Inkjet printing, originally invented for text and pattern printing, is now central to many industrial applications, such as printed electronics, flexible electronics, 3-D printing of mechanical and even biological devices. However, constrained by the droplets’ ejection mechanism, the accuracy of traditional inkjet printing is limited by the size of its orifice, and it is difficult to achieve a volume of droplets at the femtolitre scale, which hinders its further application in the above fields. To this end, we propose the confined interface vibration inkjet printing (CIVIJP) technique, which is capable of printing patterns in a liquid environment with droplet size much smaller than the orifice from which they are dispensed. Here, further systematic study of the mechanism of printing in a liquid environment was carried out with the assistance of a high-speed imaging technique. It is found for the first time that a single pulse stimulation applied on the piezo-ceramic of the inkjet nozzle can trigger damping oscillations of the oil/water interface confined by the orifice, which can last more than 500 $\mathrm {\mu }$s. By adjusting the intensity of single pulse stimulation, the size and quantity of the dispensed droplets can be controlled in a wide range, which is obviously different from traditional droplet ejection in a gaseous environment. This work reveals the underlying physics between the pulse stimulation and the interface behaviours, as well as the physics between the interface behaviours and the size and number of dispensed droplets, enriching the fundamental theory of the inkjet printing in liquid phase.

Wave forecasting in ocean and coastal waters commonly relies on spectral models based on the spectral action balance equation. These models assume that different wave components are statistically independent and as a consequence cannot resolve wave interference due to statistical correlation between crossing waves, as may be found in, for instance, a focal zone. This study proposes a statistical model for the evolution of wave fields over non-uniform currents and bathymetry that retains the information on the correlation between different wave components. To this end, the quasi-coherent model (Smit & Janssen, J. Phys. Oceanogr., vol. 43, 2013, pp. 1741–1758) is extended to allow for wave–current interactions. The outcome is a generalized action balance model that predicts the evolution of the wave statistics over variable media, while preserving the effect of wave interferences. Two classical examples of wave–current interaction are considered to demonstrate the statistical contribution of wave interferences: (1) swell field propagation over a jet-like current and (2) the interaction of swell waves with a vortex ring. In both examples cross-correlation terms lead to development of prominent interference structures, which significantly change the wave statistics. Comparison with results of the SWAN model demonstrates that retention of cross-correlation terms is essential for accurate prediction of wave statistics in shear-current-induced focal zones.

We investigate scalings of turbulence dissipation and turbulence length/time scales in the fully developed turbulent channel flow region of wall distances $y$ where the ratio of turbulence production to turbulence dissipation oscillates close to 1. First, we study averages over both time and wall-parallel streamwise ($x$) and spanwise ($z$) planes at $y$. Turbulent channel flow data with friction velocity $u_{\tau }$, and global Reynolds number $Re_{\tau }$ ranging from $550$ to $5200$, suggest that the integral length scales of streamwise fluctuating velocities along the streamwise direction, and of wall-normal fluctuating velocities along the transverse direction, tend towards scaling with $y$, and that the respective turbulence dissipation coefficients tend towards being constant with increasing $Re_{\tau }$. However, the data for integral lengths of transverse fluctuating velocities in the transverse direction suggest that these lengths obey an asymptotic scaling $\sqrt {\delta y}$ (where $\delta$ is the channel half-width) with increasing $Re_{\tau }$. The corresponding turbulence dissipation's scaling seems to tend towards $\sqrt {Re_{\tau }}/Re_{\lambda }$, which is reminiscent of the non-equilibrium turbulence dissipation scaling found in boundary-free turbulent flows, $Re_{\lambda }$ being a $y$-local Taylor-length-based Reynolds number. The data do not exclude minor corrections from these asymptotic scalings, and in fact, suggest finite Reynolds number deviations to them. Second, we remove time averaging and study time-fluctuating averages over wall-parallel planes at $y$. We find that the time fluctuations of the turbulence dissipation coefficients and the Taylor-length-based Reynolds number are very strongly anti-correlated at all wall distances $y$ considered, reflecting a dominance of turbulent kinetic energy fluctuations at the lower frequencies, but a dominance of both turbulent kinetic energy and turbulence dissipation at the higher frequencies. In the case of the turbulence dissipation coefficient corresponding to the integral length of the wall-normal velocity along the transverse direction, it is possible to determine the cross-over frequency $f_c^*$ between these two behaviours, and we find $f_c^{*}\sim u_{\tau }/y$ for $Re_{\tau } = 950$, but $f_c^* \sim u_{\tau }/\delta$ for $Re_{\tau }=2000$, where there is evidence of very-large-scale motions.

