the localised wavepackets assumed by local stability. This reveals that: (i) local instabilities generally involve multiple frequency components (in the Eulerian frame) and thus are distinct from parametric subharmonic instability; and (ii) local stability neglects altogether the effects of dispersion on wavepackets. While the local approach assumes short-scale disturbances ($1/k\rightarrow 0$) apparently without restricting the basic-wave amplitude $\epsilon$, this approximation is not uniformly valid when $\epsilon \ll 1$. In this limit, the appropriate stability eigenvalue problem balances the $\mathcal{O}(1/k)$ dispersion with the $\mathcal{O}(\epsilon )$ interaction of perturbations with the basic wave. This uniformly valid approach is applied to short-scale instabilities of small-amplitude finite-width propagating wave beams, extending to non-zero rotation and three-dimensional perturbations the results on broadband instability presented in Fan & Akylas (2021, J. Fluid Mech., vol. 913, A5). The onset of instability occurs at large, but finite $k =\mathcal{O}(1/\epsilon )$, and is beyond the reach of local stability. Rotation generally promotes three-dimensional instability.

Heterogeneous wettability surfaces can passively direct the motion of impacting droplets without external actuation. However, the mechanisms governing droplet impact across a single planar wettability boundary remain insufficiently understood, particularly when the lamella undergoes perforation and rupture. In this study, the non-orthogonal multiple-relaxation-time lattice Boltzmann method is used to examine the effects of the contact angle $\theta _R$, Weber number $\textit{We}$ and dimensionless impact deviation $D$. Increasing $\theta _R$ suppresses spreading and advances recoil. The kinetic energy valley time decreases approximately exponentially, whereas the minimum kinetic energy increases nearly linearly. The recoil-stage kinetic energy peak generally increases with $\theta _R$ but drops markedly at $\theta _R=170^\circ$, where lamella perforation disrupts coherent retraction. Increasing $\textit{We}$ raises the peak effective surface energy, vorticity and wetted area, yet reduces the normalised recoil-stage kinetic energy peak. Perforation and fragmentation redistribute energy into local deformation and viscous dissipation, thereby weakening coherent recoil and lateral migration. Shifting the impact position towards the less-wetting region suppresses spreading but enhances recoil. The recoil-stage vorticity is largest at $D=0$, while the lateral migration exhibits two deviation-dependent regimes. These results demonstrate that surface wettability contrast and lamella connectivity play important roles in directional droplet transport.

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

The method of three-dimensional curved characteristics (MOTC), built upon the three-dimensional curved shock theory (3D-CST-boos), is developed to uncover the downstream flow physics of three-dimensional shock-dominated supersonic flows. Starting from the post-shock pressure gradients and streamline curvatures supplied by 3D-CST-boos at the shock surface, MOTC advances these quantities along streamlines and characteristics to construct the complete downstream flowfield. The methodology derives a comprehensive set of governing equations, including gradient terms, along streamlines and characteristics. A key advantage over conventional osculating methods lies in its retention of the lateral pressure gradient and cross-flow information, which substantially enhances the accuracy of three-dimensional flowfield simulations. The method is verified against inviscid CFD for both external and internal flow configurations, achieving errors below 0.5 %. More importantly, the retained gradient information reveals a cross-over of the streamwise compression: near the shock, the pressure gradient is governed by the transverse shock curvature; while further downstream, the lateral pressure gradient drives flow convergence or divergence, reversing the compression ordering across different shock geometries. The lateral pressure gradient distribution is controlled by the shock axial ratio, providing a guideline for shock shape selection in forebody or inlet design. For internal flows, the reflected shock asymmetry is governed by the same shock-curvature-to-transverse-flow transition, offering a physical basis for centre-body design. The combination of accuracy, computational efficiency and the ability to trace flow physics from the shock to the far-field positions MOTC as a powerful tool for analysis and inverse design of supersonic flowfields.

Filtration flows through nanoporous membranes play a crucial role in a range of cutting-edge technologies, including water purification, osmotic power generation and targeted drug delivery. Molecular dynamics (MD) simulations are currently considered the state-of-the-art approach for modelling nano-filtration processes. However, their high computational cost makes simulating large-scale filtration systems impractical, limiting the ability to conduct extensive parametric studies and optimise design strategies. In the present paper, we merge a molecular analysis of the nano-filtration problem with a homogenisation technique, to upscale the filtration flow from the single nanopore description to the whole membrane scale phenomenon. The homogeneous model allows replacing the detailed description of the flow through the whole membrane with a simplified flow description, where the membrane is an effective smooth interface between two macroscopic fluid regions. The model rigorously quantifies jumps in the macroscopic solvent velocity and stresses across the homogeneous membrane via a set of tensorial quantities computed once and for all via MD simulations, enabling us to predictively quantify the membrane properties in the presence of nanoscopic pores. Finally, we validate the MD-homogenisation model by comparison with MD simulations of a water flow through arrays of pores, assessing the computational efficiency of the novel methodology.

