Gravity–capillary waves are waves influenced by both the effects of surface tension and gravity; these waves are at small scales with wavelength range from approximately 10 cm to less than 1 cm. Gravity–capillary waves play a significant role in air–sea interactions, and they exhibit much different features compared with gravity waves. They can be observed widely on the sea surface. Parasitic waves (capillary waves generated by and that ride on gravity and/or gravity–capillary waves) and micro-breaking can be observed on the water surface with winds; however, the presence of wind makes it difficult to analyse the mechanisms of the wave itself. In this paper, parasitic waves and micro-breaking on gravity–capillary waves are examined experimentally, both in the absence of wind. Parasitic waves and axisymmetric micro-breaking waves are generated mechanically in a convergent channel, where energy density increases due to spatial convergence. Three experimental techniques are used to measure wave properties: planar laser-induced fluorescence, particle image velocimetry and shadowgraphs. The wave profile evolution and vortices beneath the parasitic waves are studied. The micro-breaking of gravity–capillary waves is observed on a surface with added surfactant. The surfactant increases the Bond number, and makes breaking possible in these small-scale waves. Energy dissipation of parasitic waves and micro-breaking is quantified, and the enhanced dissipation caused by parasitic waves is identified through the experiments. In this study, mechanically generated breaking waves with wavelengths less than 10 cm are studied for the first time, without the effect of wind. The results yield insight into wave characteristics and energy dissipation on the air–sea interface at small scales.

Underwater stability of an air layer trapped in a micro-structure, plastron, is critical in drag reduction applications. Here, we investigate the wetting state and plastron stability of underwater superhydrophobic surfaces (SHS) under an intense acoustic drive. Flat surfaces and SHS are subjected to short acoustic pulses of different intensities. At low amplitude, the comparison between the results of various surfaces shows that plastron behaves like a water–air interface, whose presence can be detected from the phase of the reflected acoustic waves. At moderate intensity, a wetting transition towards a completely wetting state is observed and shown to be triggered by a sufficiently large acoustic radiation pressure. This wetting transition is well captured by a simplified model by balancing radiation pressure with the critical capillary pressure for the interface sliding. Cavitation clouds appear under strong excitation; their sizes and positions greatly depend on the surface acoustic boundary condition. For SHS in a Cassie–Baxter state (with an air layer), cavitation clouds appear at specific locations (from the solid surface) corresponding to the pressure anti-node of the transient standing wave generated by the reflection. This study unprecedentedly demonstrates the capability of acoustic waves to monitor and characterize plastron stability with low and moderate amplitudes, respectively.

An experiment on convective flows induced by the dielectrophoretic force was performed under the microgravity condition provided during a sounding rocket flight. The dielectrophoretic force possesses a non-conservative term that can be seen as resulting from an electric gravity. That gravity can be responsible for an electric Rayleigh–Bénard convection between a hot inner cylinder and a cold outer cylinder when an electric field is applied in the radial direction. Four cells with independent temperature and electric field controls allowed the investigation of eight different values of the electric Rayleigh number relatively close to the onset of the thermo-electric instability. A linear stability analysis is performed to predict the stability threshold and the evolution of the growth rate of the instability. The three-dimensional structure of the flow is captured by simultaneous particle image velocimetry and by shadowgraphy. The amplitude of the instability modes and the time evolution of the flow is analysed, and various methods are proposed to extrapolate the experimental critical value of the electric Rayleigh number for the onset of convection. The measured critical electric Rayleigh number is in agreement with the prediction of the linear stability theory. The comparison of the new experimental results with previous ones from parabolic flight campaigns highlights the importance of long-term microgravity for the achievement of thermal convection at low values of the control parameters.

