We present an investigation of the resonance conditions governing triad interactions of cylindrical internal waves, i.e. Kelvin modes, described by Bessel functions. Our analytical study, supported by experimental measurements, is performed both in confined and unconfined axisymmetric domains. We are interested in two conceptual questions: can we find resonance conditions for a triad of Kelvin modes? What is the impact of the boundary conditions on such resonances? In both the confined and unconfined cases, we show that sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at least a resonance condition on their frequencies of the form $\omega _0 = \pm \omega _1 \pm \omega _2$. We demonstrate that the resulting triad is also spatially resonant, but that the resonance in the radial direction may not be exact in confined geometries due to the prevalence of boundary conditions – a key difference compared with Cartesian plane waves.

Premixed turbulent flames, encountered in power generation and propulsion engines, are an archetype of a randomly advected, self-propagating surface. While such a flame is known to exhibit large-scale intermittent flapping, the possible intermittency of its small-scale fluctuations has been largely disregarded. Here, we experimentally reveal the inner intermittency of a premixed turbulent V-flame, while clearly distinguishing this small-scale feature from large-scale outer intermittency. From temporal measurements of the fluctuations of the flame, we find a frequency spectrum that has a power-law subrange with an exponent close to $-2$, which is shown to follow from Kolmogorov phenomenology. Crucially, however, the moments of the temporal increment of the flame position are found to scale anomalously, with exponents that saturate at higher orders. This signature of small-scale inner intermittency is shown to originate from high-curvature, cusp-like structures on the flame surface, which have significance for modelling the heat release rate and other key properties of premixed turbulent flames.

In a three-layer system with equal upper and lower layer thicknesses that are sufficiently thin and with the same density difference across each interface, breathers have been shown to exist using fully nonlinear governing equations. These breathers are well modelled by theoretical solutions of the mKdV equation, provided the interfaces between the layers do not cross a critical depth. The soliton-like characteristics of fully nonlinear breathers, in particular how two breathers interact, have yet to be explored. Using numerical simulations, this study addresses this shortcoming by studying fully nonlinear overtaking collisions of two breathers in a three-layer symmetric stratification. We apply the fully nonlinear and strongly dispersive FDI-3s internal wave equations, based on a variational principle, in a three-layer system. When the amplitude is small, the analytic breathers fit the wave shapes of the overtaking collision breathers. We find that the larger the upper and lower layer thicknesses are, provided they are below the critical thickness, the more the breathers behave like solitons. We show that an overtaking collision of two breathers is close to elastic.

Plenoptic particle image velocimetry and surface pressure measurements were used to analyse the early development of leading-edge vortices (LEVs) created by a flat-plate wing of aspect ratio 2 rolling in a uniform flow parallel to the roll axis. Four cases were constructed by considering two advance coefficients, $J=0.54$ and 1.36, and two wing radii of gyration, $R_g/c=2.5$ and 3.25. In each case, the wing pitch angle was articulated such as to achieve an angle of attack of $33^{\circ }$ at the radius of gyration of the wing. The sources and sinks of vorticity were quantified for a chordwise rectangular control region, using a vorticity transport framework in a non-inertial coordinate system attached to the wing. Within this framework, terms associated with Coriolis acceleration provide a correction to tilting and spanwise convective fluxes measured in the rotating frame and, for the present case, have insignificant values. For the baseline case ($J=0.54, R_g/c=3.25$), three distinct spanwise regions were observed within the LEV, with distinct patterns of vortex evolution and vorticity transport mechanisms in each region. Reducing the radius of gyration to $R_g/c=2.5$ resulted in a more stable vortex with the inboard region extending over a broader spanwise range. Increasing advance ratio eliminated the conical vortex, resulting in transport processes resembling the mid-span region of the baseline case. Although the circulation of the LEV system was generally stronger at the larger advance coefficient, the shear-layer contribution was diminished.

