The evaporation of multiple sessile droplets is both scientifically interesting and practically important, occurring in many natural and industrial applications. Although there are simple analytic expressions to predict evaporation rates of single droplets, there are no such frameworks for general configurations of droplets of arbitrary size, contact angle or spacing. However, a recent theoretical contribution by Masoud, Howell & Stone (J. Fluid Mech., vol. 927, 2021, R4) shows how considerable insight can be gained into the evaporation of arbitrary configurations of droplets without having either to obtain the solution for the concentration of vapour in the atmosphere or to perform direct numerical simulations of the full problem. The theoretical predictions show excellent agreement with simulations for all configurations, only deviating by 25 % for the most confined droplets.

Vessels – in the widest sense – travelling on a water surface continuously do work the water surrounding it, causing energy to be radiated in the form of surface waves. The concomitant resistance force, the wave resistance, can account for as much as half the total drag on the vessel, so reducing it to a minimum has been a major part of ship design research for many decades. Whether the ‘vessel’ is an ocean-going ship or a swimming duckling, the physics governing the V-shaped pattern of radiated waves behind it is in essence the same, and just as fuel economy is important for commercial vessels, it is reasonable to assume that also swimming waterfowl seek to minimise their energy expenditure. Using theory and methods from classic marine hydrodynamics, Yuan et al. (J. Fluid Mech., vol. 928, 2021, R2) consider whether, by organising themselves optimally, ducklings in a row behind a mother duck can reduce, eliminate or even reverse their individual wave resistance. They describe two mechanisms which they term ‘wave riding’ and ‘wave passing.’ The former is intuitive: the ducklings closest to the mother can receive a forward push by riding its mother's stern waves. The latter is perhaps a more striking phenomenon: when the interduckling distance is precisely right, every duckling in the row can, in principle, swim without wave resistance due to destructive wave interference. The phenomenon appears to be the same as motivates the recent US military research project Sea Train, a row of unmanned vehicles travelling in row formation.

Just as a solid object would, a liquid jet or a stream of droplets impacting a free surface deforms and perforates it. This generic flow interaction, met in everyday life but also in cutting edge industrial processes, has puzzled scientists for centuries. Lee et al. (J. Fluid Mech., vol. 921, 2021, A8) present an experimental study of a simple droplet train interacting with a liquid bath and identify two stages in the interaction: a first where a cavity elongates and finally bursts, and a second where the interface is steadily punched by the incoming stream. Each of these regimes is explained with elementary but effective models arising from first principles, thereby revealing a full and simple picture of the physics of making holes in liquids.

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.

A Lagrangian perspective has yielded many new insights in our quest to reveal the intricacies of turbulent flows. Much of this progress has been possible by following the trajectories of idealised, inertialess objects (tracers) traversing through the flow. Their spins and tumbles provide a glimpse into the underlying local velocity gradients of the turbulent field. While it is known that the spinning and tumbling rates of anisotropic particles are modified in turbulence – compared with those in a random flow field – a quantitative explanation for this has remained elusive. Now, Pujara et al. (J. Fluid Mech., vol. 922, 2021, R6) have made an attempt to predict the split between spinning and tumbling rates by accessing the particle's alignment with the local vorticity. Their analysis of filtered turbulent fields reveals a Lagrangian scale invariance, whereby key quantities relating to the particle's rotational statistics are preserved from the dissipative to the integral scale.

The hypothesis in the classical Kolmogorov picture of turbulence with perhaps the most far-reaching consequences is that of universality, the notion that small-scale turbulence dynamics are independent of the way the turbulence was generated. The assumption of universality can be evaluated by comparing measurements taken in many kinds of flows. However, up to now the range of flows that can be used to study universality from a Lagrangian viewpoint has been highly constrained, because large-scale Eulerian inhomogeneity manifests as Lagrangian non-stationarity. The recent work of Viggiano et al. (J. Fluid Mech., vol. 918, 2021, A25) significantly extends this range by showing how the dynamics along Lagrangian trajectories can be continuously renormalised using local Eulerian scales, at least in flows whose development is self-similar. They demonstrate their results on a turbulent jet, a classical flow that is well studied from the Eulerian perspective, though not in a Lagrangian sense. Their work provides an exciting roadmap for expanding the scope of Lagrangian analysis of turbulent flows.

Fascinating wake vortex patterns emerge when a circular cylinder is forced to vibrate laterally to a uniform fluid flow, deviating from the well-known Kármán vortex street and first reported by Williamson & Roshko (J. Fluids Struct., vol. 2, 1988, pp. 355–381). The two rows of single vortices (2S mode) can suddenly transition to a row of paired vortices and a row of single vortices (P+S mode) as the forcing amplitude is increased. Further increase in amplitude finds another sudden jump back to the 2S mode. Through a series of elegant and carefully crafted numerical simulations, Matharu et al. (J. Fluid Mech., vol. 918, 2021, A42) determine that the transitions occur via bifurcations, but that underlying these observed ‘jumps’, a continuous evolution of the vortex street between the modes is seen along unstable branches connecting the two modes. As the Reynolds number decreases from 100, bistability and the P+S mode are eventually suppressed.