We present a comprehensive experimental investigation on flow mode transition and heat transport in confined liquid metal convection at a Prandtl number of $ \textit{Pr} = 0.029$, using cylindrical convection cells with aspect ratios $\varGamma = 1$, $1/2$ and $1/3$. Whenever comparable data are available, the present low-$ \textit{Pr}$ results are compared with previous measurements in moderate-$ \textit{Pr}$ water convection (Xi & Xia, Phys. Fluids vol. 20, 2008, p. 055104; Weiss & Ahlers, J. Fluid Mech. vol. 676, 2011, pp. 5–40). It is found that the single-roll mode (SRM) dominates in the $\varGamma = 1$ and $1/2$ cells, whereas the double-roll mode (DRM) prevails in the $\varGamma = 1/3$ cell. The relative weight of the SRM increases with $\varGamma$, while those of the DRM and the transition mode decrease. Focusing on the $\varGamma = 1/3$ cell, three representative DRM–SRM–DRM transition routes are observed: one induced by cessations and two associated with azimuthal rotational reorganisation of the flow. Beyond the previously studied reversals of the SRM, the DRM can also reverse through either cessation or continuous azimuthal reorientation. In this strongly confined cell, the dominant DRM is asymmetric, consisting of a larger and stronger upper roll, and a smaller and weaker lower roll. These changes in flow organisation are also reflected in heat transport: the SRM transports heat slightly more efficiently than the DRM and the difference decreases with increasing Rayleigh number $ \textit{Ra}$. For $\varGamma = 1/2$, comparison with moderate-$ \textit{Pr}$ water convection further suggests that this heat-transport difference depends weakly on $ \textit{Pr}$, compared with its stronger dependence on $ \textit{Ra}$. These results deepen the understanding of large-scale flow structures in turbulent thermal convection and provide useful data for modelling large-scale flows in turbulent convection.

In real-life tunnel or flight environments, the laminar–turbulent transition of compression ramp flows can be initiated by absolute and/or convective instabilities. Currently, the relative significance of the two instabilities in such flows remains unclear. This paper addresses this issue by decoupling the effects of absolute and convective instabilities, which is an extension of our previous research (Huang et al. Phys. Fluids, vol. 37, 2025, p. 034110). Hypersonic flows over a compression ramp with a 15$^\circ$ ramp angle at Mach number 8.0 and Reynolds number ${{\textit{Re}}_{L}}=9.2\times {{10}^{5}}$ based on the flat plate length are investigated using direct numerical simulation (DNS) and several stability analysis tools. Global stability analysis (GSA) reports that the flow is intrinsically unstable. Without external disturbances, DNS shows a good agreement with GSA regarding the growth rate and the disturbance shape. The flow in DNS is dominated by the most amplified stationary mode and the low-frequency oscillatory mode. However, transition in this case cannot be accomplished in the computational domain purely by the absolute instability. With external forcing, the coexistence of absolute and convective instabilities triggers the transition. For the forcing amplitudes examined in this study, which are representative of moderately to strongly noisy wind tunnel environments, the absolute instability is not significant in affecting the transition onset location. Nonetheless, the interplay between absolute and convective instabilities can profoundly alter the dominant spanwise wavelengths, the pronounced frequency band, the shape of coherent structures, etc. In summary, the interplay between the two types of instabilities recasts the transition scenario, albeit the transition onset location is dominated by the convective instability.

