Fingering instabilities readily occur if a less viscous fluid displaces a more viscous fluid in a narrow gap due to the action of destabilising viscous forces. If the fluids are miscible, the instability can be suppressed in the limit of large advection as complicated flow structures are formed across the gap. Using a fluid to displace a monolayer of non-colloidal particles suspended in the same fluid, Luo et al. (2025 J. Fluid Mech. vol. 1011, A48) suppress the formation of the cross-gap structures and identify a new fingering mechanism which instead relies on long-range dipolar disturbance flows generated by the particle confinement.

The paper by Pružina et al. (2025) J. Fluid Mech. 1009, sheds new light on the physical processes responsible for the formation of distinct layers in double-diffusive convection. Towards this end, it discusses direct numerical simulation results within the framework of sorted buoyancy coordinates. In particular, it demonstrates that the eddy diffusivity is negative everywhere, including in the interior of the well-mixed layers. This approach holds promise for analysing other, closely related, flow configurations that give rise to the emergence of pronounced layering features.

Studying rotating convection under geo- and astrophysically relevant conditions has proven to be extremely difficult. For the rotating Rayleigh–Bénard system, van Kan et al. (J. Fluid Mech., vol. 1010, 2025,A42)have now been able to massively extend the parameter space accessible by direct numerical simulations. Their progress relies on a rescaling of the governing Boussinesq equations, which vastly improves numerical conditioning (Julien et al., arXiv:2410.02702). This opens the door for investigating previously inaccessible dynamical regimes and bridges the gap to the asymptotic branch of rapidly rotating convection.

Turbulent Taylor–Couette flow displays traces of axisymmetric Taylor vortices even at high Reynolds numbers. With this motivation, Feldmann & Avila (2025) J. Fluid Mech, 1008, R1, carry out long-time numerical simulations of axisymmetric high-Reynolds-number Taylor–Couette flow. They find that the Taylor vortices, using the only degree of freedom that remains available to them, carry out Brownian motion in the axial direction, with a diffusion constant that diverges as the number of rolls is reduced below a critical value.

In fluid dynamics, helicity measures the correlation between velocity and its curl, vorticity, over a spatial volume. Under ‘ideal’ conditions (vanishing viscosity and either homogeneneous density or when pressure may be regarded as a function of density alone), helicity is a topological invariant closely related to the knottedness of vortex lines (Moffatt 1969 J. Fluid Mech. 35 (1), 117–129). Helicity is conserved following a material volume for compact vorticity distributions, i.e. when the vorticity field is tangent to the surface of the volume. There is a related helicity invariant in ideal magnetohydrodynamics involving the correlation between the magnetic potential and its curl, the magnetic field. Helicity is a fragile invariant in the sense that relaxing any one of the ideal conditions results in non-conservation. Unlike energy and enstrophy (mean-square vorticity), helicity is not positive (or sign) definite. Viscous diffusion can create both positive and negative helicity when vortex lines reconnect, something which is topologically forbidden in an ideal fluid where vortex lines move as material curves. Moreover, variable density or more generally compressibility destroys conservation and weakens the association between helicity and vortex-line topology. Furthermore, in compressible flows, the velocity field is not entirely determined from the vorticity field. A recent paper by Boutros & Gibbon (2025) J. Fluid Mech. in this journal explains how one can extend the definition of helicity to control and limit the non-conservation of helicity. This offers a promising way forward in using helicity to characterise flow properties in computational studies of high Reynolds number flows.

We review some of the processes leading to dispersion and mixing in porous media, exploring the differences between the travel time distribution of fluid particles within a pore throat and between pore throats of different size within the porous layer. A recent paper of Liu et al. (2024) has combined a model of these travel time distributions with a continuous time random walk to quantify the dispersion as a function of the Peclet number. We describe some further problems relating to dispersive mixing of tracer which may be amenable to this approach, including dispersion caused by macroscopic lenses of different permeability, dispersion of tracer which partitions between the fluid and matrix and the effects of buoyancy on mixing.

Using an analogy between elastic and magnetic effects, Lin et al. (J. Fluid Mech., vol. 1000, 2024, R3) use viscoelastic Taylor–Couette flow (TCF) to examine the origin of turbulent mixing in accretion disks. Through direct numerical simulations, the authors find that, unlike the Newtonian case with a similar configuration, turbulence is sustained even at the lowest Reynolds numbers examined and that turbulent mixing is provided through elastic and non-hydrodynamic contributions. By comparing the torque scaling laws obtained with those in magnetized TCF, the authors are able to further support the elastic–magnetic analogy. These findings open new avenues for understanding angular momentum transport and instability mechanisms in both laboratory and astrophysical contexts.

