Flow in the inverted U-shaped tube of a conventional siphon can be established and maintained only if the tube is filled and closed, so that air does not enter. We report on siphons that operate entirely open to the atmosphere by exploiting surface tension effects. Such capillary siphoning is demonstrated by paper tissue that bridges two containers and conveys water from the upper to the lower. We introduce a more controlled system consisting of grooves in a wetting solid, formed here by pressing together hook-shaped metallic rods. The dependence of flux on siphon geometry is systematically measured, revealing behaviour different from the conventional siphon. The flux saturates when the height difference between the two container's free surfaces is large; it also has a strong dependence on the climbing height from the source container's free surface to the apex. A one-dimensional theoretical model is developed, taking into account the capillary pressure due to surface tension, pressure loss due to viscous friction, and driving by gravity. Numerical solutions are in good agreement with experiments, and the model suggests hydraulic interpretations for the observed flux dependence on geometrical parameters. The operating principle and characteristics of capillary siphoning revealed here can inform biological phenomena and engineering applications related to directional fluid transport.

Direct numerical simulation of spanwise-rotation-driven flow transitions in viscoelastic plane Couette flow from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow state followed by full relaminarization is reported for the first time. Specifically, this novel flow transition begins with a drag-reduced inertial turbulent flow state at a low rotation number $0\leqslant Ro \leqslant 0.1$, and then transitions to a rotation/polymer-additive-driven drag-enhanced inertial turbulent regime, $0.1\leqslant Ro \leqslant 0.3$. In turn, the flow transitions to a drag-enhanced elasto-inertial turbulent state, $0.3\leqslant Ro \leqslant 0.9$, and eventually relaminarizes at $Ro=1$. In addition, two novel rotation-dependent drag enhancement mechanisms are proposed and substantiated. (1) The formation of large-scale roll cells results in enhanced convective momentum transport along with significant polymer elongation and stress generated in the extensionally dominated flow between adjacent roll cells at $Ro\leqslant 0.2$. (2) Coriolis-force-generated turbulent vortices cause strong incoherent transport and homogenization of significant polymer stress in the bulk via their vortical circulations at $Ro=0.5 - 0.9$.

The wake of a notchback Ahmed body presenting a bi-stable nature is investigated by performing wind tunnel experiments and large-eddy simulations. Attention is confined to the Reynolds number ($Re$) influence on the wake state instability within $5\times 10^{4}\leq Re \leq 25\times 10^{4}$. Experimental observations suggest a wake bi-stability with low-frequency switches under low $Re$. The wake becomes ‘tri-stable’ with the increase of $Re$ with the introduction of a new symmetric state. The higher presence of the symmetric state can be considered as a symmetrization of the wake bi-stability with an increasing $Re$. The wake symmetry under high $Re$ attributed to the highly frequent switches of the wake is extremely sensitive to small yaw angles, showing the feature of bi-stable flows. The wake asymmetry is confirmed in numerical simulations with both low and high $Re$. The wake asymmetries are indicated by the wake separation, the reattachment and the wake dynamics identified by the proper orthogonal decomposition. However, the turbulence level is found to be significantly higher with a higher $Re$. This leads to a higher possibility to break the asymmetric state, resulting in highly frequent switches showing symmetry.

Rayleigh–Taylor instability of a thin liquid film overlying a passive fluid is examined when the film is attached to a periodic wavy deep corrugated wall. A reduced-order long-wave model shows that the wavy wall enhances the instability toward rupture when the interface pattern is sub-harmonic to the wall pattern. An expression that approximates the growth constant of instability is obtained for any value of wall amplitude for the special case when the wall consists of two full waves and the interface consists of a full wave. Nonlinear computations of the interface evolution show that sliding is arrested by the wavy wall if a single liquid film residing over a passive fluid is considered but not necessarily when a bilayer sandwiched by a top wavy wall and bottom flat wall is considered. In the latter case interface tracking shows that primary and secondary troughs will evolve and subsequently slide along the flat wall due to symmetry-breaking. It is further shown that this sliding motion of the interface can ultimately be arrested by the top wavy wall, depending on the holdup of the fluids. In other words, there exists a critical value of the interface position beyond which the onset of the sliding motion is observed and below which the sliding is always arrested.

We describe a mechanism that leads to the spontaneous formation of a thermohaline staircase in the high-latitude oceans. Our analysis of this mechanism is based upon a model in which uniform gradients of temperature and salinity are assumed and is applied to a simplified mean-field model of stratified turbulence. Detailed analysis employs a parametrization of turbulent diapycnal diffusivities (Bouffard & Boegman, Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). This parametrization is apparently unique in that it distinguishes between the diapycnal diffusivities for heat and salt on the basis of their Prandtl (Schmidt) numbers. Our model predicts that the temperature and salinity profiles will be susceptible to linear instability if the buoyancy Reynolds number lies in the range 0.18–91, and a nonlinear mean-field model simulation demonstrates that it evolves into a well-defined thermohaline staircase that matches the characteristics of those found in the high-latitude oceans. The criterion for initial instability is furthermore shown to be consistent with the observed regional variability of staircase occurrence in the Arctic Ocean as determined by the most recent observational datasets.