Particle-resolved direct numerical simulations are employed to investigate homogeneous steady liquid–solid suspensions over an extended range of particle–fluid density ratios ($0.05\leqslant \rho ^\ast \leqslant 5.5$). This parameter span, which includes floating ($\rho ^\ast \lt 1$), nearly neutrally buoyant ($\rho ^\ast \approx 1$) and settling ($\rho ^\ast \gt 1$) regimes, enables a systematic assessment of deviations from kinetic theory for granular flows (KTGF). We show that the Richardson–Zaki correlation for the mean relative velocity requires modification: the exponent depends on $\log \rho ^\ast$ at low Reynolds number, while the scaling law between the prefactor and an effective density ratio $(\rho ^\ast +C_m)$, implicating the virtual mass force. Analysis of particle velocity fluctuations reveals a granular temperature that departs markedly from both algebraic models and KTGF predictions, exhibiting complex coupling with $\rho ^\ast$ and particle concentration. The velocity distribution is non-Maxwellian, as evidenced by significant skewness and kurtosis. Non-exponential decay of particle velocity autocorrelations and partial autocorrelations reveal a negative decaying memory effect attributable to the history force, suggesting the need for truncated history-dependent models. The pair correlation function shows anisotropic microstructure and a cage-like arrangement at higher concentrations. The radial distribution function at contact is an order of magnitude larger than classical granular-flow models, indicating a microscopically inhomogeneous state despite macroscopic homogeneity. The collisional solid pressure and dissipation are significantly attenuated relative to KTGF predictions, implying that interphase viscous interactions weaken momentum exchange during collisions while enhancing their frequency via induced Brownian motion. These results underscore the necessity of incorporating density-ratio effects, fluid-mediated memory and enhanced collisional correlations into constitutive models for liquid–solid flows.

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

We investigate the occurrence and interpretation of an approximate $-5/3$ power law in one-dimensional velocity spectra in the wake of a circular cylinder using three-component hot-wire measurements in the mean-shear plane at $x/d=10$, 20 and 40 over Reynolds number $ \textit{Re}_d=2500$–15 000, based on the free-stream velocity $U_\infty$ and the cylinder diameter $d$. At $ \textit{Re}_d=15\,000$ and $x/d=20$, the spectra $\phi _v$ and $\phi _w$, associated with the lateral and spanwise velocity components, respectively, exhibit a broad $-5/3$ range over $y/d\simeq 0$–1.2, whereas the spectrum $\phi _u$, based on the streamwise velocity shows a narrower range: the spectra progressively deviate from $-5/3$ as $y/d$ increases. The $-5/3$ band width also depends on the streamwise location: it becomes much narrower for all spectra at $x/d=40$. As $ \textit{Re}_d$ increases from 2500 to 15 000, the magnitude of the spectral exponent for $\phi _u$ and $\phi _v$ gradually decreases toward 5/3 at $x/d = 10$, and the $-5/3$ band width widens at $x/d\geqslant 20$; the $ \textit{Re}_d$ trend differs from that in grid turbulence. At comparable low $ \textit{Re}_d$ a discernible $-5/3$ range is more readily observed in square-cylinder wakes than in the circular-cylinder wakes. A dual-scaling collapse using outer variables $(v',L_v)$ and inner Kolmogorov variables $(u_K,\eta )$ is found for $x/d=20$–40 and $y/d\simeq 0$–1.2, where $v'$ is the lateral root-mean-square velocity, $L_v$ is the lateral integral length scale, and $u_K$ and $\eta$ are the Kolmogorov velocity and length scales, respectively; at sufficiently high Taylor-microscale Reynolds number $ \textit{Re}_\lambda$, the overlap of these similarity ranges yields an apparent $-5/3$ law. Phase-conditioned statistics and physical-space scale-by-scale budgets show that coherent motions and large-scale forcing (production and diffusion) remain significant over the range of separations associated with the $-5/3$ band, supporting an interpretation in which the observed $-5/3$ band is influenced by persistent large-scale forcing, including the coherent motions, rather than being identified solely with a classical inertial subrange.

This study investigates the convective behaviour of two dielectric fluids with different Prandtl numbers under microgravity, each of which is confined between two parallel electrodes at a given temperature, and subjected to internal dielectric heating. Three-dimensional direct numerical simulations reveal a rich sequence of flow regimes as the electric Rayleigh–Roberts number increases: stable hexagonal patterns, mixed hexagonal-square structures, dominant rectangular convection and time-dependent convection. We derive scaling laws for key dimensionless quantities, including energy densities, convective Reynolds number and Nusselt number, with strong agreement across two magnitudes of the control parameter. Finally, we observe a shift in the onset of convection, with the critical electric Rayleigh–Roberts number increasing as the thermoelectric coupling parameter decreases. These results offer new insights into the role of internal dielectric heating in convective pattern formation and energy transport.