Turbulent plane-Couette flow suspended with finite-size spheroidal particles is studied using fully particle-resolved direct numerical simulations. The effects of particle aspect ratio on turbulent arguments and particle statistics are explored, leading to the same conclusions as the previous experimental findings (Wang et al., J. Fluid Mech., vol. 937, 2022, A15). By performing stress analysis, we find that the presence of particles introduces extra stresses to the system and accounts for the global drag increases. The particle-laden flow cases exhibit spectra that are consistent with the scalings $k^{-5/3}$ and $k^{-3}$ in the large and small scales, respectively. While the $k^{-3}$ scaling observed in the particle-laden flow is reminiscent of bubbly flow, an examination of the particle Reynolds number suggests that the mechanism responsible may not be attributable to the pseudo-turbulence induced by particles as in the case of bubbles. In the view of particle statistics, we observe that spherical and non-spherical particles cluster preferentially in the near-wall and the bulk region, respectively, and that the orientations of non-spherical particles are affected by their aspect ratios, especially in the near-wall region. The present numerical results, combined with previous experimental findings in Wang et al. (J. Fluid Mech., vol. 937, 2022, A15), provide in-depth information on both the fluid and the particle phase, contributing to a better understanding of particle suspension in shear flows.

In the present study, the flow–structure interaction of a starting jet through a flexible nozzle is experimentally investigated, with a focus on the optimal flexibility for thrust generation. Water slug is impulsively accelerated through a cylindrical nozzle, fabricated with silicone rubber of varying flexibility. In general, the flexible nozzle modifies the vortical structure of the jet and augments the thrust of the starting jet. The measurement of nozzle surface deformation revealed that a back-and-forth wave propagation on the nozzle surface is responsible for the jet-vortex evolution augmenting the thrust generation. Combining the hydrodynamic conservation equations and the linearized shell theory, we also formulated the governing equations, dominated by two relevant dimensionless parameters: the effective acceleration time of the jet ($\varPi _0$) and the effective nozzle stiffness ($\varPi _1$). Asymptotic analysis of the equation showed that the dimensionless wave speed ($\hat {c}$) is expressed as $\hat {c}=(\varPi _{0}^{2}\varPi _{1}/2)^{0.5}$, and the jet momentum is maximized at $\hat {c}=\hat {c}_{crit}$ ($\simeq 3.0$), the condition at which the release of elastic energy stored during nozzle contraction to the jet is synchronized with the instant of termination of jet acceleration. While $\hat {c}=\hat {c}_{crit}$, the achievable maximum jet velocity decreases with the effective acceleration time of the jet ($\varPi _0$), which is attributed to the reduced speed of the surface wave by the flow inside the nozzle.

The local streamline topology classification method of Chong et al. (Phys. Fluids A: Fluid Dyn., vol. 2, no. 5, 1990, pp. 765–777) is adapted and extended to describe the geometry of infinitesimal vortex lines. Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that the joint probability density function (p.d.f.) of the second ($q_\omega$) and third ($r_\omega$) normalized invariants of the vorticity gradient tensor asymptotes to a self-similar bell shape for $Re_\lambda > 200$. The same p.d.f. shape is also seen at the late stages of breakdown of a Taylor–Green vortex suggesting the universality of the bell-shaped p.d.f. form in turbulent flows. Additionally, vortex reconnection from different initial configurations is examined. The local topology and geometry of the reconnection bridge is shown to be nearly identical in all cases considered in this work. Overall, topological characterization of the vorticity field provides a useful analytical basis for examining vorticity dynamics in turbulence and other fluid flows.

Particle-resolved direct numerical simulations are employed to investigate the particle–particle drag force in the bidisperse gas–particle suspensions where the particles are smooth and the single-particle velocity distribution function is Maxwellian. The particle Reynolds number ranges from 6.7 to 123.8, and in this range the particle inertia is high enough that the lubrication force is not essential. It is found that the relation derived by the kinetic theory of granular flow (KTGF) highly overestimates the particle–particle drag force. This is because the pre-collision velocities of colliding particles are not completely uncorrelated with each other. From the time sequence of collision events, it is observed that the particle pair that has just collided will probably collide again after a short time due to the restriction of the particle motion in dense suspensions. Since the post-collision velocities of the first collision cannot relax entirely in such a short time, the relative velocity before the subsequent collision is statistically smaller than the domain-averaged relative velocity. Consequently, the particle–particle drag force is over-predicted when the domain-averaged relative velocity is used. For this reason, this work assumes that the particle–particle drag force is determined by the relative velocity within a local region near large particles. When the local region is set to be the spherical shells centred on the centres of large particles and with an outer radius of a mean free path of small particles, the KTGF-based relation can reasonably predict the particle–particle drag force.

