A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid flat surface and the tip of an incoming projectile. We develop a scaling for this viscous approach stage of fluid-mediated normal impact, applicable to soft impactors. Under the assumption of mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity, and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. Additionally, we elucidate why nearly incompressible solids feature (a) substantial ‘gliding’ prior to contact at the transition between regimes, (b) the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue that the above time scale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

Numerous flying and swimming creatures use the ground effect to boost their propulsive performance, with the ‘ground’ referring to either a solid boundary or a free surface. While our knowledge of how a solid boundary affects biolocomotion is relatively comprehensive, the ground effect of a free surface is not fully understood. To address this limitation, we conduct a numerical investigation on the propulsion performance of a flapping plate under a free surface, subject to a range of control parameters. When the Froude number ($Fr$) is very low (i.e. little surface deformation), the effects of a free surface are similar to those of a solid boundary, with enhanced thrust and input power but little change in efficiency. However, as $Fr$ increases (i.e. more surface deformation), our results reveal an optimal $Fr$ of approximately 0.6, where the free surface induces a more streamlined flow around the flapping plate, effectively reducing the added mass. This results in a significant decrease in input power and greatly enhanced efficiency.

Meandering designates the main manifestation of unsteady vortex dynamics observed in experiments. This study has the twofold objective to (i) develop a theoretical model describing vortex meandering and (ii) conduct a quantitative and objective evaluation of the model against experimental data. Based on an analogy with Brownian motion, we derive the theoretical model in the framework of linear response theory. Taking the form of a Langevin equation, our model explains meandering as the competition between external excitation by free-stream perturbations, counteracted by stabilising intrinsic vortex dynamics. As such, it contains the previous approaches to explaining the phenomenon as limiting cases, and clearly highlights their shortcomings. The statistical identification of characteristic regularities in experimental data as well as the assessment of their consistency with theoretical models are important problems in physics. For samples obtained from finite-length records of correlated data, these statistical characteristics are not unique and may show spurious behaviour merely induced by the finiteness of the sample. Statistical inference provides a systematic and quantitative methodology to objectively assess the reproducibility of statistical characteristics and to evaluate their consistency with theoretical models. Their systematic application to the analysis of vortex meandering has not been done before and provides statistical evidence for our proposed Brownian-motion-like model. That is, experimental vortex meandering constitutes the manifestation of a stationary Gauss–Markov random process, which implies that the dynamics admits an ergodic probability measure.

We investigate the dynamics of a columnar Taylor–Green vortex array under strong stratification, focusing on Froude numbers $0.125\leq Fr \leq 1.0$, with the aim of identifying and understanding the primary instabilities that lead to the vortices’ breakdown. Linear stability analysis reveals that the fastest-growing vertical wavenumber scales with $Fr^{-1}$, while the dimensionless growth rate remains approximately constant. The most unstable eigenmode, identified as the mixed hyperbolic mode by Hattori et al. (J. Fluid Mech., vol. 909, 2021, A4), bears significant similarities to the zigzag instability, first discovered by Billant & Chomaz (J. Fluid Mech., vol. 418, 2000, pp. 167–188). Direct numerical simulations further confirm that the zigzag instability is crucial in amplifying initial random perturbations to finite amplitude, with the flow structure and modal growth rate consistent with the linear stability analysis. In particular, the characteristic vertical length scale of turbulence matches that of the fastest-growing linear mode. These findings underscore the broader relevance of the zigzag instability mechanism beyond its initial discovery in vortex pairs, demonstrating its role in facilitating direct energy transfer from vertically uniform vortical motions to a characteristic vertical length scale proportional to $Fr$ in strongly stratified flows.

