Shock-induced fluid-layer evolution has attracted much attention but remains a challenge mainly because the coupling between layers remains unknown. Linear solutions are first derived to quantify the layer-coupling effect on the shocked dual-layer evolution. Next, the motions of the waves and interfaces of a dual layer are examined based on the one-dimensional gas dynamics theory. Shock-tube experiments on the dual-layer, single-layer and single-mode interface are then performed to validate the linear solutions and investigate the reverberating waves inside the layers. It is proved that the layer-coupling effect destabilises the dual layer, especially when the initial layers are thin, and the reverberating waves impose additional instabilities on all interfaces. Our findings suggest that a slow/fast configuration with a large thickness in a dual layer can facilitate the suppression of hydrodynamic instabilities.

The movements of some massive (${O}(100)\ \textrm {t}$) clifftop boulders, once thought to have been caused by tsunami, have been reattributed to storm waves in several recent papers. However, the precise wave-impact modes and transport mechanisms are unknown. We present preliminary linear acceleration, pressure and displacement data recorded by a $1\,{:}\,30$ scale clifftop boulder impacted by a focused breaking wave in a laboratory flume. The 8 kg boulder was placed atop a 0.25 m high platform and struck with a breaking wave of 0.34 m amplitude. Wave focus position was varied from 0.8 m fore of the platform to 0.27 m aft of the platform to alter the breaking crest shape and wave impact type while maintaining total wave spectral energy. Pressure and acceleration time series measurements from within the boulder show distinct impact types across focus positions. All impacts produced boulder displacement, ranging from 5 mm to 42 mm (0.15 m to 1.3 m at full scale, assuming Froude scaling). The largest boulder pressures were recorded when the wave crest and trough struck the boulder at the same position (flip-through). The largest boulder displacements were measured when high pressures and long impact durations occurred simultaneously and wave focusing was close to flip-through.

Particle suspensions in non-Newtonian liquid matrices are frequently encountered in nature and industrial applications. We here study the Taylor–Couette flow (TCF) of semidilute spherical particle suspensions (volume fraction $\leq 0.1$) in viscoelastic, constant-viscosity liquids (Boger fluids). We describe the influence of particle load on various flow transitions encountered in TCF of such fluids, and on the nature of these transitions. Particle addition is found to delay the onset of first- and second-order transitions, thus stabilising laminar flows. It also renders them hysteretic, suggesting an effect on the nature of bifurcations. The transition to elasto-inertial turbulence (EIT) is shown to be delayed by the presence of particles, and the features of EIT altered, with preserved spatio-temporal large scales. These results imply that particle loading and viscoelasticity, which are known to destabilise the flow when considered separately, can on the other hand compete with one another and ultimately stabilise the flow when considered together.

We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

It has been commonly observed on open waters that ducklings/goslings follow their mothers in a highly organized formation. The questions arise: (1) why are they swimming in formation? (2) what is the best swimming formation? (3) how much energy can be preserved by each individual in formation swimming? To address these questions, we established a simplified mathematical and numerical model and calculated the wave drag on a group of waterfowl in a swimming formation. We observed two new and interesting findings: wave-riding and wave-passing. By riding the waves generated by a mother duck, a trailing duckling can obtain a significant wave-drag reduction. When a duckling swims at the ‘sweet point’ behind its mother, a destructive wave interference phenomenon occurs and the wave drag of the duckling turns positive, pushing the duckling forward. More interestingly, this wave-riding benefit could be sustained by the rest of the ducklings in a single-file line formation. Starting from the third one in a queue, the wave drag of individuals gradually tended towards zero, and a delicate dynamic equilibrium was achieved. Each individual under that equilibrium acted as a wave passer, passing the waves’ energy to its trailing one without any energy losses. Wave-riding and wave-passing are probably the principal reasons for the evolution of swimming formation by waterfowl. This study is the first to reveal the reasons why the formation movement of waterfowl can preserve individuals’ energy expenditure. Our calculations provide new insights into the mechanisms of formation swimming.