Laboratory experiments and direct numerical simulations (DNSs) were conducted to examine boundary-layer transition over a standing-wave wall composed of eight sinusoidal waves of wavelength $\lambda =100$ mm and amplitude $a=5$ mm, placed downstream of a short flat-plate leading edge in a low-turbulence free stream. The DNSs reproduced two lower-frequency experimental cases for validation and extended the investigation to higher frequencies at an amplitude-based Reynolds number $\textit{Re}_a=388$, showing strong agreement in overlapping cases. The forcing is characterised by the reduced frequency $\textit{St}=f_w\lambda /U_{\mathit{c,m}}$, where $f_w$ is the wall oscillation frequency, $U_{\mathit{c,m}}$ is the mean streamwise convection velocity, which represents the number of wall-oscillation cycles during the mean convection of a coherent structure over one wall wavelength. The transition location shifts downstream on average as $\textit{St}$ increases, but also oscillates about this trend due to the phase relation between wall motion and coherent-structure convection. Near half-integer values of $\textit{St}$ (${\approx} 0.62$ and 1.7), a reinforcing phase relation strengthens shear-layer roll-up over adverse-pressure-gradient segments and advances transition, whereas near-integer values ($\textit{St}\approx 1.2$ and 2.2) produce a suppressing phase relation that weakens shear-layer amplification and delays transition. Time series of the $\lambda _2$ criterion and the corresponding spectra support this interpretation, showing that the advanced-transition cases exhibit phase-locked packet formation and spectral peaks at $f_w$ and its harmonics, whereas the delayed-transition cases remain intermittent and broadband. These results show that phase coupling among wall motion, pressure-gradient forcing and coherent-structure convection serves as the primary mechanism controlling the location of transition under standing-wave forcing.

Transonic buffet is a type of unsteady shock wave/boundary-layer interaction (SBLI) found in a wide range of aerospace applications. In this work, the focus is on the two-dimensional chordwise shock oscillations observed on span-periodic aerofoils at Strouhal numbers of ${\textit{St}} \sim [0.05, 0.1 ]$. Previous experimental and computational studies have categorised ‘laminar’ or ‘turbulent’ buffet based on the absence or presence of tripping upstream of the interaction. However, the buffet response over a full range of upstream boundary-layer states has yet to be investigated. In this work, implicit large-eddy simulations are performed at active buffet conditions for fourteen levels of numerical tripping strength, in order to obtain a full range of laminar, transitional and turbulent boundary layers upstream of the SBLI. While laminar and turbulent buffet are found to share similar low-frequency unsteadiness, a narrow band within the transitional regime is identified for the first time with partially suppressed buffet, greatly reduced shock oscillations and a 4–6$\times$ reduction in lift fluctuations. In the transitional cases, additional spectral energy content is identified over several distinct modes in the range ${\textit{St}} \sim [0.32, 1.9 ]$. Spectral proper orthogonal decomposition analysis attributed these peaks to shock-foot oscillations coupled to boundary-layer streaks and a strongly enhanced vortex-shedding mode originating from the rear of the SBLI. The partial suppression of low-frequency unsteadiness in some transitional cases is interpreted as arising from the interaction between upstream boundary-layer streaks and the shock foot and separation line, regions known to be receptive to external forcing in the context of buffet.

We investigate the evolution of Peregrine breather (PB) rogue waves in narrow-banded random background wave fields using a fully nonlinear wave model. The influence of the peak wavenumber, the significant wave height, and the spectral width of the background field on the maximum crest height, the timing of rogue wave occurrence, and the spatiotemporal distribution of rogue waves is analysed. The results show that when the background peak wavenumber matches that of the PB carrier, nonlinear focusing is enhanced and the phase distribution is modified. The maximum crest height increases by 4.4 % on average, the mean time of first occurrence decreases by 15.9 %, and rogue wave activity extends over a larger spatiotemporal domain. These effects weaken as the wavenumber detuning increases. Increasing the significant wave height of the background field enhances nonlinear interactions and leads to more pronounced changes in the relative phases among wave components, resulting in broader distributions of rogue waves. Over the range considered, the ensemble-averaged maximum crest height increases by up to 5.4 %, while the mean time of first occurrence decreases by up to 40.4 %. The influence of spectral width depends on wavenumber detuning: spectral broadening has little effect when the two peak wavenumbers coincide, but gradually reduces the maximum crest height when they are separated. These findings demonstrate that narrow-banded random background wave fields can significantly modulate the evolution of PB rogue waves through combined effects on energy distribution and phase relationships, providing new insights into rogue wave dynamics in realistic ocean environments.