The extreme mobility of droplets on non-wetting materials implies the necessity of controlling their motion, direction or speed. In this paper, we show how ridges allow us to tune drop friction. Depending on the liquid speed and viscosity, two regimes emerge: fast drops with low viscosity dynamically deform and undergo inertial friction, so that their velocity is eventually fixed by the deformations induced by the ridges; in contrast, viscous drops hardly interact with the texture, so that their velocity is classically limited by viscous dissipation, as on a flat substrate. The transition between these two regimes reveals spectacular morphological changes: drops with intermediate viscosity elongate and adopt worm-like shapes, which we qualitatively describe.

The motion of glaciers over their bedrock or drops of fluid along a solid surface can vary dramatically when these substrates are lubricated. We investigate the coupled flow of a gravity current (GC) of a strain-rate softening fluid that is lubricated by a denser, lower-viscosity Newtonian fluid. We present a set of experiments in which such GCs are discharged axisymmetrically and at constant flux over a flat surface. Using imaging techniques, we follow the evolution of the front and thickness field of each fluid. We find that, unlike purely Newtonian lubricated GCs, the fronts of the non-Newtonian and lubricating Newtonian fluids have a power-law time evolution with different exponents. Each of these exponents is similar to that of a non-lubricated GC of the same fluid. Nevertheless, the fronts of our lubricated GCs evolve faster than those of the corresponding non-lubricated GCs owing to larger intercepts. In addition, in contrast with the monotonically declining thickness of non-lubricated GCs, the thickness of the lubricated, non-Newtonian fluid is nearly uniform, and that of the lubricating fluid is non-monotonic with localised spikes. Despite these complex thickness patterns, lubricated GCs remain axisymmetric as long as the flux of the lubricating fluid is sufficiently smaller than that of the non-Newtonian fluid.

Internal waves shoaling on the continental slope can break and form materially coherent vortices called boluses. These boluses are able to trap and transport material up the continental slope, yet the global extent of bolus transport is unknown. Previous studies of bolus formation primarily focused on systems consisting of two layers of uniform density, which do not account for the presence of ocean pycnoclines of finite thickness. We use hyperbolic tangent profiles to model the density stratification in our simulations and demonstrate the impact of the pycnocline on the bolus. A spectral clustering method is used to objectively identify the bolus as a Lagrangian coherent structure that contains the material advected upslope. The bolus size and displacement upslope are examined as a function of the pycnocline thickness, incoming wave energy, density change across the pycnocline and topographic slope. The dependence of bolus transport on the pycnocline thickness demonstrates that boluses in continuous stratifications tend to be larger and transport material further than in corresponding two-layer stratifications.

The inverse Leidenfrost regime occurs when a heated object in relative motion with a liquid is surrounded by a stable vapour layer, drastically reducing the hydrodynamic drag at large Reynolds numbers due to a delayed separation of the flow. To elucidate the physical mechanisms that control separation, here we report a numerical study of the boundary layer equations describing the liquid–vapour flow around a solid sphere whose surface temperature is above the Leidenfrost point. Our analysis reveals that the dynamics of the thin layer of vaporised liquid controls the downstream evolution of the flow, which cannot be properly described substituting the vapour layer by an effective slip length. In particular, the dominant mechanism responsible for the separation of the flow is the onset of vapour recirculation caused by the adverse pressure gradient in the rearward half of the sphere, leading to an explosive growth of the vapour-layer thickness due to the accumulation of vapour mass. Buoyancy forces are shown to have an important effect on the onset of recirculation, and thus on the separation angle. Our results compare favourably with previous experiments.

