Injecting a less viscous fluid into a more viscous fluid in a Hele-Shaw cell triggers two-dimensional viscous fingering patterns which are characterised by increasingly long fingers undergoing tip splitting and branching events. These complex structures are considered to be a paradigm for interfacial pattern formation in porous media flow and other related phenomena. Over the past five years, there has been a flurry of interest in manipulating these interfacial fingering patterns by altering the physical components of the Hele-Shaw apparatus. In this Focus on Fluids article, we summarise some of this work, concentrating on a very recent study in which the alterations include replacing one of the two bounding plates with an elastic membrane (Ducloué et al., J. Fluid Mech., vol. 826, 2017, R2). The resulting experimental set-up gives rise to a wide variety of novel interfacial patterns including periodic sideways fingers, dendritic-like patterns and short, flat-tipped viscous fingers that appear to resemble molar teeth. These latter fingers are similar to those observed in the printer’s instability and when peeling off a layer of adhesive tape. This delightful work brings together a number of well-studied themes in interfacial fluid mechanics, including how viscous and surface tension forces compete to drive fingering patterns, how interfaces are affected by fluid–solid interactions and, finally, how novel strategies can be implemented to control interfacial instabilities.

Fluid flows through nano-scale channels depend sensitively on the physical and chemical properties of the walls that surround them. The sub-micron dimensions of such channels, however, are impossible to resolve optically, which rules out most methods for flow visualization. Classic calculations by Squire (Q. J. Mech. Appl. Maths, vol. IV, 1951, pp. 321–329) and Landau & Lifshitz (Fluid Mechanics, vol. 6, 1959, Pergamon) showed that the laminar flow driven outside a capillary, by fluid emerging from the end of the capillary, is identical to the flow driven by a point force proportional to the average velocity in the capillary. Secchi et al. (J. Fluid Mech. 826, R3) analyze the dispersion of a solute that is injected along with the fluid, whose concentration decays slowly with distance but with a strong angular dependence that encodes the intra-capillary velocity. Fluorescence micrographs of the concentration profile emerging from the nanocapillary can be related directly to the average fluid velocity within the nanocapillary. Beyond their remarkable capacity for nano-velocimetry, Landau–Squire plumes will likely appear throughout micro- and nano-fluidic systems.

It is becoming increasingly clear that the strong spatial and temporal fluctuations observed in a narrow Reynolds number regime around the laminar–turbulent transition in shear flows can best be understood using the concepts and techniques from a seemingly unrelated discipline – statistical mechanics. During the last few years, a consensus has begun to emerge that these phenomena reflect an underlying non-equilibrium phase transition exhibited by a model of interacting particles on a crystalline lattice, directed percolation, that seems very far from fluid mechanics. Now, Chantry et al. (J. Fluid Mech., vol. 824, 2017, R1) have developed a truncated-mode computation of a model shear flow, capable of simulating systems far larger and longer than any previous study and have for the first time generated enough statistical data that a high-precision test of theory is feasible. The results broadly confirm the theory, extending the class of flows for which the directed percolation scenario holds and removing any remaining doubts that non-equilibrium statistical mechanical critical phenomena can be exhibited by the Navier–Stokes equations.

How do the laws of physics change with changes in spatial dimension? Maybe not at all in some cases, but in important cases, the changes are dramatic. Fluid turbulence – the fluctuating, intermittent and many-degree-of-freedom state of a highly forced fluid – determines the transport of heat, mass and momentum and is ubiquitous in nature, where turbulence is found on spatial scales from microns to millions of kilometres (turbulence in stars) and beyond (galactic events such as supernovae). When the turbulent degrees of freedom are suppressed in one spatial dimension, the resulting turbulent state in two dimensions (2D) is remarkably changed compared with the turbulence in three dimensions (3D) – energy flows to small scales in 3D but towards large scales in 2D. Although this result has been known since the 1960s due to the pioneering work of Kraichnan, Batchelor and Leith, how one transitions between 3D and 2D turbulence has remained remarkably unexplored. For real physical systems, this is a highly significant question with important implications about transport in geophysical systems that determine weather on short time scales and climate on longer scales. Is the transition from 3D to 2D smooth or are there sharp transitions that signal a threshold of the dominance of one type of turbulence over another? Recent results by Benavides & Alexakis (J. Fluid Mech., vol. 822 (2017), pp. 364–385) suggest that the latter may be the case – a surprising and provocative discovery.

When an acoustic wave propagates through a viscous fluid, it progressively transfers momentum to the fluid through viscous dissipation, which results in the formation of a steady vortical flow called acoustic streaming. Although spawned by viscous effects, the magnitude of the streaming does not depend on the viscosity in most simple geometries. However, viscosity has a profound influence on the acoustic streaming as demonstrated by Riaud et al. (J. Fluid Mech., vol. 821, 2017, pp. 384–420) in their study of sessile mm-sized water–glycerol droplets placed on a piezoelectric substrate with a 20-MHz ultrasound surface acoustic wave propagating along its surface. A detailed experimental and numerical analysis reveals that streaming dynamics is driven by a few ultrasound ray caustics inside the droplet.