The so-called coffee stain effect has been intensively studied over the past decades, but most of the studies have focused on sessile droplets. In this paper, we analyse the origin of the difference between the deposition of suspended particles in a sessile drop and in an axisymmetric drop deposited on a fibre. First, we model the shape of a drop on a fibre and its evaporative flux with some approximations to derive analytical calculations. Then, for pinned contact lines, we solve the hydrodynamics equations in the liquid phase under the lubrication approximation to determine the flow velocity toward the contact lines. We comment on these results by comparison to a sessile drop of similar evaporating conditions, and we show that the substrate curvature plays a role on the contact line depinning, the local evaporative flux and the liquid flow field. The competition between the advection and the Brownian motion indicates that the transport of the particles toward the contact line occurs in a volume localised in the close vicinity of the contact lines for a drop on a fibre. Thus, the fibre geometry induces a weaker accumulation of particles at the contact line compared to a sessile drop, leading to the more homogeneous deposit observed experimentally.

When two small fluid drops are sufficiently close, the van der Waals force overcomes surface tension and deforms the surfaces into contact, initiating coalescence. The dynamics of surface deformation across an inviscid gap falls into two distinct regimes (Stokes and inertial–viscous) characterized by the forces that balance the van der Waals attraction at leading order (viscosity, and both inertia and viscosity). The previously studied Stokes regime holds for very viscous drops but fails for less viscous drops as inertia becomes significant before contact is reached. We show that the subsequent inertial–viscous dynamics is self-similar as contact is approached, with the gap width decreasing as $t{'^{3/8}}$ and the radial scale of the deformed region decreasing as $t{'^{1/2}}$ as $t{'}\to 0$, for time until contact $t'$. The self-similar behaviour is universal and is the generic asymptotic behaviour observed in time-dependent simulations. The unique self-similar gap profile of the inertial–viscous regime suggests new initial conditions for the coalescence of the drops after contact.

Many granular surface flows occur as shear flows of finite thickness, over erodible beds composed of the same granular material. Such beds may be fragile, and offer no more resistance to erosion than to sustained shear. Or they may be brittle, and offer instead an excess resistance to erosion. To take this contrast into account, new basal boundary conditions are proposed. Their implications for parallel flows down infinite slopes are then examined for three different cases: stationary flows; starting; and stopping transients. For all three cases, flow behaviour is altered significantly when beds present an excess resistance to erosion. For stationary flows, non-unique velocity profiles are obtained, implying hysteresis or history-dependence. For starting transients, a power law growth of the flow thickness is predicted, instead of the jump to finite or infinite depth that would otherwise occur. For stopping transients, flows start to decelerate with a finite basal shear rate, even over erodible substrates. Analytical solutions to the corresponding free and moving boundary problems are obtained, and checked against numerical results. Model predictions are then compared with experimental measurements. Overall, good agreement is obtained. In particular, the model describes well the very different erosional responses observed for fragile and brittle beds.

In the present work, direct numerical simulation of a laboratory-scale lean premixed reacting jet in cross-flow was performed to explore the flow–flame structures and turbulence–flame interactions. A jet of lean premixed ethylene–air mixtures (equivalence ratio $\phi = 0.6$) was injected into a hot vitiated cross-flow. Both non-reacting and reacting cases were simulated. It was found that the reacting jet penetrates deeper in the cross-flow with a weaker shear layer compared with the non-reacting one. The wake of the non-reacting and reacting jet is characterized by vertical vortices and recirculation zones, respectively. As for the flame structure of the reacting case, the reaction intensity varies considerably in different flame zones. The heat release rate on the leeward side is higher than that on the windward side, but lower than that of the corresponding laminar flame. The analysis of the turbulence–flame interactions of the reacting case showed that the large local Damköhler number ($Da$) related to reaction-induced dilatations results in an increased tendency of the scalar gradient to align with the most extensive strain rate, which is more evident in the regions with high heat release rate on the leeward side. Negative dilatation regions with positive tangential strain rate and negative normal strain rate are observed on the windward side. High positive dilatations appear on the flame front of the leeward side. The tangential strain rate is negatively correlated with the normal strain rate and curvature. Regions with a high local $Da$ on the windward side correspond with high positive curvature regions.

Partial cavity flows forming on a NACA0015 hydrofoil are visualized using high-speed cinematography and time-resolved X-ray densitometry. These observations reveal the underlying flow features that lead to the cloud cavity shedding. Previous studies have reported that both near-surface liquid re-entrant flow and bubbly shock waves can serve as the mechanisms causing cavity pinch-off and cloud shedding. We identify both mechanisms in the current study. The cavity shedding frequency was also examined and related to the underlying flow dynamics. The probability of re-entrant flow or bubbly shock-induced shedding processes are quantified, and the likelihood of each mechanism is shown to be a function of both the cavitation number and the Mach number of the bubbly mixture within the separated region of the cavity. When the Mach number of the two-phase mixture in the cavity exceeds unity, shock waves become the dominant mechanism that lead to large-scale cavity shedding and cloud cavitation.

