This paper investigates the multilayer Rayleigh–Taylor instability (RTI) using statistically stationary experiments conducted in a gas tunnel. Employing diagnostics such as particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF), we make simultaneous velocity–density measurements to study how dynamics and mixing are linked in this variable density flow. Experiments are conducted in a newly built, blow-down three-layer gas tunnel facility. Mixing between three gas streams is studied, where the top and bottom streams are comprised of air, and the middle stream is an air–helium mixture. Shear is minimized between these streams by matching their inlet velocities. The four experimental conditions investigated here consist of two different density ratios (Atwood numbers 0.3 and 0.6), each investigated at two instability development times (or equivalently, two streamwise locations), and all experiments are with the same middle stream thickness of 3 cm. The growth of the middle layer is measured using laser-based planar Mie scattering visualization. The mixing width is found to grow linearly with time at late times. Various quantitative measures of molecular mixing indicate a very high degree of molecular mixing at late times in the multilayer RTI flow. The vertical turbulent mass flux $a_y$ is calculated. In addition to mostly negative values of $a_y$, typical of buoyancy-dominated flows due to negative correlation between velocity and density fluctuations, positive regions are also observed in profiles of $a_y$ due to entrainment and erosion at the lower edge of the mixing region. Global energy budgets are calculated for the multilayer RTI flow at late times and it is found that the majority of potential energy released has been dissipated due to viscous effects, and a large value of mixing efficiency ($\sim$60 %) is observed.

Three-dimensional schools of hydrodynamically axisymmetric swimmers self-propelling at a constant velocity are studied. We introduce a low-order model for the induced velocity based on the far-field approximation. We inquire if, by holding suitable relative positions in the three-dimensional space, the swimmers can reduce the overall energy consumption of the school in comparison with the same number of isolated individuals at the same velocity. We find a considerable (several per cent) energy saving achievable by chain formations. The benefit increases asymptotically with the number of individuals, towards a finite limit that is a function of the minimum allowed spacing between each pair of neighbours.

To elucidate the effect of particle shape on the rheology of a dense, viscous suspension of frictional, non-Brownian particles, experimental measurements are presented for suspensions of polystyrene particles with different shapes in the same solvent. The first suspension is made of spheres whereas the particles which compose the second suspension are globular but with flattened faces. We present results from steady shear and shear-reversal rheological experiments for the two suspensions over a wide range of stresses in the viscous regime. Notably, we show that the rheology of the two suspensions is characterised by a shear-thinning behaviour, which is stronger in the case of the suspension of globular particles. Since the shear-reversal experiments indicate an absence of adhesive particle interactions, we attribute the shear thinning to a sliding friction coefficient which varies with stress as has been observed previously for systems similar to the first suspension. We observe that the viscosity of the two suspensions is similar at high shear stress where small sliding friction facilitates particle relative motion due to sliding. At lower shear stress, however, the sliding friction is expected to increase and the particle relative motion would be associated with rolling. The globular particles attain a higher viscosity at low shear stress than the spherical particles. We attribute this difference to a shape-induced resistance to particle rolling that is enhanced by the flattened faces. Image analysis is employed to identify features of the particle geometry that contribute to the resistance to rolling. It is shown that the apparent rolling friction coefficients inferred from the rheology are intermediate between the apparent dynamic and static rolling friction coefficients predicted on the basis of the image analysis. All three rolling resistance estimates are larger for the globular particles with flat faces than for the spherical particles and we argue that this difference yields the stronger shear thinning of the globular particle suspension.

Small differences in the densities of a river confluence's tributaries (i.e. 0.5 kg m$^{-3}$) have been proposed to cause coherent streamwise-oriented vortices (SOVs) in its mixing interface. These secondary flow structures are thought to result from density-driven gravity currents being laterally confined between the converging flows. However, empirical evidence for density SOVs and the confined gravity current mechanism is lacking. To this end, experiments are carried out in a laboratory confluence permitting a spectrum of thermal density differences between its tributaries. Particle image velocimetry and laser-induced fluorescence are used simultaneously to study the mixing interface's dynamics. The sensitivity of the mixing interface's secondary flow structure to the confluence's momentum ratio and the magnitude of the density difference is evaluated. Density SOVs are confirmed in the mixing interface and are caused by the gravity currents being confined laterally as the opposing flows merge and accelerate downstream. The SOVs are largest and most coherent when the momentum of the dense channel is greater than that of the light channel. The dynamics of these secondary flow structures is strongly coupled to periodic vertically orientated Kelvin–Helmholtz instabilities. The striking similarities between the empirically reproduced SOVs herein and those recently observed at the Coaticook-Massawippi confluence (Quebec, Canada), despite a two-order magnitude difference in physical scale, suggest density SOVs are a scale-independent flow structure at confluences when specific, yet relatively common, hydraulic and density conditions align.