Rotating flow in which the angular velocity decreases outward while the angular momentum increases is known as ‘quasi-Keplerian’. Despite the general tendency of shear flow to break down into turbulence, this type of flow seems to maintain stability at very large Reynolds number, even when nonlinearly perturbed, a behaviour that strongly influences our understanding of astrophysical accretion discs. Investigating these flows in the laboratory is difficult because secondary Ekman flows, caused by the retaining Couette cylinders, can become turbulent on their own. A recent high Reynolds number numerical study by Lopez & Avila (J. Fluid Mech., vol. 817, 2017, pp. 21–34) reconciles apparently discrepant laboratory experiments by confirming that this secondary flow recedes toward the axial boundaries of the container as the Reynolds number is increased, a result that enhances our understanding of nonlinear quasi-Keplerian flow stability.

Natural convection is omnipresent on Earth. A basic and well-studied model for it is Rayleigh–Bénard convection, the fluid flow in a layer heated from below and cooled from above. Most explorations of Rayleigh–Bénard convection focus on spatially uniform, perfectly conducting thermal boundary conditions, but many important geophysical phenomena are characterized by boundary conditions which are a mixture of conducting and adiabatic materials. For example, the differences in thermal conductivity between continental and oceanic lithospheres are believed to play an important role in plate tectonics. To study this, Wang et al. (J. Fluid Mech., vol. 817, 2017, R1), measure the effect of mixed adiabatic–conducting boundary conditions on turbulent Rayleigh–Bénard convection, finding experimental proof that even if the total heat transfer is primarily affected by the adiabatic fraction, the arrangement of adiabatic and conducting plates is crucial in determining the large-scale flow dynamics.

The whirling helical structure obtained when pouring honey onto toast may seem like an easy enough problem to solve at breakfast. Specifically, one would hope that a quick back-of-the-envelope scaling argument would help rationalize the observed behaviour and predict the coiling frequency. Not quite: multiple forces come into play, both in the part of the flow stretched by gravity and in the coil itself, which buckles and bends like a rope. In fact, the resulting abundance of regimes requires the careful numerical continuation method reported by Ribe (J. Fluid Mech., vol. 812, 2017, R2) to build a complete phase diagram of the problem and untangle this sticky situation.

Birds have to flap their wings to generate the needed thrust force, which powers them through the air. But how exactly do flapping wings create such force, and at what amplitude and frequency should they operate? These questions have been asked by many researchers. It turns out that much of the secret is hidden in the wake left behind the flapping wing. Exemplified by the study of Andersen et al. (J. Fluid Mech., vol. 812, 2017, R4), close examination of the flow pattern behind a flapping wing will inform us whether the wing is towed by an external force or able to generate a net thrust force by itself. Such studies are much like looking at the footprints of terrestrial animals as we infer their size and weight, figuring out their walking and running gaits. A map that displays the collection of flow patterns after a flapping wing, using flapping frequency and amplitude as the coordinates, offers a full picture of its flying ‘gaits’.

Stirring olive oil and vinegar to make salad dressing creates an emulsion of vinegar droplets in oil. More vigorous stirring gives smaller droplets, while if left to sit the droplets will begin to coalesce and the two fluids will separate. In this vein, Dodd & Ferrante (J. Fluid Mech., vol. 806, 2016, pp. 356–412) present a new analysis of how homogeneous turbulence in a carrier fluid interacts with a suspension of droplets of an immiscible liquid. Based on a set of direct numerical simulations, the authors provide new insights on how turbulence affects the motion of the droplets, their shape and size; then in turn how the droplets alter the flow including effects of interfacial surface energy on the kinetic energy of the flow.

It was only a matter of time before deep neural networks (DNNs) – deep learning – made their mark in turbulence modelling, or more broadly, in the general area of high-dimensional, complex dynamical systems. In the last decade, DNNs have become a dominant data mining tool for big data applications. Although neural networks have been applied previously to complex fluid flows, the article featured here (Ling et al., J. Fluid Mech., vol. 807, 2016, pp. 155–166) is the first to apply a true DNN architecture, specifically to Reynolds averaged Navier Stokes turbulence models. As one often expects with modern DNNs, performance gains are achieved over competing state-of-the-art methods, suggesting that DNNs may play a critically enabling role in the future of modelling complex flows.

Radko’s recent article (J. Fluid Mech., vol. 805, 2016, pp. 147–170) entitled Thermohaline layering in dynamically and diffusively stable shear flows, is slated to become a seminal reference in the field of fluid dynamics. It proposes an elegant solution to the long-standing question of why thermohaline staircases form in the high-latitude oceans. Equally importantly, it provides a rare and interesting example of how two physical processes that are both strongly stable when considered individually, can trigger a linear instability when they interact.

