Eukaryotic swimming cells such as spermatozoa, algae or protozoa use flagella or cilia to move in viscous fluids. The motion of their flexible appendages in the surrounding fluid induces propulsive forces that balance viscous drag on the cells and lead to a directed swimming motion. Here, we use our recently built database of cell motility (BOSO-Micro) to investigate the extent to which the shapes of eukaryotic swimming cells may be optimal from a hydrodynamic standpoint. We first examine the morphology of flexible flagella undergoing waving deformation and show that their amplitude-to-wavelength ratio is near that predicted theoretically to optimise the propulsive efficiency of active filaments. Next, we consider ciliates, for which locomotion is induced by the collective beating of short cilia covering their surface. We show that the aspect ratios of ciliates are close to that predicted to minimise the viscous drag of the cell body. Both results strongly suggest a key role played by hydrodynamic constraints, in particular viscous drag, in shaping eukaryotic swimming cells.

A data-driven framework using snapshots of an uncontrolled flow is proposed to identify, and subsequently demonstrate, effective control strategies for different objectives in supersonic impinging jets. The open-loop, feed-forward control approach, based on a dynamic mode decomposition reduced-order model (DMD-ROM), computes forcing receptivity in an economical manner by projecting flow and actuator-specific forcing snapshots onto a reduced subspace and then evolving the dynamics forwards in time. Since it effectively determines a linear response around the unsteady flow in the time domain, the method differs materially from typical techniques that use steady basic states, such as stability or input–output approaches that employ linearized Navier–Stokes operators in the frequency domain. The method presented naturally accounts for factors inherent to the snapshot basis, including configuration complexity and flow parameters such as Reynolds number. Furthermore, gain metrics calculated in the reduced subspace facilitate rapid assessments of flow sensitivities to a wide range of forcing parameters, from which optimal actuator inputs may be selected and results confirmed in scale-resolved simulations or experiments. The DMD-ROM approach is demonstrated from two different perspectives. The first concerns asymptotic feedback resonance, where the effects of harmonic pressure forcing are estimated and verified with nonlinear simulations using a blowing–suction actuator. The second examines time-local behaviour within critical feedback events, where the phase of actuation becomes important. For this, a conditional space–time mode is used to identify the optimal forcing phase that minimizes convective instability growth within the resonance cycle.

The impact of fluid drops on solid substrates is a cardinal fluid dynamics phenomenon intrinsically related to many fields. Although these impacting objects are very often non-spherical and non-Newtonian, previous studies have mainly focused on spherical Newtonian drops. As a result, both shape and rheological effects on the drop-spreading dynamics remain largely unexplored. In the present work we use a mixed approach combining experiments with multiphase three-dimensional numerical simulations to extend the work reported by Luu & Forterre (J. Fluid Mech., vol. 632, 2009, pp. 301–327) by highlighting the fundamental role of shape in the normal impact of viscoplastic drops. Such complex fluids are highly common in various industrial domains and ideally behave either like a rigid body or a shear-rate-dependent liquid, according to the stress solicitation. Spherical, prolate, cylindrical and prismatic drops are considered. The results show that, under negligible capillary effects, the impacting kinetic energy of the drop is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: (i) inertio-viscous, (ii) inertio-plastic, and (iii) mixed inertio-visco-plastic. These regimes are deeply affected by the drop initial aspect ratio, which in turn reveals the possibility of using drop shape to control spreading. The physical mechanisms driving the considered phenomenon are underlined by energy budget analyses and scaling laws. The results are summarised in a two-dimensional diagram linking the drop maximum spreading, minimum height and final shape with different spreading regimes through a single dimensionless parameter, here called the impact number.

While capillary imbibition in tubes or porous materials has been studied extensively in the past, less attention has been paid to imbibition into a swellable porous material. However, swelling is commonly observed when a polymeric network, such as the cellulose composing paper fibres or sponges, absorbs a solvent. The incompressibility of the fluid leads to an elastic expansion of the polymeric matrix. In a porous material, swelling can affect the geometry of the pores, thus affecting the capillary flow. To describe this complex problem, we propose a model experiment, namely the capillary imbibition in a model pore composed of two parallel and stretched elastomeric fibres. In this configuration, one can observe both the progression of a capillary meniscus and the swelling of the fibres. We show that swelling enables a capillary imbibition for fibres placed further apart than the critical distance existing for non-swelling fibres. In this swelling-dominated regime, we identify a new imbibition dynamic at constant velocity which we rationalize using a linear poro-elastic theory. Finally, we describe the elastocapillary collapse of our model pore which is observed when capillary forces overcome the restoring tension force within the fibres.