Research on the settling dynamics of snow particles, considering their complex morphologies and real atmospheric conditions, remains scarce despite extensive simulations and laboratory studies. Our study bridges this gap through a comprehensive field investigation into the three-dimensional (3-D) snow settling dynamics under weak atmospheric turbulence, enabled by a 3-D particle tracking velocimetry (PTV) system to record over a million trajectories, coupled with a snow particle analyser for simultaneous aerodynamic property characterization of four distinct snow types (aggregates, graupels, dendrites, needles). Our findings indicate that while the terminal velocity predicted by the aerodynamic model aligns well with the PTV-measured settling velocity for graupels, significant discrepancies arise for non-spherical particles, particularly dendrites, which exhibit higher drag coefficients than predicted. Qualitative observations of the 3-D settling trajectories highlight pronounced meandering in aggregates and dendrites, in contrast to the subtler meandering observed in needles and graupels, attributable to their smaller frontal areas. This meandering in aggregates and dendrites occurs at lower frequencies compared with that of graupels. Further quantification of trajectory acceleration and curvature suggests that the meandering frequencies in aggregates and dendrites are smaller than that of morphology-induced vortex shedding of disks, likely due to their rotational inertia, and those of graupels align with the small-scale atmospheric turbulence. Moreover, our analysis of vertical acceleration along trajectories elucidates that the orientation changes in dendrites and aggregates enhance their settling velocity. Such insights into settling dynamics refine models of snow settling velocity under weak atmospheric turbulence, with broader implications for more accurately predicting ground snow accumulation.

We propose a simple method to identify unstable parameter regions in general inviscid unidirectional shear flow stability problems. The theory is applicable to a wide range of basic flows, including those that are non-monotonic. We illustrate the method using a model of Jupiter's alternating jet streams based on the quasi-geostrophic equation. The main result is that the flow is unstable if there is an interval in the flow domain for which the reciprocal Rossby Mach number (a quantity defined in terms of the zonal flow and potential vorticity distribution), surpasses a certain threshold or ‘hurdle’. The hurdle height approaches unity when we can take the hurdle width to greatly exceed the atmosphere's intrinsic deformation length, as holds on gas giants. In this case, the Kelvin–Arnol’d sufficient condition of stability accurately detects instability. These results improve the theoretical framework for explaining the stable maintenance of Jupiter and Saturn's jets over decadal time scales.

When a partially miscible binary mixture is quenched below its critical temperature, it transitions from its single-phase to a two-phase region, undergoing phase separation. The processes of formation and coalescence of droplets are driven by diffusive and convective phenomena, taking place isotropically in the system. The application of an external force field, which exerts a different contribution on the two species, breaks the symmetry of phase separation, leading to the segregation of two equilibrated phases separated by a single interface. This study investigates the dynamics of phase segregation under an external force. The effects of various force magnitudes, captured by the Bond number, in both high- and low-viscosity mixtures, distinguished by different fluidity numbers, are quantified via numerical simulations by using the phase field model. The intricate dynamics of formation, floating and coalescence of droplets towards complete segregation are described along with the quantification of the segregation time, revealing different patterns for high and low Bond numbers. Results show that in none of the cases, formation and floating can be regarded as strictly serial processes. A universal scaling between segregation time, Bond number, fluidity number and domain size is not possible, with a power-law dependence emerging only under the diffusion-dominated regime.