Inertia-gravity waves in the atmosphere and ocean are transported and refracted by geostrophic turbulent currents. Provided that the wave group velocity is much greater than the speed of geostrophic turbulent currents, kinetic theory can be used to obtain a comprehensive statistical description of the resulting interaction (Savva et al., J. Fluid Mech., vol. 916, 2021, A6). The leading-order process is scattering of wave energy along a surface of constant frequency, $\omega$, in wavenumber space. The constant-$\omega$ surface corresponding to the linear dispersion relation of inertia-gravity waves is a cone extending to arbitrarily high wavenumbers. Thus, wave scattering by geostrophic turbulence results in a cascade of wave energy to high wavenumbers on the surface of the constant-$\omega$ cone. Solution of the kinetic equations shows establishment of a wave kinetic energy spectrum $\sim k_h^{-2}$, where $k_h$ is the horizontal wavenumber.

Turbulent wall-flow research often includes documenting and describing mean flow and turbulence properties under variations in Reynolds number or other relevant parameters. Concomitant efforts are associated with clarifying the flow dynamics and energetics that accompany the observed statistical behaviours. Relative to these aims, the so-called canonical wall flows (pipe, channel and flat plate boundary layer flows) comprise an important baseline. Additionally, flows that add complexity relative to the canonical baseline while retaining analytically idealized properties provide unique opportunities to clarify the nature of wall-flow turbulence and its response to modifying influences. In this regard, the meticulously conducted study by Ferro et al. (J. Fluid Mech., vol. 915, 2021, A80) provides significant and remarkable contributions by both demonstrating that the idealized flow state of the turbulent asymptotic suction boundary layer (TASBL) is realizable in a laboratory experiment, and by providing a high fidelity documentation of the mean flow and streamwise velocity fluctuation properties in the TASBL flow.

A recent statistical analysis, proposed by Shnapp (J. Fluid Mech., vol. 913, 2021, R2), of Lagrangian velocity measurements in a wind tunnel in the presence of a canopy (a forest or urban morphology), using three-dimensional particle tracking velocimetry (Shnapp et al., Sci. Rep., vol. 9, issue 1, 2019, pp. 1–13), is a great read. In this strongly anisotropic situation, despite the additional roughness induced by the canopy, it is shown that fluctuations of Lagrangian velocity increments over small time scales display very similar behaviour as those observed in homogeneous and isotropic turbulent flows. This is all the more true when focussing on the non-Gaussian and intermittent nature of these fluctuations. At much larger time scales, of the order and greater than the characteristic turnover time scale of the flow, anisotropies implied by the presence of the canopy are quantified using averages of the fluctuating kinetic energy conditioned upon the direction of Lagrangian velocity with respect to the mean Eulerian flow. Shnapp (2021) evidences that, indeed, the canopy modifies the velocity along the trajectories at large scales, in particular its variance, but leaves unchanged its local regularity, as it is pinpointed by the power-law exponents of the structure functions.

Extreme events in turbulent flow are associated with intense stretching of concentrated vortices, intermittent in both space and time. The occurrence of such events has been investigated in a turbulent flow driven by counter-rotating propellors (Debue et al., J. Fluid Mech., 2021), and local flow structures have been identified. Interesting theoretical problems arise in relation to this work; these are briefly considered in this focus paper.

The motion of a sphere in a viscous gas has been studied since the time of Sir George Gabriel Stokes who explored linear, steady and unsteady flows. While the unsteady Stokes equation is often used to calculate these flows, this continuum treatment cannot capture some key physical phenomena. This includes propulsion of a sphere by temperature gradients on its surface, without convection. Taguchi et al. (J. Fluid Mech., 2021) now calculate the flow generated by the impulsive rotation of a sphere in a gas, a problem first proposed by Stokes, using the linearised Boltzmann-BGK (Bhatnagar, Gross, Krook) equation. This statistical mechanical approach naturally captures continuum through to collisionless flows; the latter occurs even when the gas mean free path is small. The heat flow generated by the sphere is also determined – a non-continuum effect – showing its direction reverses as the flow evolves. The predicted phenomena are yet to be observed in experiment.

Slender sheets of viscous liquid can show features characteristic of elastic materials, such as buckling under compression. Likewise, thin sheets of solid material subject to sufficiently high stress can deform plastically, i.e. flow. In this volume, Hewitt & Balmforth (J. Fluid Mech., vol. 908, 2021, A5) explore the territory between these regimes, by developing asymptotic theories for thin viscoelastic and elasto-viscoplastic sheets, focusing primarily on regimes in which bending deformations dominate stretching. Their results reveal a rich phenomenology and provide new theoretical tools with which to probe thin layers of soft materials.