Impact dynamics have long fascinated due to their ubiquity in everyday phenomena, from rain droplets splashing on windscreens to stone-skimming on the surface of the ocean. Impacts are characterized by rapid changes over disparate length scales, which make them expensive or sensitive to capture experimentally and computationally. Here, reduced mathematical models come to the fore, offering a way to get significant physical insight at reduced cost. In this volume, Phillips & Milewski (J. Fluid Mech., 2024) develop a mathematical model allowing for air–water interactions in the low-impact speed regime, in which an impactor bounces or rebounds rather than splashes. Their model offers a reliable way to capture air effects in bouncing, with a range of potential applications including hydrodynamic-quantum analogues and biomimetic water walkers.

The paper by Castaing et al. (J. Fluid Mech., vol. 204, 1989, pp. 1–30) on turbulent Rayleigh–Bénard convection has been one of the most impactful papers on the subject – not by giving the right and complete answers but by developing versatile concepts and by asking the right questions, namely: (i) What is the overall flow organization? (ii) What is the dependence of the Nusselt number ${\textit {Nu}}$ (the dimensionless heat transport) on the Rayleigh number ${\textit {Ra}}$ (the thermal driving strength)? (iii) What is the ultimate state of turbulence for extremely large ${\textit {Ra}}$? Thanks to Castaing et al. having asked the right questions, the field has made tremendous progress over the last 35 years.

The motion of a bubble of negligible viscosity, such as air, forced down a tube filled with a viscous fluid which wets the walls of the tube has become a classic of the fluid dynamical literature. The differential motion of the bubble and the fluid are determined by the thin film which surrounds the bubble, whose shape and thickness are set by the interplay between gradients in surface tension and viscous shear stresses. Bretherton (J. Fluid Mech., vol. 10, issue 2, 1961, p. 166) provided a first, clear mathematical analysis in the lubrication limit coupled with carefully constructed experimental confirmation of the thin films deposited by a bubble moving in the confining geometry of the capillary tube. Its lasting impact has been not only in the migration of bubbles, but in a host of related fluid dynamical, industrial, biological and environmental processes for which thin lubricating films on the sometimes convoluted geometries of complex microstructures, such as porous media, determine the large-scale behaviour.

Since its publication in 2010, the paper by Schmid (J. Fluid Mech., vol. 656, 2010, pp. 5–28) has wielded considerable influence, an impact we examine here. That seminal work introduced dynamic mode decomposition, a method for performing flow-field spectral analysis of snapshot sequences of data. As a data-driven approach aimed at uncovering spatial and temporal patterns or modes within datasets, its applicability has extended far beyond fluid mechanics, reaching into a wide array of fields.

The entrainment hypothesis states that the mean inflow velocity across the boundary of a turbulent flow is proportional to a characteristic velocity of the flow. Proposed by G. I. Taylor approximately 80 years ago, it is still a common model of turbulence closure widely used in environmental engineering and geophysical fluid mechanics. Although it is a very simple concept and mathematical model, it has proven to be able to predict the entrainment in a variety of geophysical flows, e.g. convective clouds and plumes from erupting volcanoes in the atmosphere; dense water overflows and turbidity currents in the ocean; magma injection in a magma chamber in the interior of the Earth, to name just a few. In a seminal paper, Turner (J. Fluid Mech., vol. 173, 1986, pp. 431–471) presents a variety of laboratory and geophysical flows to illustrate the success of the entrainment hypothesis and discusses why such a simple hypothesis works so well even when the original assumptions are no longer valid.

The featured article ‘Break-up of a falling drop containing dispersed particles’ (Nitsche and Batchelor, J. Fluid Mech., 1997, vol. 340, pp. 161–175) is G. K. Batchelor's last published paper with his former postdoctoral associate J. M. Nitsche. The objective of the study was to investigate the randomness of the velocities of interacting rigid particles falling under gravity through a viscous fluid at a small Reynolds number and its consequence for the breakup of a falling cloud of particles. The study focused on a quintessential problem of the collective dynamics of interacting particles and has been an inspiration for subsequent work.