It is shown that shape anisotropy and intrinsic surface slip lead to equilibrium tilt of slippery particles in a creeping simple shear flow, even for nearly shape-isotropic particles with a cross-section that is close to circular provided the Navier-slip length is sufficiently large. We study a rigid particle with an elliptical cross-section, and of infinite extent in the vorticity direction, in simple shear. A Navier-slip boundary condition is imposed on its surface. When a Navier-slip length parameter $\lambda$ is infinite, an analytical solution is derived for the Stokes flow around a particle tilting in equilibrium at an angle $(1/2)\cos ^{-1}((1-k)/(1+k))$ to the flow direction where $0 \le k \le 1$ is the ratio of the semi-minor to semi-major axes of its elliptical cross-section. A regular perturbation analysis about this analytical solution is then performed for small values of $1/\lambda$ and a numerical continuation method implemented for larger values. It is found that an equilibrium continues to exist for any anisotropic particle $k < 1$ provided $\lambda \ge \lambda _{crit}(k)$ where $\lambda _{crit}(k)$ is a critical Navier-slip length parameter determined here. As the case $k \to 1$ of a circular cross-section is approached, it is found that $\lambda _{crit}(k) \to \infty$, so the range of Navier-slip lengths allowing equilibrium tilt shrinks as shape anistropy is lost. Novel theoretical connections with equilibria for constant-pressure gas bubbles with surface tension are also pointed out.

The wake of a finite wall-mounted circular cylinder of diameter $D$ and height $H$ is investigated for aspect ratios $3\leq H/D \leq 7$ and boundary layer thickness of $\delta /D \approx 0.98$ using tomographic particle image velocimetry. The Reynolds number based on $D$ is $Re = 750$. The mean wake topology is related to the evolution of the periodically shed vortices, educed from a low-order representation based on proper orthogonal decomposition of the three-dimensional velocity field. The main topological features are an arch vortex, defining the recirculating base region, and a quadrupole structure consisting of two pairs of opposite-sign vorticity concentrations extending downstream behind the obstacle-free end and wall junction. The quadrupole is the time-averaged signature of shed vortices. Vortex-tilting terms in the base region act to reorient flow-normal vorticity components streamwise, resulting in the reorientation of the ends of vortices initially shed parallel to the cylinder side walls. Through the action of the vortex-stretching terms, the bent ends connect successive vortices in a continuous chain. The influence of $H/D$ on the development of the quadrupole is characterized. The results demonstrate that the quadrupole in the mean field emerges as an imprint of the shed full-loop structures. This work reconciles mean and instantaneous interpretations satisfying the solenoidal condition on the vorticity field.

Direct numerical simulations have been performed for heat and momentum transfer in internally heated turbulent shear flow with constant bulk mean velocity and temperature, $u_{b}$ and $\theta _{b}$, between parallel, isothermal, no-slip and permeable walls. The wall-normal transpiration velocity on the walls $y=\pm h$ is assumed to be proportional to the local pressure fluctuations, i.e. $v=\pm \beta p/\rho$ (Jiménez et al., J. Fluid Mech., vol. 442, 2001, pp. 89–117). The temperature is supposed to be a passive scalar, and the Prandtl number is set to unity. Turbulent heat and momentum transfer in permeable-channel flow for the dimensionless permeability parameter $\beta u_b=0.5$ has been found to exhibit distinct states depending on the Reynolds number $Re_b=2h u_b/\nu$. At $Re_{b}\lesssim 10^4$, the classical Blasius law of the friction coefficient and its similarity to the Stanton number, $St\approx c_{f}\sim Re_{b}^{-1/4}$, are observed, whereas at $Re_{b}\gtrsim 10^4$, the so-called ultimate scaling, $St\sim Re_b^0$ and $c_{f}\sim Re_b^0$, is found. The ultimate state is attributed to the appearance of large-scale intense spanwise rolls with the length scale of $O(h)$ arising from the Kelvin–Helmholtz type of shear-layer instability over the permeable walls. The large-scale rolls can induce large-amplitude velocity fluctuations of $O(u_b)$ as in free shear layers, so that the Taylor dissipation law $\epsilon \sim u_{b}^{3}/h$ (or equivalently $c_{f}\sim Re_b^0$) holds. In spite of strong turbulence promotion there is no flow separation, and thus large-amplitude temperature fluctuations of $O(\theta _b)$ can also be induced similarly. As a consequence, the ultimate heat transfer is achieved, i.e. a wall heat flux scales with $u_{b}\theta _{b}$ (or equivalently $St\sim Re_b^0$) independent of thermal diffusivity, although the heat transfer on the walls is dominated by thermal conduction.

Air exchange between people has emerged in the COVID-19 pandemic as the important vector for transmission of the SARS-CoV-2 virus. We study the airflow and exchange between two unmasked individuals conversing face-to-face at short range, which can potentially transfer a high dose of a pathogen, because the dilution is small when compared to long-range airborne transmission. We conduct flow visualization experiments and direct numerical simulations of colliding respiratory jets mimicking the initial phase of a conversation. The evolution and dynamics of the jets are affected by the vertical offset between the mouths of the speakers. At low offsets the head-on collision of jets results in a `blocking effect', temporarily shielding the susceptible speaker from the pathogen carrying jet, although, the lateral spread of the jets is enhanced. Sufficiently large offsets prevent the interaction of the jets. At intermediate offsets (8-10 cm for 1 m separation), jet entrainment and the inhaled breath assist the transport of the pathogen-loaded saliva droplets towards the susceptible speaker's mouth. Air exchange is expected, in spite of the blocking effect arising from the interaction of the respiratory jets from the two speakers.

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$, we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

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.