Electrohydrodynamic instabilities at liquid interfaces continue to defy our intuition, from the pioneering work of Taylor (Proc. R. Soc. Lond. A, vol. 280, issue 1382, 1964, pp. 383–397) on conical tips of electrified droplets to a recent numerical study by Wagoner et al. (J. Fluid Mech., vol. 904, 2020, R4). The problem studied by Wagoner et al. (2020) consists of a droplet immersed in a more conducting and more dielectric liquid medium, in a strong electrical field. When the droplet is more viscous than the outer medium, the droplet develops a biconcave shape which might eventually evolve to a torus shape (or doughnut). In contrast, when the droplet is less viscous, it adopts a lenticular shape and emits a thin fluid sheet from its equator which in turn breaks up into droplets. These droplets form a ring of satellites around the original droplet, which justifies its appellation ‘Saturnian droplet’. The numerical simulations bring light to this complex phenomenon and confirm the robustness of the leaky-dielectric framework (Melcher & Taylor, Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111–146).

The flow around a rotating circular cylinder has a parameter regime with a complex pattern of periodic solutions and multiple steady states. Sierra et al. (J. Fluid Mech., vol. 905, 2020, A2) provide a complete bifurcation analysis of this regime. The numerical computations are guided by a qualitative analysis of the bifurcations stemming from a highly degenerate singular dynamical system. Surprisingly, the dynamics of the singular system itself cannot be realized as a specific flow, but acts mathematically as an organizer of the physical bifurcation diagram.

Reduced-order models are often sought to efficiently represent key dynamical phenomena present among the broad range of temporal and spatial scales associated with unsteady and turbulent flow problems. Linear ‘input–output’ approaches and resolvent analyses reveal that important information about the most dangerous (most amplified) disturbances and the corresponding fluctuation response can be found with knowledge only of the base flow, or the turbulent mean field. In the work by Padovan et al. (J. Fluid Mech., vol. 900, 2020, A14), an important advance is made with regards to flows which have a periodically time-varying base flow, for example during unsteady vortex shedding from a body. By forming a harmonic resolvent relative to this base flow, limitations associated with the traditional linear resolvent are overcome to determine efficient bases for modelling of limit cycle flows and reveal novel information about key triadic (resonant) interactions.

Although the relative importance of airborne transmission of the SARS-CoV-2 virus is controversial, increasing evidence suggests that understanding airflows is important for estimation of the risk of contracting COVID-19. The data available so far indicate that indoor transmission of the virus far outstrips outdoor transmission, possibly due to longer exposure times and the decreased turbulence levels (and therefore dispersion) found indoors. In this paper we discuss the role of building ventilation on the possible pathways of airborne particles and examine the fluid mechanics of the processes involved.

The theory of Kolmogorov, enunciated for very large Reynolds numbers, has progressively been shown to be inoperative for characterizing flows of practical relevance. Yet, in a recent study by Alves Portela et al. (J. Fluid Mech., vol. 896, 2020, A16), the turbulence statistics in the very near wake of a square prism at modest Reynolds numbers, reveal a significant portion of scales complying with a cascade of Kolmogorov type. By resorting to a generalized version of the Kármán–Howarth–Kolmogorov equation, this intriguing observation is shown to be an illusion, hiding a measurable influence of coherent structures and statistical inhomogeneity. This striking conclusion highlights that a complete statistical theory of turbulence cannot dispense with the influence of large scales, possibly coherent, motions.

Inclining a fluid layer subjected to a temperature gradient introduces a profusion of fascinating patterns and regimes. Previous experimental and computational studies form the starting point for an extensive numerical bifurcation study by Reetz & Schneider (J. Fluid Mech., vol. 898, 2020, A22) and Reetz et al. (J. Fluid Mech., vol. 898, 2020, A23). Intricate trajectories passing through multiple steady and periodic states organize the dynamics. The consequences for chaotic patterns in large geometries is discussed.

Convection in a container, heated from below, cooled from above and rapidly rotated around a vertical axis, starts from its sidewall. When the imposed vertical temperature gradient is not sufficiently large for bulk modes to set in, thermal convection can start in the form of wall modes, which are observed near the sidewall as pairs of hot ascending and cold descending plumes that drift along the wall. With increasing temperature gradient, different wall and bulk modes occur and interact, leading finally to turbulence. A recent numerical study by Favier & Knobloch (J. Fluid Mech., 895, 2020, R1) reveals an extreme robustness of the wall states. They persist above the onset of bulk modes and turbulence, thereby relating them to the recently discovered boundary zonal flows in highly turbulent rotating thermal convection. More exciting is that the wall modes can be thought of as topologically protected states, as they are robust with respect to the sidewall shape. They stubbornly drift along the wall, following its contour, independent of geometric obstacles.