A long-wave asymptotic model is developed for the flow of an axisymmetric viscous film lining the interior of a tube for the case where slip occurs at the tube wall. Both the case of a falling film with a passive air core and that of a film driven up the tube by pressure-driven airflow are considered. The impact of slip on the net liquid volume flux is discussed, and linear stability analysis of the evolution equation is conducted to identify the impact of slip on the phase speed and growth rates of disturbances in each case. The presence of slip enhances the growth rates, though its impact on phase speed depends on the film thickness and the strength of the core airflow. For some parameter combinations, slip can modify the phase speed without altering the base flow. The nonlinear evolution of the free surface is then studied numerically. For falling films, increasing the slip length reduces the critical thickness required for plug formation to occur. Families of travelling wave solutions are found via continuation and are used to derive a simple formula for the dependence of this critical thickness on the slip length; this formula is shown to hold for small slip length. For air-driven films, the topology of streamlines in the film can be altered by slip at the wall; if the slip length is large enough, it can prevent regions of recirculation from forming at the wave crest.

The general problem of tracer diffusion in non-equilibrium baths is important in a wide range of systems, from the cellular level to geographical length scales. In this paper, we revisit the archetypical example of such a system: a collection of small passive particles immersed in a dilute suspension of non-interacting dipolar microswimmers, representing bacteria or algae. In particular, we consider the interplay between thermal (Brownian) diffusion and hydrodynamic (active) diffusion due to the persistent advection of tracers by microswimmer flow fields. Previously, it has been argued that even a moderate amount of Brownian diffusion is sufficient to significantly reduce the persistence time of tracer advection, leading to a significantly reduced value of the effective active diffusion coefficient $D_A$ compared to the non-Brownian case. Here, we show by large-scale simulations and kinetic theory that this effect is in fact practically relevant only for microswimmers that effectively remain stationary while still stirring up the surrounding fluid – so-called shakers. In contrast, for moderate and high values of the swimming speed, relevant for biological microswimmer suspensions, the effect of Brownian motion on $D_A$ is negligible, leading to the effects of advection by microswimmers and Brownian motion being additive. This conclusion contrasts with previous results from the literature, and encourages a reinterpretation of recent experimental measurements of $D_A$ for tracer particles of varying size in bacterial suspensions.

Drag for wall-bounded flows is directly related to the spatial flux of spanwise vorticity outward from the wall. In turbulent flows a key contribution to this wall-normal flux arises from nonlinear advection and stretching of vorticity, interpretable as a cascade. We study this process using numerical simulation data of turbulent channel flow at friction Reynolds number $Re_\tau =1000$. The net transfer from the wall of spanwise vorticity created by downstream pressure drop is due to two large opposing fluxes, one which is ‘down-gradient’ or outward from the wall, where most vorticity concentrates, and the other which is ‘up-gradient’ or toward the wall and acting against strong viscous diffusion in the near-wall region. We present evidence that the up-gradient/down-gradient transport occurs by a mechanism of correlated inflow/outflow and spanwise vortex stretching/contraction that was proposed by Lighthill. This mechanism is essentially Lagrangian, but we explicate its relation to the Eulerian anti-symmetric vorticity flux tensor. As evidence for the mechanism, we study (i) statistical correlations of the wall-normal velocity and of wall-normal flux of spanwise vorticity, (ii) vorticity flux cospectra identifying eddies involved in nonlinear vorticity transport in the two opposing directions and (iii) visualizations of coherent vortex structures which contribute to the transport. The ‘D-type’ vortices contributing to down-gradient transport in the log layer are found to be attached, hairpin-type vortices. However, the ‘U-type’ vortices contributing to up-gradient transport are detached, wall-parallel, pancake-shaped vortices with strong spanwise vorticity, as expected by Lighthill's mechanism. We discuss modifications to the attached eddy model and implications for turbulent drag reduction.