Canopy flows in the atmospheric surface layer play important economic and ecological roles, governing the dispersion of passive scalars in the environment. The interaction of high-velocity fluid and large-scale surface-mounted obstacles in canopy flows produces drag and causes intense, inhomogeneous and anisotropic turbulence. In this work, we focus on the turbulent dispersion of passive scalars by studying the ‘pair dispersion’ – a statistical measure of relative motion between particles. We analyse the results of a three-dimensional particle tracking velocimetry experiment in a wind-tunnel canopy flow, focusing on small scales. We confirm the existence of local isotropy of pair dispersion at scales smaller than a characteristic shear length scale $L_\varGamma =(\epsilon /\varGamma ^3)^{1/2}$, where $\epsilon$ and $\varGamma$ are the mean dissipation rate and shear rate, respectively. Furthermore, we show that pair dispersion in this locally isotropic regime is a scale-dependent super-diffusive process, similar to what occurs in homogeneous isotropic turbulent flows. In addition, we measure the pair relative velocity correlation function, showing that its de-correlation occurs in the locally isotropic regime, and discuss the implications of this observation for modelling pair dispersion. Thus, our study extends the fundamental understanding of turbulent pair dispersion to the anisotropic inhomogeneous turbulent canopy flow, bringing valuable information for modelling scalar dispersion in the atmospheric surface layer.

We report an experimental investigation of the heat transport and flow field in a rectangular Rayleigh–Bénard convection (RBC) cell with two immiscible fluids: silicone oil and glycerol. The global heat transport of the system is divided into three ranges corresponding to the different flow structures formed in the glycerol layer. In range I, the glycerol layer is dominated by conduction, and no plume is formed over the interface. In range II, cellular rolls are formed in the glycerol layer and the horizontal motion of rolls causes an oscillation of temperature in the interface. In range III, the cellular pattern is time-independent, and the interface forms a group of wavelets with wave numbers consistent with the mode of the cellular pattern. In lower-thin glycerol, the Nusselt (Nu) grows from conduction to convection through an oscillating subcritical bifurcation at critical Rayleigh number $Ra_c$. The value of $Ra_c$ in the present work is smaller than the theoretical prediction of both-rigid boundaries and greater than the prediction of one-rigid and one-free boundaries. In the upper-thick silicone oil layer, $Nu$ increases with increasing $Ra$, but it is smaller than that of traditional RBC. For the silicone oil layer in two-layer RBC, the hot plumes emitting over the liquid–liquid interface showed different shape and different velocity from cold plumes emitting from the top rigid plate. This implies that the velocity boundary condition strongly influences the flow structure in turbulent convection.

A classic lift decomposition (Von Kármán & Sears, J. Aeronaut. Sci., vol. 5, 1938, pp. 379–390) is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behaviour provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for ${A{\kern-4pt}R}\ {\rm (aspect\ ratio)} <1.5$ occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within $20\,\%$ of its value when $St\ {\rm (Strouhal\ number)} < 0.45$. For $St \ge 0.45$ there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effects, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization.

A transcritical domain with a sharp two-phase interface may exist during the early times of liquid hydrocarbon fuel injection at supercritical pressure. Thus, two-phase dynamics are sustained before substantial heating of the liquid and drive the early three-dimensional deformation and atomisation. A recent study of a transcritical liquid jet showed distinct deformation features caused by interface thermodynamics, low surface tension and intraphase diffusive mixing. In the present work, the compressible vortex identification method $\lambda _\rho$ is used to study the vortex dynamics in a cool liquid n-decane transcritical jet surrounded by a hotter oxygen gaseous stream at supercritical pressures. The relationship between vortical structures and the liquid surface evolution is detailed, along with the vorticity generation mechanisms, including variable-density effects. The roles of hairpin and roller vortices in the early deformation of lobes, the layering and tearing of liquid sheets and the formation of fuel-rich gaseous blobs are analysed. At these high pressures, enhanced intraphase mixing and ambient gas dissolution affect the local liquid structures (i.e. lobes). Thus, liquid breakup differs from classical sub-critical atomisation. Near the interface, liquid density and viscosity drop by up to 10 % and 70 %, respectively, and the liquid is more easily affected by the vortical motion (e.g. liquid sheets wrap around vortices). Despite the variable density, compressible vorticity generation terms are smaller than the vortex stretching and tilting. Layering traps and aligns the vortices along the streamwise direction while mitigating the generation of new rollers.