We use multiphase direct numerical simulations to identify, analyse and quantify components of wall-normal heat flux distributions in evaporative vertical falling films with surface modifications at industrially relevant conditions. Previous experiments showed a potential increase of the heat transfer rate through the film by up to 100 % using various types of modifications. We show that the modifications induce significant advective heat transport and hypothesise that four synergistic mixing mechanisms are behind the heat transfer rate improvement. Additionally, we examine how the important surface topology parameters, pitch $\hat {p}$ (distance between modifications), height $\hat {h}$ and the liquid Prandtl number $\mathit {Pr}_l$, influence the mode of heat transport and the Nusselt number $\mathit {Nu}$. We show that $\hat {p}/\hat {h} \approx 10$ maximises $\mathit {Nu}$ and that the optimal pitch is related to the recirculation zone length $L_r$ behind the modification. We find that $L_r/\hat {h} \approx 3.5$ and that $\mathit {Nu} \propto \mathit {Pr}_l^{0.42}$ in the investigated parameter ranges. We also show that all our cases on both smooth and modified surfaces have $\mathit {Pe}_l \gg 1$ and collapse well on a line $\mathit {Nu} \propto (\mathit {Pe}_l/\mathit {Re})^{0.35}$. This relation suggests that $\mathit {Nu}$ is governed by the balance of film mixing, thermal resistance and diffusivity, and that the ratio $\mathit {Pe}_l/\mathit {Re}$ can be used to estimate $\mathit {Nu}$. Our methodology and findings extend the knowledge concerning the mechanisms behind the heat transfer improvement due to surface modifications and facilitate guidelines for designing more efficient modified surfaces in industrial evaporators.

Solving the three-dimensional boundary layer equations carries theoretical significance and practical applications, which also poses substantial challenges due to its inherent complexity. In this paper, the laminar boundary layer equations for the symmetry plane of three-dimensional bodies are derived in an orthogonal curvilinear coordinate system associated with the principal curvatures. The derivation of the boundary layer equations is based not only on the common symmetric properties of the flow, as given by Hirschel et al. (Three-Dimensional Attached Viscous Flow, 2014, Academic Press, pp. 183–187), but also incorporates the geometric symmetry properties of the body. The derived equations are more representative and simplified. Notably, these equations can degenerate to a form consistent with or equivalent to the commonly used boundary layer equations for special bodies such as flat plates, cones and spheres. Furthermore, for hypersonic flows, the crossflow velocity gradient at the boundary layer edge on the symmetry plane is derived based on Newtonian theory. Subsequently, this parameter can provide the necessary boundary condition needed for solving the boundary layer equations using existing methods. Finally, as examples, the equations developed in this paper are solved using the difference-differential method for several typical three-dimensional blunt shapes that appeared on hypersonic vehicles. They prove to be useful in the analysis and interpretation of boundary layer flow characteristics in the symmetry plane of blunt bodies.

We numerically study the influence of a soluble surfactant on the microjetting mode of the liquid–liquid flow focusing configuration. The surfactant adsorbs on the interface next to the feeding capillary and accumulates in front of the emitted jet, significantly lowering the surface tension there. The resulting Marangoni stress substantially alters the balance of the tangential stresses at the interface but does not modify the interface velocity. The global stability analysis at the minimum flow rate stability limit shows that the Marangoni stress collaborates with soluto-capillarity to stabilize the microjetting mode. Our analysis unveils the noticeable effect of the Marangoni stress associated with the surface tension perturbation. Surfactant diffusion and desorption hardly affect the stability limit. Transient numerical simulations show how subcritical and supercritical base flows respond to a spatially localized initial perturbation. Our parametric study indicates that the minimum flow rate ratio depends on the adsorption constant and the surfactant concentration through the product of these two variables. The surfactant stabilizing effect increases with the outer stream flow rate. We show that surfactants not only stabilize the microemulsion resulting from the jet breakup in hydrodynamic focusing, but also allow for the reduction of droplet size. Our findings advance the fundamental understanding of the complex role of surfactants in tip streaming via hydrodynamic focusing. In particular, our results contradict the common assumption that adding surfactant favours tip streaming simply because it reduces the meniscus tip surface tension.

