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.

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.

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.

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.

Surfactant transport from foam film to foam film is an essential (yet poorly understood) aspect of the viscoplastic yielding behaviour of flowing foam. Recent experimental and modelling work by Bussonnière & Cantat (J. Fluid Mech., vol. 922, 2021, A25) has, however, helped to advance understanding of the relevant surfactant transport processes: the significance of that work is described herein.

We present a new, simple and physically motivated parameterization, based on the ratio of Thorpe and Ozmidov scales, for the irreversible turbulent flux coefficient $\varGamma _{\mathcal {M}}= {\mathcal {M}}/\epsilon$, i.e. the ratio of the irreversible rate ${\mathcal {M}}$ at which the background potential energy increases in a stratified flow due to macroscopic motions to the dissipation rate of turbulent kinetic energy $\epsilon$. Our parameterization covers all three key phases (crucially, in time) of a shear-induced stratified turbulence life cycle: the initial, ‘hot’ growing phase, the intermediate energetically forced phase and the final ‘cold’ fossilization decaying phase. Covering all three phases allows us to highlight the importance of the intermediate one, to which we refer as the ‘Goldilocks’ phase due to its apparently optimal (and so neither too hot nor too cold, but just right) balance, in which energy transfer from background shear to the turbulent mixing is most efficient. The value of $\varGamma _{\mathcal {M}}$ is close to 1/3 during this phase, which we demonstrate appears to be related to an adjustment towards a critical or marginal Richardson number for sustained turbulence ${\sim }0.2\text {--}0.25$. Importantly, although buoyancy effects are still significant at leading order for the turbulent dynamics during this intermediate phase, the marginal balance in the flow ensures that the turbulent mixing of the (density) scalar is nevertheless effectively ‘locked’ to the turbulent mixing of momentum. We present supporting evidence for our parameterization through comparison with six oceanographic datasets that span various turbulence generation regimes and a wide range of geographical location and depth. Using these observations, we highlight the significance of parameterizing an inherently variable flux coefficient for capturing the turbulent flux associated with rare energetic, yet fundamentally shear-driven (and so not strongly stratified) overturns that make a disproportionate contribution to the total mixing. We also highlight the importance of representation of young turbulent patches in the parameterization for connecting the small scale physics to larger scale applications of mixing such as ocean circulation and tracer budgets. Shear-induced turbulence is therefore central to irreversible mixing in the world's oceans, apparently even close to the seafloor, and it is critically important to appreciate the inherent time dependence and evolution of mixing events: history matters to mixing.

A Lagrangian analysis is performed to measure the rate at which recirculating fluid is replaced (depleted) in pulsatile flows. Based on this approach, we then investigate how depletion is affected in dense suspensions. Experiments are conducted for pure liquid as well as suspensions with volume fractions of $\varPhi =5\,\%$, 10 % and 20 %. Using Lagrangian tracking and pathline extension techniques, the depletion of the recirculation region is quantified via the trajectories of individual fluid parcels exiting the domain. Pulsatile flows with varying concentrations of hydrogel beads, up to a volume fraction of 20 %, are compared at mean Reynolds numbers of $Re=4800$, 9600 and 14 400, while the Strouhal number ($St=0.04$, 0.08 and 0.15) and amplitude ratio ($\lambda =0.25$, 0.50 and 0.95) are systematically varied. A so-called ‘depletion efficiency’ is calculated for each test case, which is shown to increase with increasing Strouhal number and amplitude ratio. For most pulsatile cases, periodic vortex formation significantly increases depletion efficiency through enhanced entrainment of recirculating fluid. Conversely, low-amplitude pulsatile flows are dominated by Kelvin–Helmholtz instabilities, which do not penetrate into the recirculation region, and thus their depletion efficiency is markedly lower as a result. The efficiency trends and depletion mechanisms remain virtually unchanged between the pure liquid and each of the suspension concentrations under almost all flow conditions, which forms an unexpected conclusion. The only exception is for low-amplitude and steady flows, where increasing the suspension volume fraction is shown to suppress fluid transport across the shear layer, which in turn slows depletion and decreases the overall depletion efficiency.