An increased number of rogue waves, relative to standard distributions, can be induced by unidirectional waves passing over abrupt decreases in water depth. We investigate this phenomenon in a more general setting of multidirectional waves. We examine the influence of the directionality on the occurrence probability of rogue waves using laboratory experiments and fully nonlinear potential flow simulations. Based on the analysis of the statistics of random waves, we find that directional spreading reduces the formation probability of rogue waves relative to unidirectional seas. Nevertheless, for typical values of directional spreading in the ocean ($15^{\circ }\unicode{x2013}30^{\circ }$), our numerical results suggest that there is still a significant enhancement to the number of rogue waves just beyond the top of a depth discontinuity.

The temporally developing self-similar turbulent jet is fundamentally different from its spatially developing namesake because the former conserves volume flux and has zero cross-stream mean flow velocity whereas the latter conserves momentum flux and does not have zero cross-stream mean flow velocity. It follows that, irrespective of the turbulent dissipation's power-law scalings, the time-local Reynolds number remains constant, and the jet half-width $\delta$, the Kolmogorov length $\eta$ and the Taylor length $\lambda$ grow identically as the square root of time during the temporally developing self-similar planar jet's evolution. We predict theoretically and confirm numerically by direct numerical simulations that the mean centreline velocity, the Kolmogorov velocity and the mean propagation speed of the turbulent/non-turbulent interface (TNTI) of this planar jet decay identically as the inverse square root of time. The TNTI has an inner structure over a wide range of closely spatially packed iso-enstrophy surfaces with fractal dimensions that are well defined over a range of scales between $\lambda$ and $\delta$, and that decrease with decreasing iso-enstrophy towards values close to $2$ at the viscous superlayer. The smallest scale on these isosurfaces is approximately $\eta$, and the length scales between $\eta$ and $\lambda$ contribute significantly to the surface area of the iso-enstrophy surfaces without being characterised by a well-defined fractal dimension. A simple model is sketched for the mean propagation speeds of the iso-enstrophy surfaces within the TNTI of temporally developing self-similar turbulent planar jets. This model is based on a generalised Corrsin length, on the multiscale geometrical properties of the TNTI, and on a proportionality between the turbulent jet volume's growth rate and the growth rate of $\delta$. A prediction of this model is that the mean propagation speed at the outer edge of the viscous superlayer is proportional to the Kolmogorov velocity multiplied by the $1/4$th power of the global Reynolds number.

The statistical properties of uniform momentum zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatiotemporally resolved velocity dataset, covering a field of view of $8 \times 9\,{\rm m}^2$, was obtained in the atmospheric surface layer using super-large-scale particle image velocimetry (SLPIV), as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA). Wind tunnel data from a previous study are included for comparison (Heisel et al., J. Fluid Mech., vol. 887, 2020, R1). The probability density function of UMZ attributes such as their thickness, modal velocity and averaged vertical velocity are built at varying elevations and modelled using log-normal and Gaussian distributions. Inverse transform sampling of the distributions is used to generate synthetic step-like velocity profiles that are spatially and temporally uncorrelated. Results show that in the wide range of wall-normal distances and $Re_\tau$ up to $\sim O(10^6)$ investigated here, shear velocity scaling is manifested in the velocity jump across shear interfaces between adjacent UMZs, and attached eddy behaviour is observed in the linear proportionality between UMZ thickness and their wall normal location. These very same characteristics are recovered in the generated instantaneous profiles, using both fully stochastic and data-driven hybrid stochastic (DHS) models, which address, in different ways, the coupling between modal velocities and UMZ thickness. Our method provides a stochastic approach for generating an ensemble of instantaneous velocity profiles, consistent with the structural organisation of UMZs, where the ensemble reproduces the logarithmic mean velocity profile and recovers significant portions of the Reynolds stresses and, thus, of the streamwise and vertical velocity variability.