Free transverse oscillations of an elastically mounted circular cylinder with low mass-damping are studied with a focus on the effects of the cylinder end condition on structural oscillations and vortex shedding. While the top end of the cylinder pierces the free surface of a water channel, the lower end is changed to have three end conditions: an attached endplate, an endplate unattached from the cylinder at varying gaps and no endplate. All three response branches are examined, with the reduced velocity sweeping $2 \le {U^\ast } \le 15$ (corresponding to a Reynolds number range of $2000 \le Re \le 14\;700$). Although the cylinder oscillations are unaffected by the end condition in the initial and upper branches, they show significant dependency on the end condition in the lower branch. When the endplate is attached or unattached with a small gap, the upper-to-lower branch transition occurs with a sudden decrease in oscillation amplitude, after which the lower branch maintains a near-constant amplitude. For larger gaps or no endplate, with increasing reduced velocity, the oscillation amplitude decreases gradually from its peak without any discernible sign of transition between the upper and lower branches. The three-dimensional effects of the gap are the basis for these differences in oscillation. Atop the strong tip vortex, a low-magnitude streamwise velocity region develops downstream of the cylinder, which delays upper-to-lower branch transition over the cylinder span that sees this low-velocity region. With increasing gap, this low-velocity region and the delay in transition spread over larger spanwise extents, forcing the overall body to oscillate at larger amplitudes.

The electroosmotic flow (EOF) fields in the vicinity of solids with high dielectric permittivity are studied for the case of charge-asymmetric electrolyte solutions. Corresponding solutions of the coupled Poisson–Nernst–Planck and Navier–Stokes equations are obtained analytically and numerically. When a direct-current (DC) electric field is applied to a high-permittivity uncharged sphere, a net EOF develops that translates into a non-zero electrophoretic mobility of the sphere, although it does not carry any charge. Similarly, a DC field acting on a channel in a high-permittivity material results in a net flow through the channel, although the solid is uncharged. Such phenomena are expected to occur frequently whenever high-permittivity solids are immersed in charge-asymmetric electrolyte solutions and do not rely on special scenarios such as ion crowding. Also, the net flow velocities are very significant for realistic values of the electric field strength. The derived scaling relationships even predict giant net flow velocities through nanochannels of the order of metres per second for practically relevant scenarios.

The injection of ${\rm CO}_2$ into depleted reservoirs carries the potential for significant Joule–Thomson cooling, when dense, supercritical ${\rm CO}_2$ is injected into a strongly under-pressured reservoir. The resulting low temperatures around the wellbore risk causing thermal fracturing of the well/near-well region or causing freezing of pore waters or formation of gas hydrates which would reduce injectivity and jeopardise well and reservoir integrity. These risks are particularly acute during injection start-up when ${\rm CO}_2$ is in the gas stability field. In this paper we present a model of non-isothermal single-phase flow in the near-wellbore region. We show that during radial injection, with fixed mass injection rate, transient Joule–Thomson cooling can be described by similarity solutions at early times. The positions of the ${\rm CO}_2$ and thermal fronts are described by self-similar scaling relations. We show that, in contrast to steady-state flow, transient flow causes slight heating of ${\rm CO}_2$ and reservoir gas either side of the thermal front, as pressure diffuses into the reservoir. The scaling analysis here identifies the parametric dependence of Joule–Thomson cooling. We present a sensitivity analysis which demonstrates that the primary controls on the degree of cooling are reservoir permeability, reservoir thickness, injection rate and Joule–Thomson coefficient. The analysis presented provides a computationally efficient approach for assessing the degree of Joule–Thomson cooling expected during injection start-up, providing a complement to complex, fully resolved numerical simulations.

Large-scale coherent structures in incompressible turbulent pipe flow are studied for a wide range of Reynolds numbers ($Re_\tau =180, 550, 1000, 2000$ and $5200$). Employing the Karhunen–Loève decomposition and a novel approach based on the Voronoi diagram, we identify and classify statistically coherent structures based on their location, dimensions and $Re_{\tau }$. With increasing $Re_{\tau }$, two distinct classes of structures become more energetic, namely wall-attached and detached eddies. The Voronoi methodology is shown to delineate these two classes without the need for specific criteria or thresholds. At the highest $Re_{\tau }$, the attached eddies scale linearly with the wall-normal distance with a slope of approximately $l_y\sim 1.2y/R$, while the detached eddies remain constant at the size of $l_y \approx 0.26R$, with a progressive shift towards the pipe centre. We extract these two classes of structures and describe their spatial characteristics, including radial size, helix angle and azimuthal self-similarity. The spatial distribution could help explain the differences in mean velocity between pipe and channel flows, as well as in modelling large and very-large-scale motions (LSM and VLSM). In addition, a comprehensive description is provided for both wall-attached and detached structures in terms of LSM and VLSM.