This study investigates the effect of vibration on the flow structure transitions in thermal vibrational convection (TVC) systems, which occur when a fluid layer with a temperature gradient is excited by vibration. Direct numerical simulation (DNS) of TVC in a two-dimensional enclosed square box is performed over a range of dimensionless vibration amplitudes $0.001 \le a \le 0.3$ and angular frequencies $10^{2} \le \omega \le 10^{7}$, with a fixed Prandtl number of 4.38. The flow visualisation shows the transition behaviour of flow structure upon the varying frequency, characterising three distinct regimes, which are the periodic-circulation regime, columnar regime and columnar-broken regime. Different statistical properties are distinguished from the temperature and velocity fluctuations at the boundary layer and mid-height. Upon transition into the columnar regime, columnar thermal coherent structures are formed, in contrast to the periodic oscillating circulation. These columns are contributed by the merging of thermal plumes near the boundary layer, and the resultant thermal updrafts remain at almost fixed lateral position, leading to a decrease in fluctuations. We further find that the critical point of this transition can be described nicely by the vibrational Rayleigh number ${{Ra}}_{vib}$. As the frequency continues to increase, entering the so-called columnar-broken regime, the columnar structures are broken, and eventually the flow state becomes a large-scale circulation (LSC), characterised by a sudden increase in fluctuations. Finally, a phase diagram is constructed to summarise the flow structure transition over a wide range of vibration amplitude and frequency parameters.

We study the effect of continuum breakdown on the two-dimensional thermoacoustic radiation of a thin plate set in a perfect monatomic gas. The plate is heated harmonically in time and the acoustic field is investigated in the entire range of gas rarefaction rates. Analytical approximations are obtained in the limits of high (free-molecular) and low (continuum limit) gas rarefaction, accompanied by direct simulation Monte Carlo calculations at intermediate flow conditions. While the source acoustic field is of a monopole type in the continuum regime, it turns non-isotropic at non-continuum conditions, exhibiting dipole directivity and exponential decay rate in the collisionless limit. The combined effects of source heating frequency and gas Knudsen number on the far-field acoustic radiation are illustrated and rationalized.

Deep-water surface wave breaking affects the transfer of mass, momentum, energy and heat between the air and sea. Understanding when and how the onset of wave breaking will occur remains a challenge. The mechanisms that form unforced steep waves, i.e. nonlinearity or dispersion, are thought to have a strong influence on the onset of wave breaking. In two dimensions and in deep water, spectral bandwidth is the main factor that affects the roles these mechanism play. Existing studies, in which the relationship between spectral bandwidth and wave breaking onset is investigated, present varied and sometimes conflicting results. We perform potential-flow simulations of two-dimensional focused wave groups on deep water to better understand this relationship, with the aim of reconciling existing studies. We show that the way in which steepness is defined may be the main source of confusion in the literature. Locally defined steepness at breaking onset reduces as a function of bandwidth, and globally defined (spectral) steepness increases. The relationship between global breaking onset steepness and spectral shape (using the parameters bandwidth and spectral skewness) is too complex to parameterise in a general way. However, we find that the local surface slope of maximally steep non-breaking waves, of all spectral bandwidths and shapes that we simulate, approaches a limit of $1/\tan ({\rm \pi} /3)\approx 0.5774$. This slope-based threshold is simple to measure and may be used as an alternative to existing kinematic breaking onset thresholds. There is a potential link between slope-based and kinematic breaking onset thresholds, which future work should seek to better understand.

Two-way momentum-coupled direct numerical simulations of a particle-laden turbulent channel flow are addressed to investigate the effect of the particle Stokes number and of the particle-to-fluid density ratio on the turbulence modification. The exact regularised point-particle method is used to model the interphase momentum exchange in presence of solid boundaries, allowing the exploration of an extensive region of the parameter space. Results show that the particles increase the friction drag in the parameter space region considered, namely the Stokes number $St_+ \in [2,80]$, and the particle-to-fluid density ratio $\rho _p/\rho _f \in [90,5760]$ at a fixed mass loading $\phi =0.4$. It is noteworthy that the highest drag occurs for small Stokes number particles. A measurable drag increase occurs for all particle-to-fluid density ratios, the effect being reduced significantly only at the highest value of $\rho _p/\rho _f$. The modified stress budget and turbulent kinetic energy equation provide the rationale behind the observed behaviour. The particles’ extra stress causes an additional momentum flux towards the wall that modifies the structure of the buffer and of the viscous sublayer where the streamwise and wall-normal velocity fluctuations are increased. Indeed, in the viscous sublayer, additional turbulent kinetic energy is produced by the particles’ back-reaction, resulting in a strong augmentation of the spatial energy flux towards the wall where the energy is ultimately dissipated. This behaviour explains the increase of friction drag in particle-laden wall-bounded flows.