Partially molten rock is a densely packed, melt-saturated, granular medium, but it has seldom been considered in these terms. In this paper we extend the continuum theory of partially molten rock to incorporate the physics of granular media. Our formulation includes dilatancy in a viscous constitutive law and introduces a non-local fluidity. We analyse the resulting poro-viscous–granular theory in terms of two modes of liquid–solid segregation that are observed in published torsion experiments: localisation of liquid into high-porosity sheets and radially inward liquid flow. We show that the newly incorporated granular physics brings the theory into agreement with experiments. We discuss these results in the context of grain-scale physics across the nominal jamming fraction at the high homologous temperatures relevant in geological systems.

The dynamics of the interaction of a system of two thin volatile liquid droplets resting on a soft viscoelastic solid substrate are investigated theoretically. The developed model fully considers the effect of evaporative cooling and the generated Marangoni stresses due to the induced thermal gradients, while also accounting for the effect of the gas phase composition and the diffusion of vapour in the atmosphere of the droplets. Using the framework of lubrication theory, we derive evolution equations for both the droplet profile and the displacement of the elastic solid, which are solved in combination with Laplace's equation for the vapour concentration in the gas phase. A disjoining-pressure/precursor-film approach is used to describe contact-line motion. The evolution equations are solved numerically, using the finite-element method, and we present a thorough parametric analysis to investigate the physical properties and mechanisms that affect the dynamics of droplet interactions. The results show that the droplets interact through both the soft substrate and the gas phase. In the absence of thermocapillary phenomena, the combined effect of non-uniform evaporation due to the increased vapour concentration between the two droplets and elastocapillary phenomena determines whether the drop–drop interaction is attractive or repulsive. The Marangoni stresses suppress droplet attraction at the early stages of the drying process and lead to longer droplet lifetimes. For substrates with intermediate stiffness, the emergence of spontaneous symmetry breaking at late stages of evaporation is found. The rich dynamics of this complex system is explored by constructing a detailed map of the dynamic regimes.

We investigate how inhomogeneity influences the $k^{-5/3}$ inertial range scaling of turbulent kinetic energy spectra (with $k$ the wavenumber). For weak statistical inhomogeneity, the energy spectrum can be described as an equilibrium spectrum plus a perturbation. Theoretical arguments suggest that this latter contribution scales as $k^{-7/3}$. This prediction is assessed using direct numerical simulations of three-dimensional Kolmogorov flow.

This paper introduces a new modification to the convective Cahn–Hilliard equation and a lattice Boltzmann framework to simulate liquid–solid phase transitions in multicomponent systems. The model takes into account changes in properties, such as density, caused by solidification, which leads to volume expansion or contraction. After validating the proposed model against classical problems and experimental data, the solidification of a sessile droplet was investigated in detail. Results of numerical simulations suggest that the environmental conditions are as important as the surface condition in deciding the freezing time and the final shape of the droplet. The environmental properties can also affect the freezing time indirectly through interaction with surface wettability. It has been demonstrated that hydrophobic surfaces may lose their advantages over hydrophilic surfaces in terms of anti-icing performance when primary solidification is initiated from the interface between the droplet and the environment fluid. The deformations of droplets, either with contraction or expansion, were confirmed and compared in different environments. This study offers a new perspective on droplet solidification by exposing the strong influence of environmental conditions and meanwhile provides a useful numerical method to predict the phase change process.

From industrial-scale production to small-scale fabrication of functional films, the blade coating method is used widely to apply a uniform thin liquid film on a moving substrate. However, conventional hydrodynamic models are inadequate for laboratory-scale low-speed blade coating, where capillary forces dominate. In this study, the low-speed blade coating of non-evaporative Newtonian fluids was investigated in experimental, computational and analytical approaches. The transient free boundary problem was solved utilizing a two-dimensional finite element method, and a simple viscocapillary model was developed to describe the viscous stress and capillary forces within the puddle, and predict the thickness of the wet film as a function of the speed of the substrate. Comparing the predicted film thickness with the computational results, and a flow visualization experiment of blade coating with silicone oil, respectively, confirmed the model's validity. The study indicates that the proposed model may be a useful tool for optimizing laboratory coating processes, as it provides a greater understanding of the low-speed blade coating system on a laboratory scale.