Using numerical simulations, we investigate the near-field temporal variability of axisymmetric helium plumes as a function of inlet-based Richardson (${Ri}_0$) and Reynolds (${Re}_0$) numbers. Previous studies have shown that ${Ri}_0$ plays a leading-order role in determining the frequency at which large-scale vortices are produced (commonly called the ‘puffing’ frequency). By contrast, ${Re}_0$ dictates the strength of localized gradients, which are important during the transition from laminar to turbulent flow. The simulations presented here span a range of ${Ri}_0$ and ${Re}_0$, and use adaptive mesh refinement to achieve high spatial resolutions. We find that as ${Re}_0$ increases for a given ${Ri}_0$, the puffing motion undergoes a transition at a critical ${Re}_0$, marking the onset of chaotic dynamics. Moreover, the critical ${Re}_0$ decreases as ${Ri}_0$ increases. When the puffing instability is non-chaotic, time series of different variables are well-correlated, exhibiting only modest changes in the dynamics (including period doubling and flapping). Once the flow becomes chaotic, denser ambient fluid penetrates the core of the plume, similar to penetrating ‘spikes’ formed by Rayleigh–Taylor instabilities, leading to only moderately correlated flow variables. These changes result in a non-trivial dependence of the puffing frequency on ${Re}_0$. Specifically, at sufficiently low ${Re}_0$, the puffing frequency falls below the prediction from Wimer et al. (J. Fluid Mech., vol. 895, 2020). As ${Re}_0$ increases beyond the critical ${Re}_0$, the puffing frequency increases and then drops back down to the predicted scaling. The dependence of the puffing frequency on ${Re}_0$ provides a possible explanation for previously observed changes in the scaling of the puffing frequency for high ${Ri}_0$.

The influence of a horizontal wall on the evolution of the long-wave instability in equal strength counter-rotating vortex pairs is studied with direct numerical simulation. The two vortices descend under mutual induction and interact with a ground plane, as would aircraft trailing vortices in ground effect. Both the linear and nonlinear development of the pair is studied for three initial heights above the wall, representative of three modes of interaction identified by experiment. A study of two vortex core sizes over a range of Reynolds numbers ($1000\leqslant Re\leqslant 2500$) is used to verify parameter independence. The vortex system undergoes complex topological changes in the presence of a wall, with the separation of wall generated vorticity into hairpin-like vortex tongues and axial flow development in the primary pair. The secondary structures are rotated and stretched around the primary vortices, strongly influencing the resultant flow evolution and are comparable with those observed for oblique ring–wall interaction. Of the three modes, the small-amplitude mode shows the formation of four principal tongues per long wavelength of the Crow instability, with the secondary vortex remaining connected. The large-amplitude mode undergoes a re-connective process to form two non-planar secondary vortex structures per wavelength, and a simulation of the large ring mode in its first formation develops six tongues per wavelength. These secondary structures ‘rebound’ from the wall and interact at the symmetry plane prior to dissipation, governing the bending, stretching and trajectory of the primary vortex pair.

We study the decay of compressible magnetohydrodynamic (MHD) turbulence, emphasizing exchanges of energy between compressive and incompressive kinetic energies, magnetic energy, and thermal energy. A recently developed high order finite difference code is employed for compressible runs with a Mach number up to 2. Varying the nature of the initial conditions (magnitudes of velocity and magnetic fluctuations), and initial Mach numbers permits examination of various dynamical regimes characterized here by the changes between different energy reservoirs. Acoustic waves are responsible for the oscillatory exchange between compressive kinetic and thermal energy through the pressure dilatation term. The results indicate that exchange between kinetic and magnetic energy is dominated by interactions involving the solenoidal velocity. Several systematic rapid adjustments are found to be reproducible with simple scalings derived from the empirical data.