High-speed vehicles experience a highly challenging environment in which the freestream Mach number and surface temperature greatly influence aerodynamic drag and heat transfer. The interplay of these two parameters strongly affects the near-wall dynamics of high-speed turbulent boundary layers (TBLs) in a non-trivial way, breaking similarity arguments on velocity and temperature fields, typically derived for adiabatic cases. We present direct numerical simulations of flat-plate zero-pressure-gradient TBLs spanning three freestream Mach numbers $[2,4,6]$ and four wall temperature conditions (from adiabatic to very cold walls), emphasising the choice of the wall-cooling parameter to recover a similar flow organisation at different Mach numbers. We link qualitative observations on flow patterns to first- and second-order statistics to explain the decoupling of temperature–velocity fluctuations that occurs at reduced wall temperatures and high Mach numbers. For these cases, we discuss the formation of a secondary peak of thermal production in the viscous sublayer, which is in contrast with the monotonic behaviour of adiabatic profiles. We propose different physical mechanisms induced by wall-cooling and compressibility that result in apparently similar flow features, such as a higher peak in the streamwise velocity turbulence intensity, and distinct features, such as the separation of turbulent scales.

The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.

A microscale lubrication flow of a gas between eccentric circular cylinders is studied on the basis of kinetic theory. The dimensionless curvature, defined by the mean clearance divided by the radius of the inner cylinder, is small, and the rotation speed of the inner cylinder is also small. The Knudsen number, defined by the mean free path divided by the mean clearance, is arbitrary. The Boltzmann equation is studied analytically using the slowly varying approximation following the method proposed in the author's previous study (Doi, Phys. Rev. Fluids, vol. 7, 2022, 034201). A macroscopic lubrication equation, which is a microscale generalization of the Reynolds lubrication equation, is derived. To assess this, a direct numerical analysis of the Boltzmann equation in a bipolar coordinate system is conducted using the Bhatnagar–Gross–Krook–Welander kinetic equation. It is demonstrated that the solution of the derived lubrication equation approximates that of the Boltzmann equation over a wide range of the eccentricity and the whole range of the Knudsen number. It is also demonstrated that another lubrication equation derived by a formal application of the slowly varying approximation produces a non-negligible error of the order of the square root of the dimensionless curvature for large Knudsen numbers.

We study the coupled settling, deformation and mixing dynamics of a dense blob of fluid falling in an axially (vertically) linearly stratified Taylor–Couette cell (operated in a laminar stable regime). This configuration allows the independent analysis of stretching dynamics, driven by radial (horizontal) velocity variations, and settling dynamics, driven by buoyancy forces associated with vertical density variations. As the blob settles, it is stretched in the horizontal plane and forms an elongated lamella. Through the competing effects of transverse compression of the lamella due to this shear-induced stretching and broadening due to diffusion, the lamella irreversibly mixes with ambient fluid, thus progressively adjusting its own density towards that of the ambient fluid. Eventually, the lamella settling stops at a final equilibrium position that depends on the ambient vertical density gradient and the rate at which it has been deformed by the horizontal shear. We show how this final position is determined by stretching-enhanced diffusion, i.e. mixing. We demonstrate that a theoretical mixing model compares favourably with experiments with various Froude numbers (quantifying the relative strength of the horizontal shear and the vertical stratification) and construct a new criterion for the energetic ‘efficiency’ of this mixing process that explicitly captures its inherently diffusive character.

Direct numerical simulations up to Reλ = 1445 show that the scaling exponents for the enstrophy and the dissipation rate extrema are different and depend on the Reynolds number. A similar Reynolds number dependence of the scaling exponents is observed for the moments of the dissipation rate, but not for the moments of the enstrophy. Significant changes in the exponents occur at approximately Reλ ≈ 250, where Reλ is the Taylor based Reynolds number, which coincides with structural changes in the flow, in particular the development of large-scale shear layers. A model for the probability density functions (PDFs) of the enstrophy and dissipate rate is presented, which is an extension of our existing model (Proc. R. Soc. A, vol. 476, 2020, p. 20200591) and is based on the mentioned development of large-scale layer regions within the flow. This model is able to capture the observed Reynolds number dependencies of the scaling exponents, in contrast to the existing theories which yield constant exponents. Moreover, the model reconciles the scaling at finite Reynolds number with the theoretical limit, where the enstrophy and dissipation rate scale identically at infinite Reynolds number. It suggests that the large-scale shear layers are vital for understanding the scaling of the extrema. Furthermore, to reach the theoretical limit, the scaling exponents must remain Reynolds number dependent beyond the present Reλ range.