Heat transfer by large deformable drops in a turbulent flow is a complex and rich-in-physics system, in which drop deformation, breakage and coalescence influence the transport of heat. We study this problem by coupling direct numerical simulation (DNS) of turbulence with a phase-field method for the interface description. Simulations are run at fixed-shear Reynolds and Weber numbers. To evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on macroscopic flow properties, like mean temperature or heat transfer rates, we consider four different values of the Prandtl number, which is the momentum to thermal diffusivity ratio: $Pr=1$, $Pr=2$, $Pr=4$ and $Pr=8$. The drop volume fraction is $\varPhi \simeq 5.4\,\%$ for all cases. Drops are initially warmer than the turbulent carrier fluid and release heat at different rates depending on the value of $Pr$, but also on their size and on their own dynamics (topology, breakage, drop–drop interaction). Computing the time behaviour of the drops and carrier fluid average temperatures, we clearly show that an increase of $Pr$ slows down the heat transfer process. We explain our results by a simplified phenomenological model: we show that the time behaviour of the drop average temperature is self-similar, and a universal behaviour can be found upon rescaling by $t/Pr^{2/3}$. Accordingly, the heat transfer coefficient $\mathcal {H}$ (respectively its dimensionless counterpart, the Nusselt number $Nu$) scales as $\mathcal {H}\sim Pr^{-2/3}$ (respectively $Nu\sim Pr^{1/3}$) at the beginning of the simulation, and tends to $\mathcal {H}\sim Pr^{-1/2}$ (respectively $Nu\sim Pr^{1/2}$) at later times. These different scalings can be explained via the boundary layer theory and are consistent with previous theoretical/numerical predictions.

A gas volume rising in a vertical tube is called a Taylor bubble when its equivalent spherical diameter is greater than the diameter of the tube. Continuity dictates that the rising velocity of such bullet-shaped bubbles must be such that the drainage flow in the liquid film separating the gas from the tube wall equals the rate at which space is vacated by the bubble tail on its rise. The numerical simulations presented here show that, if the volume of the bubble is made to execute small-amplitude oscillations, this drainage flow can be markedly decreased so that the bubble slows down so much as to very nearly stop. The mechanism is a subtle nonlinear interplay between the upward flow imposed by the bubble expansion and the inertia of the falling liquid. Two manners of excitation are considered. In the first one the liquid column above the bubble is forced to oscillate sinusoidally, e.g. by a piston. In the second one, an oscillating pressure is imposed on the top liquid surface. With the first arrangement the bubble slows down during its entire ascent by an amount depending on the oscillation frequency and amplitude. With the second one, for a given frequency, the bubble slows down only in the neighbourhood of a certain resonant depth at which the volume oscillations are maximized, but is little affected at deeper and shallower depths.

The super-temporal-resolution (STR) reconstruction of turbulent flows is an important data augmentation application for increasing the data reach in measurement techniques and understanding turbulence dynamics. This paper proposes a data assimilation (DA) strategy based on weak-constraint four-dimensional variation to conduct an STR reconstruction in a turbulent jet beyond the Nyquist limit from given low-sampling-rate observations. Highly resolved large-eddy simulation (LES) data are used to produce synthetic measurements, which are used as observations and for validation. A segregated assimilation procedure is realised to assimilate the initial condition, inflow boundary condition and model error separately. Different types of observational data are tested. The first type is down-sampled LES data containing many small-scale turbulence structures with or without synthetic noise. The DA results show that the temporal variation of the small-scale structures is well recovered even with noise in the observations. The spectra are resolved to a frequency approximately one order of magnitude higher than what can be captured within the Nyquist limit. The second type of observation is low-sampling-rate tomographic particle image velocimetry (tomo-PIV) data with or without the injection of small-scale structures. The modulation between the large-scale structures contained in the tomo-PIV fields and the small scales injected from the observations is improved. The resultant small scales in the STR reconstruction have the characteristics of authentic turbulence to a considerable extent. Additionally, DA yields much smaller errors in the prediction of particle positions when compared with the Wiener filter, demonstrating the great potential for Lagrangian particle tracking in measurement techniques.