We numerically investigate stalling flow around a static airfoil at high Reynolds numbers using the Reynolds-averaged Navier–Stokes equations (RANS) closed with the Spalart–Allmaras turbulence model. An arclength continuation method allows to identify three branches of steady solutions, which form a characteristic inverted S-shaped curve as the angle of attack is varied. Global stability analyses of these steady solutions reveal the existence of two unstable modes: a low-frequency mode, which is unstable for angles of attack in the stall region, and a high-frequency vortex shedding mode, which is unstable at larger angles of attack. The low-frequency stall mode bifurcates several times along the three steady solutions: there are two Hopf bifurcations, two solutions with a two-fold degenerate eigenvalue and two saddle-node bifurcations. This low-frequency mode induces a cyclic flow separation and reattachment along the airfoil. Unsteady simulations of the RANS equations confirm the existence of large-amplitude low-frequency periodic solutions that oscillate around the three steady solutions in phase space. An analysis of the periodic solutions in the phase space shows that, when decreasing the angle of attack, the low-frequency periodic solution collides with the unstable steady middle-branch solution and thus disappears via a homoclinic bifurcation of periodic orbits. Finally, a one-equation nonlinear stall model is introduced to reveal that the disappearance of the limit cycle, when increasing the angle of attack, is due to a saddle-node bifurcation of periodic orbits.

The problem of interaction of a uniform current with a submerged horizontal circular cylinder in an ice-covered channel is considered. The fluid flow is described by linearized velocity potential theory and the ice sheet is treated as a thin elastic plate. The potential due to a source or the Green function satisfying all boundary conditions apart from that on the body surface is first derived. This can be used to derive the boundary integral equation for a body of arbitrary shape. It can also be used to obtain the solution due to multipoles by differentiating the Green function with its position directly. For a transverse circular cylinder, through distributing multipoles along its centre line, the velocity potential can be written in an infinite series with unknown coefficients, which can be determined from the impermeable condition on a body surface. A major feature here is that different from the free surface problem, or a channel without the ice sheet cover, this problem is fully three-dimensional because of the constraints along the intersection of the ice sheet with the channel wall. It has been also confirmed that there is an infinite number of critical speeds. Whenever the current speed passes a critical value, the force on the body and wave pattern change rapidly, and two more wave components are generated at the far-field. Extensive results are provided for hydroelastic waves and hydrodynamic forces when the ice sheet is under different edge conditions, and the insight of their physical features is discussed.

Apparent inconsistency between (i) experimental and direct numerical simulation (DNS) data that show the significant influence of differential diffusion on the turbulent burning rate and (ii) recent complex-chemistry DNS data that indicate mitigation of the influence of differential diffusion on conditioned profiles of various local flame characteristics at high Karlovitz numbers, is explored by analysing new DNS data obtained from lean hydrogen–air turbulent flames. Both aforementioned effects are observed by analysing the same DNS data provided that the conditioned profiles are sampled from the entire computational domain. On the contrary, the conditioned profiles sampled at the leading edge of the mean flame brush do not indicate the mitigation, but are significantly affected by differential diffusion phenomena, e.g. because reaction zones are highly curved at the leading edge. This observation is consistent with a significant increase in the computed turbulent burning velocity with decreasing Lewis number, with all the results considered jointly being consonant with the leading point concept of premixed turbulent combustion. The concept is further supported by comparing DNS data obtained by allowing for preferential diffusion solely for a single species, either atomic or molecular hydrogen.

Transient Marangoni convection induced by an isothermal sidewall of a rectangular pool under a zero-gravity condition is studied using scaling analysis. Scaling analysis shows that there exist a number of flow regimes in each evolution scenario, depending on the Marangoni number, the Prandtl number and the aspect ratio. In a typical evolution scenario, a horizontal surface flow and a vertical flow adjacent to the sidewall may appear. Additionally, a number of scaling laws of the velocity and thickness of transient Marangoni convection are obtained. Further, numerical simulation is performed for validation of the selected scaling laws. There exits good agreement between the numerical results and the scaling predictions.