In the present paper, the sloshing flow in a cuboid tank forced to oscillate horizontally is investigated with both experimental and numerical approaches. The filling depth chosen is $h/L=0.35$ (with h the water depth and L the tank height), which is close to the critical depth. According to Tadjbakhsh & Keller (J. Fluid Mech., vol. 8, issue 3, 1960, pp. 442–451), as the depth passes through this critical value the response of the resonant sloshing dynamics changes from ‘hard spring’ to ‘soft spring’. The experimental tank has a thickness of $0.1L$, reducing three-dimensional effects. High-resolution digital camera and capacitance wave probes are used for time recording of the surface elevation. By varying the oscillation period and the amplitude of the motion imposed on the tank, different scenarios are identified in terms of free-surface evolution. Periodic and quasi-periodic regimes are found in most of the frequencies analysed but, among these, sub-harmonic regimes are also identified. Chaotic energetic regimes are found with motions of greater amplitude. Typical tools of dynamical systems, such as Fourier spectra and phase maps, are used for the regime identification, while the Hilbert–Huang transform is used for further insight into doubling-frequency and tripling-period bifurcations. For the numerical investigation, an advanced and well-established smoothed particle hydrodynamics method is used to aid the understanding of the physical phenomena involved and to extend the range of frequencies investigated experimentally.

Separation induced by impinging shock is a fundamental feature in supersonic and hypersonic flows; however, it is difficult to predict the pressure plateau due to a limited theoretical understanding of the effect of impinging shock strength. In this study, the evolution of the separation configuration and pressure distribution with changes in impinging shock angle is examined, and a theoretical equation for predicting the pressure plateau based on minimum entropy production is proposed. For validation, an experimental device that can measure wall pressure in the separation region at high spatiotemporal resolution is developed, and schlieren visualization is employed to capture the flow structure. Accordingly, the fine characteristics of pressure distributions along the centreline of the separation region as well as the reattachment region induced by shock impingement at various angles ($8.5^\circ$ to $30.5^\circ$) are obtained in a flow of Mach number 5 and Reynolds number ${\approx }1.4\times 10^7\ {\rm m}^{-1}$. The experimental results agree well with the theoretical results; both indicate that the pressure distribution is strongly related to the impinging shock strength and that there is a critical flow deflection angle $\alpha ^\ast$ (${\approx }20.8^\circ$ for Mach 5). The pressure in the separation region grows nearly linearly with increasing impinging shock strength when the flow deflection angle of the impinging shock is less than $\alpha ^\ast$; the pressure stops growing and resides in a small range when the flow deflection angle is larger than $\alpha ^\ast$. Therefore, the impinging shock strength should be considered a main factor when predicting the pressure plateau.

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a periodic pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are unstable to perturbations of sufficiently small wavenumber regardless of parameter values, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication.

Fast agglomeration by emulsion binders to capture fine, hydrophobic particles has been developed in the past few years as an alternative to froth flotation by small air bubbles. This new method consists of mixing a particle suspension and saltwater-filled droplets covered with semi-permeable oil layers. These droplets expand due to an osmotic flux of water caused by the presence of salt inside the droplets. To better understand the physics underlying this novel particle capture method, we investigate binary interactions between droplets and particles. The current work examines the dynamics of a rigid spherical particle and a semi-permeable spherical drop that expands due to osmosis in an external, pure-extensional flow field. The droplet is governed by an expansion-diffusion problem, which is coupled to the set of dynamical equations governing the relative particle trajectory. By performing multiple trajectory simulations, we calculate transient collision efficiencies, which can be used to determine the collision kernel for population dynamics. We also use these simulations to better understand the evolution of the microstructure by determining the transient behaviour of the pair distribution function. Our results indicate that the presence of drop expansion increases the collision efficiency of the system, especially for very small particles, which are the most difficult to capture by froth flotation. Moreover, although the presence of slow salt diffusion inside the drops can mitigate this improvement, the contribution of expansion to the collision efficiency may still be considerable, even in the absence of hydrophobic or other attractive forces.