The diffusiophoresis of charged hydrophobic nanoparticles (NPs) governed by an imposed ionic concentration gradient is analysed. The main objective is to elucidate the impact of the laterally mobile adsorbed surface ions at the interface on the propulsion of the hydrophobic NPs in diffusiophoresis. In addition, the dielectric polarization due to the difference in dielectric constant between the NPs and the suspension medium is also considered. The mobile surface ions create a friction as well as an electric force at the hydrophobic surface, which leads to a modification of the slip velocity condition and the slip length. We obtain an exact numerical solution of the governing electrokinetic equations in their full form by adopting a control volume formulation. The numerical model is supplemented by analytical solutions derived based on the Debye–Hückel linearization. We find that the lateral mobility of the surface ions obstruct the coions to diffuse from the higher concentration side to the lower concentration side, which results in a repulsive force to the particle leading to the occurrence of a negative mobility. Based on the numerical results and analytical solutions, we have shown that for a fully mobile surface charge, the diffusiophoresis of a hydrophobic NP is identical to the diffusiophoresis of a liquid droplet whose viscosity is related to the slip length of the hydrophobic particle. We establish that the dielectric polarization enhances the velocity of a hydrophobic particle, which has potential applications in the practical context.

Flow resistance reduction, quantified as a change in flow rate with respect to a reference isothermal flow driven by the same pressure gradient, is realizable in a channel flow using a thermal wave applied on the bounding wall. Countercurrent waves provide a resistance-reducing effect at any wave velocity, Reynolds number and wavenumber considered. Cocurrent waves can reduce resistance only if the wave velocity is lower than a certain threshold, and the Reynolds number is larger than a certain threshold, otherwise, such waves increase resistance. The increase of the wave amplitude increases resistance reduction and resistance increase up to a specific limit. It is possible to reduce resistance up to 20 times compared with the isothermal channel using proper waves. It is shown that the same effect is achieved regardless of the waves applied at the upper and lower walls. The wave-modified flows are shown to be stable for the conditions used in this study.

We conducted an axisymmetric numerical study of drop impact on a thin film of the same liquid in order to generate maps identifying the fluid elements in the drop and film that are transferred to the corolla during impact. We find that mass contribution from the drop comes from a surprisingly thin surface layer on the drop, and furthermore, that the shape of this layer in the drop and the film scales with film thickness, not the Weber number and Reynolds number as one might expect. The maps could be used to tailor drop composition for applications such as coatings or encapsulations.

The shoreline hazard posed by ocean long waves such as tsunamis and meteotsunamis critically depends on the fraction of energy transmitted across the shallow near-shore shelf. In linear setting, bathymetric inhomogeneities of length comparable to the incident wavelength act as a protective high-pass filter, reflecting long waves and allowing only shorter waves to pass through. Here, we show that, for weakly nonlinear waves, the transmitted energy flux fraction can significantly depend on the amplitude of the incoming wave. The basis of this mechanism is the formation of dispersive shock waves (DSWs), a salient feature of nonlinear evolution of long water waves, often observed in tidal bores and tsunami/meteotsunami evolution. Within the framework of the Boussinesq equations, we show that the DSWs efficiently transfer wave energy into the high wavenumber band, where reflection is negligible. This is phenomenologically similar to self-induced transparency in nonlinear optics: small amplitude long waves are reflected by the bathymetric inhomogeneity, while larger amplitude waves that develop DSWs blueshift into the transparency regime and pass through. We investigate this mechanism in a simplified setting that retains only the key processes of DSW disintegration and reflection, while the effects such as bottom dissipation and breaking are ignored. The results suggests that the phenomenon is a robust, order-one effect. In contrast, the increased transmission due to the growth of bound harmonics associated with the steepening of the wave is weak. The results of the simplified modelling are validated by simulations with the FUNWAVE-TVD Boussinesq model.