In droplet impacts, transitions between coalescence and bouncing are determined by complex interplays of multiple mechanisms dominating at various length scales. Here we investigate the mechanisms and governing parameters comprehensively by experiments and scaling analyses, providing a unified framework for understanding and predicting the outcomes when using different fluids. Specifically, while bouncing had not been observed in head-on collisions of water drops under atmospheric conditions, it was found in our experiments to appear on increasing the droplet diameter sufficiently. Contrarily, while bouncing was always observed in head-on impacts of alkane drops, we found it to disappear on decreasing the diameter sufficiently. The variations are related to gas draining dynamics in the inter-droplet film and suggest an easier means for controlling bouncing as compared to alternating the ambient pressure usually sought. The scaling analysis further shows that for a given Weber number, enlarging droplet diameter or fluid viscosities, or lowering surface tension contributes to a larger characteristic minimum thickness of the gas film, thus enhancing bouncing. The key dimensionless group $(O{h_{g,l}},\;O{h_l},\;{A^\ast })$ is identified, referred to as the two-phase Ohnesorge number, the Ohnesorge number of liquid and the Hamaker constant, respectively. Our thickness-based model indicates that as ${h^{\prime}_{m,c}} > 21.1{h_{cr}}$, where ${h^{\prime}_{m,c}}$ is the maximum value of the characteristic minimum film thickness $({h_{m,c}})$ and ${h_{cr}}$ is the critical thickness, bouncing occurs in both head-on and off-centre collisions. That is, when $1.2O{h_{g,l}}/(1 - 2O{h_l}) > \sqrt[3]{{{A^\ast }}}$, a fully developed bouncing regime occurs, thereby yielding a lower coalescence efficiency. The transitional Weber number is found universally to be 4.

We present a field study of snow settling dynamics based on simultaneous measurements of the atmospheric flow field and snow particle trajectories. Specifically, a super-large-scale particle image velocimetry (SLPIV) system using natural snow particles as tracers is deployed to quantify the velocity field and identify vortex structures in a 22 m $\times$ 39 m field of view centred 18 m above the ground. Simultaneously, we track individual snow particles in a 3 m $\times$ 5 m sample area within the SLPIV using particle tracking velocimetry. The results reveal the direct linkage among vortex structures in atmospheric turbulence, the spatial distribution of snow particle concentration and their settling dynamics. In particular, with snow turbulence interaction at near-critical Stokes number, the settling velocity enhancement of snow particles is multifold, and larger than what has been observed in previous field studies. Super-large-scale particle image velocimetry measurements show a higher concentration of snow particles preferentially located on the downward side of the vortices identified in the atmospheric flow field. Particle tracking velocimetry, performed on high resolution images around the reconstructed vortices, confirms the latter trend and provides statistical evidence of the acceleration of snow particles, as they move toward the downward side of vortices. Overall, the simultaneous multi-scale particle imaging presented here enables us to directly quantify the salient features of preferential sweeping, supporting it as an underlying mechanism of snow settling enhancement in the atmospheric surface layer.

The liquid evaporation from nanoscale pores has attracted much attention from researchers due to its importance in water treatment and device cooling related applications. It is crucial to investigate the receded liquid case as the vapour flow resistance in a nanopore has high impacts on the evaporation rate. This paper proposed a semi-empirical analysis on nanoporous evaporation with a receded liquid surface under the influence of the Knudsen number. The vapour flow dynamics in a nanopore was examined considering the multiple reflections of vapour molecules. We calculated the value of pore transmissivity based on transitional gas flow correlation which incorporated the effect of the Knudsen number. Direct simulation Monte Carlo method was employed to provide validation for the present model. The vapour density jump near the liquid surface and the pressure ratio between the far field and saturation value were predicted by our model with good precision. It was shown that the vapour flow resistance in the nanopore accounted for more than 90 % of the total resistance in present cases. With increasing Knudsen number, the pressure ratio gradually drops and reaches an asymptotic level. This suggested a relatively higher evaporation resistance in free molecular regimes. The present work revealed the importance of the Knudsen number in nanoporous evaporation with receded liquids, providing insights into the governing factors under various Knudsen regimes.

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

Drop coalescence occurs through the rapid growth of a liquid bridge that connects the two drops. At early times after contact, the bridge dynamics is typically self-similar, with details depending on the geometry and viscosity of the liquid. In this paper we analyse the coalescence of two-dimensional viscous drops that float on a quiescent deep pool; such drops are called liquid lenses. The analysis is based on the thin-sheet equations, which were recently shown to accurately capture experiments of liquid lens coalescence. It is found that the bridge dynamics follows a self-similar solution at leading order, but, depending on the large-scale boundary conditions on the drop, significant corrections may arise to this solution. This dynamics is studied in detail using numerical simulations and through matched asymptotics. We show that the liquid lens coalescence can involve a global translation of the drops, a feature that is confirmed experimentally.