Recently, Bonnefoy et al. (J. Fluid Mech., vol. 805, 2016, R3) studied the resonant interaction of oblique surface gravity waves in a large $50~\text{m}\times 30~\text{m}\times 5~\text{m}$ wave basin. Their experimental results are in excellent quantitative agreement with predictions of the weakly nonlinear wave theory, and provide additional evidence to the strength of this widely used mathematical formulation. In this article, the reader is introduced to the many facets of the weakly nonlinear theory for surface gravity waves, and to its current and possible future applications, deterministic as well as stochastic.

A pipe conveying fluid is a model problem in fluid–structure interactions and nonlinear dynamics. Several experimental and theoretical studies exist on this problem and very rich nonlinear dynamics have been observed including super- and subcritical instabilities as well as various routes to chaos. Despite all the existing studies, we had not yet seen the fluid inside an oscillating pipe as the pipe undergoes different types of flow-induced instabilities. But the wait is over.

The recent study of Laurence et al. (J. Fluid Mech., vol. 797, 2016, pp. 471–503) develops a new Schlieren-based technique for investigating instabilities and transition in hypersonic boundary layers. This method enables pioneering measurements in a reflected-shock wind tunnel of the characteristics of the second mode of instability on a slender cone, within very short time scales (approximately 1 ms). The visualization technique was shown to resolve the structural evolution of individual wave packets. It was revealed that the disturbance strength concentrates near the wall for high-enthalpy conditions.

In a recent paper, Chu & Prosperetti (J. Fluid Mech., vol. 798, 2016, pp. 787–811) calculate the dissolution of a two-component droplet in an immiscible liquid. Here we discuss in what sense their results go much beyond the Epstein–Plesset solution of a dissolving single-component droplet and hitherto used approximations for dissolving multicomponent droplets. We also highlight the relevance of Chu & Prosperetti’s result for liquid–liquid extraction processes for chemical analysis.

Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol. XLV, 1987, pp. 561–571) started these developments with snapshot proper orthogonal decomposition, a particularly simple method. The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design. A winning argument for proper orthogonal decomposition (POD) is the optimality property, i.e. the guarantee of the least residual for a given number of modes. The price is unpleasant frequency mixing in the modes which complicates their physical interpretation. In contrast, temporal Fourier modes and dynamic mode decomposition (DMD) provide pure frequency dynamics but lose the orthonormality and optimality property of POD. Sieber et al. (J. Fluid Mech., vol. 792, 2016, pp. 798–828) bridge the least residual and pure frequency behaviour with an ingenious interpolation, called spectral proper orthogonal decomposition (SPOD). This article puts the achievement of the TU Berlin authors in perspective, illustrating the potential of SPOD and the challenges ahead.

Few fluid phenomena are as beautiful, fragile and ephemeral as the crown splash that is created by the impact of an object on a liquid. The crown-shaped phenomenon and the physics behind it have mesmerised and intrigued scientists for over a century, and still the scientific world has not yet uncovered all of the secrets of the splash. This is exemplified in a particularly striking manner in Marston et al. (J. Fluid Mech., vol. 794, 2016, pp. 506–529) where a 6 m tall vacuum chamber is employed to study the splash formed upon impact of a sphere onto a deep liquid pool, at both atmospheric and reduced ambient pressures. They shed light into the classical problem of the surface seal and study the buckling of the splash. With an almost magical touch they devise a method to create a splash without the liquid and the sphere ever coming into contact. The images that accompany the paper – taken with state-of-the-art high-speed cameras – are as stunning as the physics that is uncovered in them.

A new paradigm of rheological characterization, oscillatory simple shear with infinite forcing amplitudes, is introduced by Khair (J. Fluid Mech., vol. 791, 2016, R5). This pushes the technique of large-amplitude oscillatory shear (LAOS) to have two extremely large amplitudes (both strain-rate and strain), which we might call XXLAOS. Model-specific analytical predictions are derived for a suspension of nearly spherical rigid particles subject to Brownian rotational diffusion. The work illuminates a new regime of rheological characterization that may serve as a distinct proving ground for constitutive model selection and for probing the flow physics of rheologically complex fluids.

An observed, spectacular and puzzling distinctive feature of wall-bounded flows transitioning to/from turbulence is the large-scale ordered coexistence of laminar and turbulent flow over a wide range of Reynolds numbers. In their article, Chantry et al. (J. Fluid Mech., vol. 791, 2016, R8) circumvent the problem of turbulence modulation in genuine plane Couette flow by replacing no-slip boundary conditions at the walls with effective stress-free conditions constraining the interior part of the flow only. In so doing, they are able to collect relevant information on the laminar–turbulent patterning. The approach is then adapted to plane Poiseuille and pipe flow, giving to it a more universal value. Taking advantage of the stress-free conditions, they derive reduced models efficient at capturing the laminar–turbulent coexistence. Such models would be useful to interpret recent findings in the large-aspect-ratio limit.