Losses due to wake interactions between wind turbines can significantly reduce the power output of wind farms. The possibility of active flow control by wake deflection downstream of yawed horizontal-axis wind turbines has motivated research on the fluid mechanics involved. We summarize the findings of a wind tunnel study (Bastankhah & Porté-Agel, J. Fluid Mech., vol. 806, 2016, pp. 506–541) of the flow associated with a yawed model wind turbine, and the insights and modelling developments that have followed this important study.

A long-standing issue in pipe flow physics is whether the friction of the fluid follows a logarithmic or an algebraic decay. In 2005, McKeon et al. (J. Fluid Mech., vol. 538, 2005, pp. 429–443) published a detailed analysis of new measurements in the Princeton facility, and apparently settled the debate by showing that ‘the log is the law’. Almost 20 years later, no better data are presently available to reinforce their statement. Still, the story may not be totally over, and this is bad news for mathematicians who were hoping to get a long awaited final answer to one of their most elusive questions.

In recent years, microfluidic systems have underpinned a wealth of biotechnology applications and proposed solutions for complex problems, including the sorting and enrichment of deformable particle suspensions. Motivated by such applications of microfluidic systems, Lu et al. (J. Fluid Mech., vol. 923, 2021, A11) present a three-dimensional computational study of a train of deformable capsules flowing through a branched microchannel. Insights into the intricacies of the underlying complex fluid–structure interactions between the suspended capsules and the surrounding fluid can inform experimental scenarios whereby strong capsule interactions are avoided, facilitating precise operating control of microfluidic devices for sorting and enrichment.

The nanoscale is the new frontier of fluid dynamics and its phenomenology can echo at the macroscale as in the canonical example of drop impact on a planar substrate. Unprecedented advances in measurement technology have recently equipped fluid dynamicists with the ability to probe nanoscale effects. The paper by Li et al. (J. Fluid Mech., vol. 785, 2015, R2) uses ultrafast imaging at the hundreds of nanoseconds scale to resolve the first contact between the drop and the substrate and thereby reveal the effect of prescribed nano-roughness on contact line motion.

Boundary layers are present in many natural and industrial fluid flows. The concept of boundary layers can be traced back to Leonardo da Vinci's paintings of pipe flow, where he was aware of a higher velocity away from the walls. During the 19th century, the physics of boundary conditions had been extensively debated, and the well-known Maxwell–Navier slip length was proposed in 1823. In most cases, the no-slip boundary condition is valid at a fluid–solid interface. However, with the advancement of measurement techniques, slip lengths ranging from nanometre to micrometre scales were experimentally measured, raising questions regarding the applicability of the no-slip condition. In 2003, Lauga & Stone (J. Fluid Mech., vol. 489, 2003, pp. 55–77) proposed a simple model to elucidate the effect of surface heterogeneities on the slip length, elegantly bridging the microscopic structure of the wall-boundary conditions to the macroscopic effective slip length.

In an open channel flow, deviations to the lower topography can induce abrupt changes in the wave height, known as hydraulic jumps. This phenomenon occurs when the flow switches from subcritical to supercritical (or vice versa), and is commonly observed in rivers, flumes and weirs. Theoretical insight is typically sought through the study of reduced models such as the forced Korteweg–de Vries equation, in which previous work has predominantly focused on either stationary formulations or the initial transient behaviour caused by perturbations. In a joint theoretical and numerical study of the free-surface Euler equations, Keeler & Blyth (J. Fluid Mech., vol. 993, 2024, A9) have detected a new class of unsteady solutions to this problem. These emerge from an unstable steady solution, and feature large-amplitude time-periodic ripples emitted from a sudden decrease in the water depth forced by topography, known as a hydraulic fall.

Adding polymers to turbulent Newtonian fluid flows can have dramatic effects. A well-known example is a significant drag reduction by flexible polymers in turbulent wall-bounded flows. In numerical studies of polymer drag reduction, polymers are often modelled as dumbbells of two beads connected by a finitely extensible nonlinear elastic (FENE) spring. There are natural queries whether this highly simplified coarse-grained model is adequate for describing a polymer macromolecule in turbulent flows. By carrying out Eulerian–Lagrangian simulations of polymers, described by different models, in a turbulent pipe flow, Serafini et al. (J. Fluid Mech., vol. 987, 2024, R1) have demonstrated that the FENE dumbbell model can accurately capture polymer extension statistics as compared with the realistic Kuhn chain model. Their work further reveals the surprising result that increasing the number of beads in a FENE chain worsens its accuracy in characterizing polymer spatial conformations at large Weissenberg numbers.