Droplet impingement on a heated substrate is the fundamental process underlying various technologies, ranging from spray cooling to inkjet printing. Understanding the coupled effects of fluid dynamics and heat transfer patterns during droplet jumping, boiling and evaporation, which determine the outcomes of the impingement process, is essential. Here, we developed two-colour planar laser-induced fluorescence and micro-particle image velocimetry technologies to measure quantitatively the velocity and temperature distributions inside the droplet during an impingement process with high temporal and spatial resolution. With our novel measuring system, the hot spots at the solid–liquid interface are discovered for the first time. The influence of contact boiling on the droplet internal mixing, which impedes droplet recoiling and reduces the rebounding velocity, is discussed. A significant enhancement in heat absorption for partially rebounding droplets is discovered, where the impingement heat transfer rate is doubled compared to other vapour-layer-covered droplets. The scaling correlations of viscous dissipation rate and contact time of rebounding droplets, as well as the time variation of droplet temperature rise, are proposed. More detailed patterns inside droplets can be captured by these experimental methods, which will help to reveal more intrinsic mechanisms lying in thermally induced flow, complex fluids and droplet-impacting-based technologies.

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.

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.

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.

The propagation paths of oceanic internal tides are influenced by their interactions with vortices. We examine the scattering effect that an isolated vortex in (cyclo)geostrophic balance has on a rotating shallow-water plane wave. We run a suite of simulations in which we vary the non-dimensional vorticity of the vortex, $Ro$, the relative scale of the vortex size to the Rossby radius of deformation, $Bu$, and the size of the vortex compared with the plane wave wavelength, $K$. We compare the scattered wave flux pattern with ray-tracing predictions. Ray-tracing predictions are relatively insensitive to $K$ in the $1< K<4$ range we investigate; however, they generally underestimate the broad angles of the shallow-water wave scattering patterns, especially for the lower end of the $K$ range. We then measure the ratio of the scattered wave energy flux to the incoming wave energy flux, denoted by $S$, for each simulation. We find that $S$ follows a power law $S \propto (FrK)^2$ when $S < 0.2$, where $Fr = Ro/\sqrt {Bu}$ is the Froude number. When $S>0.2$, it starts plateauing.

The gas dynamics of shock-induced gas filtration through densely packed granular columns with vastly varying shock intensity and the structural parameters are numerically investigated using a coupled Eulerian–Lagrangian approach. The results shed fundamental light on the thermal effects of the shock-induced gas filtration manifested by a distinctive self-heating hot gas layer traversing the medium. The characteristics of the thermal effects in terms of the thermal intensity and uniformity are found to vary with the shock Mach number, Ms, and the filtration coefficient of the granular media, Π. As the incident shock transitions from weak to strong, and (or) the filtration coefficient increases from O(10−5) to O(104), the heating mechanisms transition between three distinct heating modes. A phase diagram of heating modes is established on the parameter space (Ms, Π), which enables us to predict the characteristics of the thermal effect in different shock-induced gas filtrations. The thermal effects markedly accelerate the pressure diffusion due to the additional heat influx when the time scale of the former is smaller than or comparable to the latter. Based on the contour map displaying the coupling degree of the thermal effects and the pressure diffusion, we identify a decoupling criterion whereby the isothermal assumption holds if only the pressure diffusion is concerned. The thermal effects may well bring about considerable thermal shocks which pose a great threat to the integrity of the solid skeleton and further reduce the overall shock resistance performance of the porous media.

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 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.

Low-frequency phenomena in an incompressible pressure-induced laminar separation bubble (LSB) on a flat plate is investigated using direct numerical simulation. The LSB configuration of Spalart and Strelets (J. Fluid Mech., vol. 403, 2000, pp. 329–349) is used. Wall pressure spectra indicate low-frequency-flapping $(St \sim 0.08)$ and high-frequency-shedding $(St \sim 1.52)$ regimes. Conditional velocity averages based on the fraction of reversed flow reveal the low frequency as an expansion/contraction of the LSB. While the high frequency only exhibits exponential growth within the LSB up to breakdown of the spanwise rollers, the low frequency and velocity fluctuations exhibit exponential growth upstream of separation. Instantaneous flow fields reveal large streamwise streaky structures forming within the LSB and extending past reattachment, much like high and low speed streaks in turbulent boundary layers. A predominance of sweep-like events ($Q4$) is observed during contraction and of ejection-like events ($Q2$) during expansion. These motions appear as dominant low-frequency modes in three-dimensional proper orthogonal and dynamic mode decompositions, exhibiting spatial amplification from separation to reattachment. The advection of a group of spanwise alternating streaky structures past the LSB results in an overall contraction after which the bubble expands to its ‘unforced’ state in the absence of the streaks. The low frequency then corresponds to the time it takes for streaks to form, amplify and advect past the LSB from separation to reattachment. This behaviour is linked to the mean flow deformation reported by Marxen and Rist (J. Fluid Mech., vol. 660, 2010, pp. 37–54), where the presence of streaks results in reduced mean bubble size. The formation of these streaky structures, in the absence of free stream turbulence, may be attributed to an absolute instability of the LSB due to the development of a secondary bubble within the primary.

For several applications there are advantages in writing turbulent flow equations in a coordinate frame aligned with the streamlines and several two-dimensional examples of this approach have appeared in the literature. In this paper, we extend this approach to general three-dimensional flows. We find that, in any flow that has a component of its vorticity aligned in the streamline direction, congruences of its streamlines do not form integrable manifolds. This limits the development of a streamline coordinate description of such flows, although some useful results can still be obtained. However, in the case of general three-dimensional complex-lamellar flows, where the mean velocity and mean vorticity are everywhere orthogonal, a complete streamline coordinate description can be derived. Furthermore, we show that general complex-lamellar flows are a good approximation to boundary layers and thin free shear layers. We derive the underlying true coordinate system for such flows, where the orthogonal coordinate surfaces are two stream surfaces and a modified potential surface. From this we obtain physical equations, where flow variables have the same dimensions they would have in a Cartesian coordinate frame. Finally, we show that rational approximations to these equations, which describe small-perturbation flows, contain some terms that have been ignored in previous applications and we detail some practical applications of the theory in modelling and analysis.