Linear stability analyses are performed to investigate the boundary layer instabilities developing in an incompressible flow around the whole leading-edge of swept ONERA-D and Joukowski airfoils of infinite span. The stability analyses conducted in our study are global in the chordwise direction and local in the spanwise direction. A neutral curve is drawn at a given leading-edge Reynolds number $Re_R$ and several overlapping regions, called ‘lobes’, are identified on a physical basis. A detailed study of the marginal modes reveals the presence of attachment-line and cross-flow instabilities, as well as modes whose features do not fall within the standards of a specific type. Connected cross-flow/Tollmien–Schlichting modes, that show a dominant spatial structure reminiscent of Tollmien–Schlichting waves but whose destabilization is linked to a cross-flow mechanism, have been identified. The comparison of several neutral curves at different $Re_R$ values reveals the greater stabilizing effect of the increase of $Re_R$ on the cross-flow instability compared with the attachment-line instability. The influence of the airfoil shape is also studied by comparing the neutral curves of the ONERA-D with the neutral curves of the Joukowski airfoil. These curves reveal similar characteristics with the presence of distinct lobes and their comparison at constant sweep angle shows that, under the conditions studied, the ONERA-D airfoil is more stable than the Joukowski airfoil, even for cross-flow instabilities. The absolutely or convectively unstable nature of the flow in the spanwise direction is also tackled and our results suggest that the flow is only convectively unstable.

The alteration of the near-wall flow field of a turbulent boundary layer flow subjected to spanwise travelling transversal surface waves at a friction Reynolds number $Re_\tau \approx 1525$ is investigated. The results of a spatial noise-assisted multivariate empirical mode decomposition reveal that this flow control method periodically induces near-wall large-scale bursts while simultaneously lowering the energetic content of small-scale features. The increasing occurrence of intense large-scale ejections in the near-wall region is of particular importance for reducing the wall-shear stress since these ejections balance large-scale sweeps originating from the outer layer. Thus, they corrupt the outer-layer impact on the near-wall dynamics and, consequently, the overall fluctuation intensity at the wall is attenuated. This disturbed top-down momentum exchange is highlighted by an inner–outer interaction analysis, which further reveals an increased bottom-up communication provoked by the large-scale ejections. Moreover, it is shown that the periodic secondary flow field induced by the actuation interferes with the quasi-streamwise vortices in the near-wall region. The velocity gradients of the secondary flow field deform the vortices’ cross-section into an elliptic shape, which yields an unstable vortex state resulting in vortex disintegration. In combination with the effect of the large-scale ejections, the reduced number of quasi-streamwise vortices compared with the undisturbed boundary layer flow results in a decreased wall-normal momentum exchange and the widening and weakening of near-wall streaks. This yields a reduced fluctuation intensity in the near-wall region that lowers the overall wall-shear stress level.

We carry out direct numerical simulations (DNS) of turbulent flow and heat transfer in pressure-driven plane channels, by considering cases with heating on both walls, as well as asymmetric heating limited to one of the channel walls. Friction Reynolds numbers up to ${Re}_{\tau } \approx 2000$ are considered, and Prandtl numbers from ${Pr}=0.025$ to ${Pr} = 4$, the temperature field being regarded as a passive scalar. Whereas cases with symmetric heating show close similarity between the temperature and the streamwise velocity fields, with turbulent structures confined to either half of the channel, in the presence of one-sided heating the temperature field exhibits larger regions with coherent fluctuations extending beyond the channel centreline. Validity of the logarithmic law for the mean temperature is confirmed, as well as universality of the associated von Kármán constant, which we estimate to be $k_{\theta } = 0.459$. Deviations from the logarithmic behaviour are much clearer in cases with one-sided heating, which feature a wide outer region with parabolic mean temperature profile. The DNS data are exploited to construct a predictive formula for the heat transfer coefficient as a function of both Reynolds and Prandtl number. We find that the reduction of the thermal efficiency in the one-sided case is approximately $20\,\%$ at unit Prandtl number; however, it can become much more significant at low Prandtl number.