Accelerated glacier melt and the loss of perennial snowfields have been associated with increased warming in polar regions, at rates up to four times faster than the rest of the world, thereby reinforcing the critical need for improved models (and predictions) of glacier melt. An essential requirement for such models is an improved understanding of the sensible heat fluxes over glaciers. Since their complexity makes them difficult to model, and direct measurements of sensible turbulent heat fluxes over real glaciers are both rare and impractical, the present work involves simultaneous hot-wire anemometry and cold-wire thermometry measurements of two components of velocity and temperature above a melting glacier model in a series of wind-tunnel experiments. Both single- and multi-variable statistics were used to compare the turbulent velocity field measured over melting ice with that of a similar flow in the absence of ice. The results demonstrate that the ice's presence reduces the magnitude of the Reynolds stresses and vertical velocity variance, but also increases the streamwise velocity variance. The transient evolution of temperature statistics throughout the melt process was also investigated and found to be similar when suitably non-dimensionalized. The velocity and temperature fields were furthermore evaluated at an equivalent non-dimensional time during the melt process, in which statistics of the temperature field, and joint statistics of the vertical velocity and temperature, were studied. The present work lays the foundation for future laboratory-scale replications of the flow above melting glaciers, and provides additional insight into turbulent heat transfer over melting ice.

The irreversible behaviour of a highly confined non-Brownian suspension of spherical particles at low Reynolds number in a Newtonian fluid is studied experimentally and numerically. In the experiment, the suspension is confined in a thin rectangular channel that prevents complete particle overlap in the narrow dimension and is subjected to an oscillatory pressure-driven flow. In the small cross-sectional dimension, particles rapidly separate to the walls, whereas in the large dimension, features reminiscent of shear-induced migration in bulk suspensions are recovered. Furthermore, as a consequence of the channel geometry and the development and application of a single-camera particle tracking method, three-dimensional particle trajectories are obtained that allow us to directly associate relative particle proximity with the observed migration. Companion simulations of a steadily flowing suspension highly confined between parallel plates are conducted using the force coupling method, which also show rapid migration to the walls as well as other salient features observed in the experiment. While we consider relatively low volume fractions compared to most prior work in the area, we nevertheless observe significant and rapid migration, which we attribute to the high degree of confinement.

The effect of variations in the integral length scale of incoming free-stream turbulence on a NACA0012 wing is investigated with the use of force, moment and particle image velocimetry measurements. At a chord-based Reynolds number ($Re = U_\infty c/\nu$ where c is the chord length, $U_\infty$ is the free-stream velocity and $\nu$ is the kinematic viscosity) of $2\times 10^5$, an active grid generates turbulence intensities of 15 % at normalised integral length scales ranging from 0.5$c$ to 1$c$. The introduction of turbulence improves the time-averaged performance characteristics of the wing by delaying stall and increasing the peak lift coefficient. It is found that for half-chord integral length scales, the magnitude of the fluctuations in forces and moments is larger than that of full-chord integral length scales, as the former amplifies the naturally occurring unsteadiness in the flow (when there is no free-stream turbulence). The increase in magnitude is ascribed to a larger density of smaller-scale vortices within the separated flow and wake region of the wing.

From biological tissues to microactuators and absorption of solvents into layers of paint, macroscopically non-porous materials with the capacity to swell when in contact with a solvent are ubiquitous. In these systems, owing to strong solid–fluid interactions, chemically driven flows can yield large geometric changes. We study experimentally and theoretically the canonical problem of the swelling of a thin hydrogel layer by a single water drop. Using a bespoke experimental set-up, we observe fast absorption leading to a radially spreading axisymmetric blister. We use a fully three-dimensional linear poroelastic framework with nonlinear kinematic equations to obtain governing equations, which we then reduce with thin-layer scalings to a one-dimensional nonlinear diffusion equation for the evolution of the blister geometry. In the limits of large and small deformations, the evolution of the blister characteristic height and radius are self-similar, following power laws in time. Our experimental measurements show that the evolution of the blister is broadly within the theoretical predictions in the large and small deformation regimes. In the general intermediate deformation regime, the measurements are well captured by our reduced one-dimensional diffusion model, which does not require the sophisticated and computationally expensive numerical approaches necessary for the original two-dimensional nonlinear coupled transport problem. By adapting modelling techniques from the fluid dynamics of thin porous elastic layers to a polymer swelling problem, our modelling framework extends the range of polymer swelling problems that can be treated with semi-analytical methods. Moreover, our detailed experimental data can serve as a test case for future nonlinear poroelastic frameworks of swelling polymer materials.