Orthogonal time-of-flight mass spectrometry has been used to characterize the kinetic energy and charged species distributions from an in vacuo electrospray ion source for four different ionic liquids at volumetric flow rates between 0.3 and 3.3 nanolitres per second. In all cases, the mass spectra revealed charged species consisting of singly charged and multiply charged ions as well as two broad, unresolved droplet distributions occurring in the 104 to 106 atomic mass unit per charge range. The mean jet velocity and mean jet breakup potential were established from analysis of the energy profile of the high mass-to-charge droplets. At the jet breakup point, we find the energy loss and the jet diameter flow rate dependence of the electrospray beam to be similar to that determined by Gamero-Castaño (Phys. Fluids, vol. 20, 2008, 032103; Phys. Rev. Fluids, vol. 8, 2021, 013701) for 1-ethyl-3-methylimidazolium bis(trifluromethylsulfonyl)imide at similar volumetric flow rates. Similar trends are observed for all four liquids over the flow regime. A jet instability analysis revealed that jet electrification and viscous effects drive the jet breakup from the case of an uncharged, inviscid jet; jet breakup occurs at droplet and jet radius ratios that deviate from 1.89. Using the analytically determined ratio and the beam profile, different species are modelled to reconstruct the mass spectra; primary droplets constitute only a fraction of the total species present. The populations of the species are discussed.

The linear convective instability of a mixture of dry air, water vapour and liquid water, with a stable unsaturated layer residing on an unstable saturated layer, is studied. It may serve as a prototype model for understanding the instability that causes mixing at the top of stratocumulus cloud or fog. Such a cloud-clear air interface is modelled as an infinitely thin saturation interface where radiative and evaporative cooling take place. The interface position is determined by the Clausius–Clapeyron equation, and can undulate with the evolution of moisture and temperature. In the small-amplitude regime two physical mechanisms are revealed. First, the interface undulation leads to the undulation of the cooling source, which destabilizes the system by superposing a vertical dipole heating anomaly on the convective cell. Second, the evolution of the moisture field induces non-uniform evaporation at the interface, which stabilizes the system by introducing a stronger evaporative cooling in the ascending region and vice versa in the descending region. These two mechanisms are competing, and their relative contribution to the instability is quantified by theoretically estimating their relative contribution to buoyancy flux tendency. When there is only evaporative cooling, the two mechanisms break even, and the marginal stability curve remains the same as the classic two-layer Rayleigh–Bénard convection with a fixed cooling source.

We present a local stability analysis of an idealized model of the stratified vortices that appear in geophysical settings. The base flow comprises an axisymmetric vortex with background rotation and an out-of-plane stable stratification, and a radial stratification in the thermal wind balance with the out-of-plane momentum gradient. Solving the local stability equations along fluid particle trajectories in the base flow, the dependence of short-wavelength instabilities on the Schmidt number $Sc$ (ratio between momentum and mass diffusivities) is studied, in the presence of curvature effects. In the diffusion-free limit, the well-known symmetric instability is recovered. In the viscous, double-diffusive regime, instability characteristics are shown to depend on three non-dimensional parameters (including $Sc$), and two different instabilities are identified: (i) a monotonic instability (same as symmetric instability at $Sc = 1$), and (ii) an oscillatory instability (absent at $Sc = 1$). Separating the base flow and perturbation characteristics, two each of base flow and perturbation parameters (apart from $Sc$) are identified, and the entire parameter space is explored for the aforementioned instabilities. In comparison with $Sc = 1$, monotonic and oscillatory instabilities are shown to significantly expand the instability region in the space of base flow parameters as $Sc$ moves away from unity. Neutral stability boundaries on the plane of $Sc$ and a modified gradient Richardson number are then identified for both these instabilities. In the absence of curvature effects, our results are shown to be consistent with previous studies based on normal mode analysis, thus establishing that the local stability approach is well suited to capturing symmetric and double-diffusive instabilities. The paper concludes with a discussion of curvature effects, and the likelihood of monotonic and oscillatory instabilities in typical oceanic settings.