The present study investigates streamwise ($\overline {u^2}$) energy-transfer mechanisms in the inner and outer regions of turbulent boundary layers (TBLs). Particular focus is placed on the $\overline {u^2}$ production, its inter-component and wall-normal transport as well as dissipation, all of which become statistically significant in the outer region with increasing friction Reynolds number ($Re_{\tau }$). These properties are analysed using published data sets of zero, weak and moderately strong adverse-pressure-gradient (APG) TBLs across a decade of $Re_{\tau }$, revealing similarity in energy-transfer pathways for all these TBLs. It is found that both the inner and outer peaks of $\overline {u^2}$ are always associated with local maxima in the $\overline {u^2}$ production and its inter-component transport, and the regions below/above each of these peaks are always dominated by wall-ward/away-from-wall transport of $\overline {u^2}$, thereby classifying the $\overline {u^2}$ profiles into four distinct regimes. This classification reveals existence of phenomenologically similar energy-transfer mechanisms in the ‘inner’ and ‘outer’ regions of moderately strong APG TBLs, which meet at an intermediate location coinciding with the minimum in $\overline {u^2}$ profiles. Conditional averaging suggests existence of similar phenomena even in low $Re_{\tau }$ canonical and/or weak APG TBLs, albeit with the outer-region mechanisms weaker than those in the inner region. This explains the absence of their $\overline {u^2}$ outer peak and the dominance of $\overline {u^2}$ wall-normal transport away from the wall, which potentially originates from the inner region. Given that the wall-ward/away-from-wall transport of $\overline {u^2}$ is governed by the $Q_4$(sweeps)/$Q_2$(ejections) quadrants of the Reynolds shear stress, it is argued that the emergence of the $\overline {u^2}$ outer peak corresponds with the statistical dominance of $Q_4$ events in the outer region. Besides unravelling the dynamical significance of $Q_2$ and $Q_4$ events in the outer region of TBLs, the present analysis also proposes new phenomenological arguments for testing on canonical wall-turbulence data at very high $Re_{\tau }$.

Standing acoustic waves have been known to generate Eulerian time-mean ‘streaming’ flows at least since the seminal investigation of Lord Rayleigh in the 1880s. Nevertheless, a recent body of numerical and experimental evidence has shown that inhomogeneities in the ambient density distribution lead to much faster flows than arise in classical Rayleigh streaming. The emergence of these unusually strong flows creates new opportunities to enhance heat transfer in systems in which convective cooling cannot otherwise be easily achieved. To assess this possibility, a theoretical study of acoustic streaming in an ideal gas confined in a rectangular channel with top and bottom walls maintained at fixed but differing temperatures is performed. A two time scale system of equations is utilized to efficiently capture the coupling between the fast acoustic waves and the slowly evolving streaming flow, enabling strongly nonlinear regimes to be accessed. A large suite of numerical simulations is carried out to probe the streaming dynamics, to highlight the critical role played by baroclinically generated wave vorticity and to quantify the additional heat flux induced by the standing acoustic wave. Proper treatment of the two-way coupling between the waves and mean flow is found to be essential for convergence to a self-consistent steady state, and the variation of the resulting acoustically enhanced steady-state heat flux with both the amplitude of the acoustic wave and the $O(1)$ aspect ratio of the channel is documented. For certain parameters, heat fluxes almost two orders of magnitude larger than those realizable by conduction alone can be attained.