Thermal convection of fluid is a more efficient way than diffusion to carry heat from hot sources to cold places. Here, we experimentally study the Rayleigh–Bénard convection of aqueous glycerol solution in a cubic cell with suspensions of rod-like particles made of polydimethylsiloxane. The particles are inertial due to their large thermal expansion coefficient and finite sizes. The thermal expansion coefficient of the particles is three times larger than that of the background fluid. This contrast makes the suspended particles lighter than the local fluid in hot regions and heavier in cold regions. The heat transport is enhanced at relatively large Rayleigh number ($\textit {Ra}$) but reduced at small $\textit {Ra}$. We demonstrate that the increase of Nusselt number arises from the particle–boundary layer interactions: the particles act as ‘active’ mixers of the flow and temperature fields across the boundary layers.

We investigate the large-scale signature of the random switches between two mirrored turbulent wake states of flat-backed bodies. A direct numerical simulation (DNS) of the flow around an Ahmed body at a Reynolds number ($Re$) of 10 000 is considered. Using proper orthogonal decomposition (POD), we identify the most energetic modes of the velocity field and build a low-dimensional model based on the first six fluctuating velocity modes capturing the characteristics of the flow dynamics during and between switches. In the absence of noise, the model produces random switches with characteristic time scales in agreement with the simulation and experiments. This chaotic model suggests that random switches are triggered by the increase of the vortex shedding activity. However, the addition of noise results in a better agreement in the temporal spectra of the coefficients between the model and the simulation.

The problem of unidirectional shoaling of a water-wave field with a narrow energy spectrum is treated by using a new Alber equation. The stability of the linear stationary solution to small non-stationary disturbances is analysed; and numerical solutions for its subsequent long-distance evolution are presented. The results quantify the physics which causes the gradual decay in the probability of freak-wave occurrence, when moving from deep to shallow coastal waters.

We derive an accurate estimate for the diffusive evaporation rates of multiple droplets of different sizes and arbitrary contact angles placed on a horizontal substrate. The derivation, which is based on a combination of Green's second identity and the method of reflections, simply makes use of the solution for the evaporation of a single droplet. The theoretical results can serve as a guide for future computational and experimental studies on the collective evaporation of arrays of droplets, as well as similar multi-body, diffusion-dominated transport problems.

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$, the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$, together with lower and upper estimates.

We analyse the stability of the interface between two immiscible fluids both flowing in the horizontal direction in a thin cell with vertically varying gap width. The dispersion relation for the growth rate of each mode is derived. The stability is approximately determined by the sign of a simple expression, which incorporates the density difference between the fluids and the effect of surface tension in the along- and cross-cell directions. The latter arises from the varying channel width: if the non-wetting fluid is in the thinner part of the channel, the interface is unstable as it will preferentially migrate into the thicker part. The density difference may suppress or complement this effect. The system is always stable to sufficiently large wavenumbers owing to the along-flow component of surface tension.

Particle–wall interactions have broad biological and technological applications. In particular, some artificial microswimmers capitalize on their translation–rotation coupling near a wall to generate directed propulsion. Emerging biomedical applications of these microswimmers in complex biological fluids prompt questions on the impact of non-Newtonian rheology on their propulsion. In this work, we report some intriguing effects of shear-thinning rheology, a ubiquitous non-Newtonian behaviour of biological fluids, on the translation–rotation coupling of a particle near a wall. One particularly interesting feature revealed here is that the wall-induced translation by rotation can occur in a direction opposite to what might be intuitively expected for an object rolling on a solid substrate. We elucidate the underlying physical mechanism and discuss its implications on the design of micromachines and bacterial motion near walls in complex fluids.