Three-dimensional simulations are performed to investigate swimming and prey capture by a paddling jellyfish. First, the three-dimensional vortex–vortex and vortex–body interactions are revealed, as the jellyfish swims forwards through several cycles of active muscle contraction followed by passive energy recapture via shape recovery. For varied transient paddling force and paddling frequency, we analyse the resultant changes of a jellyfish's swimming speed, interactive power, cost of transport and prey clearance rate. The pressure field around the periodically deformed elastic bell and the circulation generated by starting and stopping vortex rings are presented in greater detail to better understand the biophysical interactions that support swimming. Second, to reveal prey-specific interception and feeding behaviour, using a dynamical-system-based approach and modified Maxey–Riley equation, we compute the trajectories of the surrounding infinitesimal, inertial, opposite and normally escaping prey or plankton that hover around the medusa and are swept differently via the paddling-created velocity field. Accordingly, the diverse prey trajectories are obtained with varied paddling force, resonant driving of the elastic bell and for two different bell fineness ratios. These trajectories are then used to compute the finite-time Lyapunov exponent fields and identify particle Lagrangian coherent structures for various motile/strategically evasive prey, for five swimming cycles. The detected geometric separatrices unambiguously map and demarcate differently driven upstream fluid regions of a medusa and illustrate precisely from where an intercepted prey can be brought into the jellyfish bell, or safely stored in a capture region for ingestion, and from where a prey will surely escape. Hereby, for the first time, the prey-specific target regions, the physically well-defined three-dimensional capture surfaces and the generated cycle-to-cycle prey clearance rate are presented/analysed like never before, which provide a significantly advanced understanding on diverse predator–prey interactions and resultant success rate in prey capture. Several supplementary movies that show detailed fluid–structure interactions, transient entrainment of the floating prey and eventual prey confinement inside a secured capture surface are provided for two different jellyfish morphologies (fineness ratios 0.3 and 0.5) that help to better comprehend the natural prey encounter and hunting processes.

The motion of a long gas bubble in a confined capillary tube is ubiquitous in a wide range of engineering and biological applications. While the understanding of the deposited thin viscous film near the tube wall in Newtonian fluids is well developed, the deposition dynamics in commonly encountered non-Newtonian fluids remains much less studied. Here, we investigate the dynamics of a confined bubble moving in shear-thinning fluids with systematic experiments, varying the zero-shear-rate capillary number $Ca_0$ in the range of $O(10^{-3}\unicode{x2013}10^2)$ considering the zero-shear-rate viscosity. The thickness of the deposited liquid film, the bubble speed and the bubble front/rear menisci are measured, which are further rationalized with the recent theoretical studies based on appropriate rheological models. Compared with Newtonian fluids, the film thickness decreases for both the carboxymethyl cellulose and Carbopol solutions when the shear-thinning effect dominates. We show that the film thickness follows the scaling law from Aussillous & Quéré (Phys. Fluids, vol. 12, no. 10, 2000, pp. 2367–2371) with an effective capillary number $Ca_e$, considering the characteristic shear rate in the film as proposed by Picchi et al. (J. Fluid Mech., vol. 918, no. A7, 2021, pp. 1–30). $Ca_e$ is calculated by the Carreau number and the power-law index from the Carreau–Yasuda rheological model. The shear-thinning effect also influences the bubble speed and delays the transition to the parabolic region in the bubble front and rear menisci. In particular, a high degree of undulations on the bubble surface results in an intricate rear viscosity distribution for the rear meniscus and the deviation between the experiments and theory may require a further investigation to resolve the axial velocity field. Our study may advance the fundamental understandings and engineering guidelines for coating processes involving thin-film flows and non-Newtonian fluids.