The aim of the present study is to understand the role of steam/cold-air inhalation on the mucus layer dynamics in the proximal airways. We model these flows as a viscoelastic liquid (lining the inner side of a tube) sheared by a turbulent airflow and subjected to a radial heat flow. The linear stability analysis of the resulting flow is carried out using numerical and thin-film approaches. The air–mucus interface tension, coupled with the azimuthal curvature, leads to the previously predicted axisymmetric capillary mode responsible for airway closure in distal airways. The viscoelasticity of the mucus leads to axisymmetric and new non-axisymmetric elastic modes, with the former possessing a higher growth rate. The axisymmetric elastic and capillary modes merge to give rise to a new ‘elasto-capillary mode’ possessing a growth rate nearly equal to the combined growth rate of the elastic and capillary modes. The analysis predicts a strong stabilising effect of the thermocapillarity induced by steam inhalation on the elasto-capillary mode. Thus steam decreases airway resistance, which could explain the observed therapeutic effect of steam inhalation. The opposite is the case when the inhaled air is colder than the body temperature, in agreement with the observations. The theoretical predictions are corroborated by the physical mechanism explaining the suppression/amplification of the elasto-capillary mode due to thermocapillarity.

For a Mach $4.5$ flat-plate adiabatic boundary layer, we study the sensitivity of the first, second Mack modes and streaks to steady wall-normal blowing/suction and wall heat flux. The global instabilities are characterised in frequency space with resolvent gains and their gradients with respect to wall-boundary conditions are derived through a Lagrangian-based method. The implementation is performed in the open-source high-order finite-volume code BROADCAST and algorithmic differentiation is used to access the high-order state derivatives of the discretised governing equations. For the second Mack mode, the resolvent optimal gain decreases when suction is applied upstream of Fedorov's mode $S$/mode $F$ synchronisation point, leading to stabilisation, and the converse when applied downstream. The largest suction gradient is in the region of branch I of mode $S$ neutral curve. For heat-flux control, strong heating at the leading edge stabilises both the first and second Mack modes, the former being more sensitive to wall-temperature control. Streaks are less sensitive to any boundary control in comparison with the Mack modes. Eventually, we show that an optimal actuator consisting of a single steady heating strip located close to the leading edge manages to damp the linear growth of all three instability mechanisms.

The axisymmetric steady two-phase flow of a differentially heated thermocapillary liquid bridge in air and its linear stability is investigated numerically, taking into account dynamic interfacial deformations in the basic flow. Since most experiments require a high temperature difference to drive the flow into the three-dimensional regime, the temperature dependence of the material properties must be taken into account. Three different models are investigated for a high-Prandtl-number thermocapillary liquid bridge with nominal Prandtl number ${\textit {Pr}}=28.8$: the Oberbeck–Boussinesq (OB) approximation, a linear temperature dependence of all material properties and a full nonlinear temperature dependence of all material properties. For all models, critical Reynolds numbers are computed as functions of the volume of the liquid bridge, its aspect ratio, its dimensional size and as a function of the strength of a forced axial flow in the ambient air. Under most circumstances the OB approximation overpredicts and the linear model underpredicts the critical Reynolds number, compared with the model based on the full temperature dependence of the material properties. Among the main influence factors are the proper selection of the reference temperature and, at larger temperature differences, the temperature dependence of the viscosity of the liquid.

This paper introduces a viscous vortex model for predicting the optimal drag reduction of riblet surfaces, eliminating the need for expensive direct numerical simulations (DNSs) or experiments. The footprint of a typical quasi-streamwise vortex, in terms of the spanwise and wall-normal velocities, is extracted from smooth-wall DNS flow fields in close proximity to the surface. The extracted velocities are then averaged and used as boundary conditions in a Stokes-flow problem, wherein riblets with various cross-sectional shapes are embedded. Here, the same smooth-wall-based boundary conditions can be used for riblets, as we observe from the DNSs that the quasi-streamwise vortices remain unmodified apart from an offset. In particular, the position of these vortices remain unpinned above small riblets. The present approach is compared with the protrusion-height model of Luchini et al. (J. Fluid Mech., vol. 228, 1991, pp. 87–109), which is also based on a Stokes calculation, but represents the vortex with only a uniform spanwise velocity boundary condition. The key novelty of the present model is the introduction of a wall-normal velocity component into the boundary condition, thus inducing transpiration at the riblet crests, which becomes relevant as the riblet size increases. Consequently, the present model allows for the drag-reduction prediction of riblets up to the optimal size. The present approach does not rely on the scale separation formally required by homogenisation techniques, which are only applicable for vanishingly small riblets.