The response of a semi-infinite ocean to a slowly travelling atmospheric perturbation crossing the coast provides a simple example of the breakdown of nearly geostrophic balance induced by a boundary. We examine this response in the linear shallow-water model at small Rossby number $\varepsilon \ll 1$. Using matched asymptotics, we show that a long Kelvin wave, with $O(\varepsilon ^{-1})$ length scale and $O(\varepsilon )$ amplitude relative to quasi-geostrophic response, is generated as the perturbation crosses the coast. Accounting for this Kelvin wave restores the conservation of mass that is violated in the quasi-geostrophic approximation.

Herein, exact algebraic expressions for the non-circulatory (added-mass) forces on elliptic airfoils are derived for any two-dimensional motion – including simultaneous rectilinear acceleration and rotation – embedded in a steady free-stream flow. Despite the lengthy history of the added-mass concept and its widespread application to cylinders of various cross-sections, such closed-form expressions for elliptic cylinders, in terms of kinematic and geometric parameters alone, have remained absent from the literature until now. Inspection of the derived equations reveals that for pure pitching about a point on the chord-line, increasing thickness always decreases the added-mass force magnitude. For any given motion of the chord-line, the difference in force between thick and thin airfoils is proportional to the square of the thickness, although this difference may be positive or negative for the general three-degree-of-freedom case. In the special case of zero thickness and small pitch angles, Theodorsen's added-mass lift force on rigid thin airfoils is recovered; for large pitch angles, an exact generalization of Theodorsen's expression, applicable to the chord-normal direction, is given.

During the impact of a liquid droplet on a sufficiently heated surface, bubble nucleation reduces the contact area between the liquid and the solid surface. Using high-speed imaging combined with total internal reflection, we measure and report how the contact area decreases with time for a wide range of surface temperatures and impact velocities. We also reveal how formation of the observed fingering patterns contributes to a substantial increase in the total length of the contact line surrounding the contact area.

The discovery of wake bistability has generated an upsurge in experimental investigations into the wakes of simplified vehicle geometries. Particular focus has centred on the probabilistic switching between two asymmetrical bistable wake states of a square-back Ahmed body; however, the majority of this research has been undertaken in wind tunnels with turbulence intensities of less than $1\,\%$, considerably lower than typical atmospheric levels. To better simulate bistability under on-road conditions, in which turbulence intensities can easily reach levels of $10\,\%$ or more, this experimental study investigates the effects of free-stream turbulence on the bistability characteristics of the square-back Ahmed body. Through passive generation and quantification of the free-stream turbulent conditions, a monotonic correlation was found between the switching rate and free-stream turbulence intensity.

Explicit formulas are given for the hydrodynamic slip lengths associated with longitudinal shear flow over a superhydrophobic grating where the menisci have partially invaded the cavities and are only weakly curved. For flat menisci that have depinned from the top of the grating and have displaced downwards into the cavities, the axial velocity is determined analytically and the slip length extracted from it. This solution is then combined with an integral identity to determine the first-order correction to the slip length when the displaced menisci bow weakly into the cavity. It is argued that the new formulas provide useful upper bounds for quantifying slip in microchannel flows involving partially filled cavities. The new solutions are natural extensions of prior results due to Philip (Z. Angew. Math. Phys., vol. 23, 1972, pp. 353–372) for shear flow over mixed no-slip/no-shear surfaces and due to Bechert & Bartenwerfer (J. Fluid Mech., vol. 206, 1989, pp. 105–129) for shear flow over blade-shaped riblets.

In jet engines and gas turbines, the annular shape of the combustion chamber allows the appearance of self-oscillating azimuthal thermoacoustic modes. We report experimental evidence of a new type of modal dynamics characterised by periodic switching of the spinning direction and develop a theoretical model that fully reproduces this phenomenon and explains the underlying mechanisms. It is shown that tiny asymmetries of the geometry, the mean temperature field, the thermoacoustic response of the flames or the acoustic impedance of the walls, present in any real systems, can induce these heteroclinic orbits. The model also explains experimental observations showing a statistically dominant spinning direction despite the absence of swirling flow, or pairs of preferred nodal line directions.