The flow behind impulsively started circular and polygonal plates is investigated experimentally, using particle image velocimetry at several azimuthal angles. Observing plates accelerating up to a steady Reynolds number $Re=27\,000$, the three invariants of the motion, circulation $\Gamma$, hydrodynamic impulse $I$ and kinetic energy $E$, were scaled against four candidate lengths: the hydraulic diameter, perimeter, circumscribed diameter and the square root of the area. Of these, the square root of the area was found to best collapse all the data. Investigating the three-dimensionality of the flow, it is found that, while a single-plane measurement can provide a reasonable approximation for $\Gamma$ behind plates, multiple planes are necessary to accurately estimate $E$ and $I$.

From particle lifting in atmospheric boundary layers to dust ingestion in jet engines, the transport and deposition of inertial particles in wall-bounded turbulent flows are prevalent in both nature and industry. Due to triboelectrification during collisions, solid particles often acquire significant charges. However, the impacts of the resulting electrostatic interaction on the particle dynamics remain less understood. In this study, we present four-way coupled simulations to investigate the deposition of charged particles onto a grounded metal substrate through a fully developed turbulent boundary layer. Our numerical method tracks the dynamics of individual particles under the influence of turbulence, electrostatic forces and collisions. We first report a more pronounced near-wall accumulation and an increased wall-normal particle velocity due to particle charging. In addition, contrary to predictions from the classic Eulerian model, the wall-normal transport rate of inertial particles is significantly enhanced by electrostatic forces. A statistical approach is then applied to quantify the contributions from turbophoresis, biased sampling and electrostatic forces. For charged particles, a sharper gradient in wall-normal particle fluctuation velocity is observed, which substantially enhances turbophoresis and serves as the primary driving force of near-wall particle accumulation. Furthermore, charged particles are found to sample upward-moving fluids less frequently than neutral particles, thereby weakening the biased-sampling effect that typically pushes particles away from the wall. Finally, the wall-normal electric field is shown to depend on the competition between particle–wall and particle–particle electrostatic interactions, which helps to identify the dominant electrostatic force across a wide range of scenarios.

Delaying the laminar–turbulent transition of a boundary layer reduces the skin-friction drag and can thereby increase the efficiency of any aerodynamic device. A passive control strategy that has reaped success in transition delay is the introduction of boundary layer streaks. Surface-mounted vortex generators have been found to feature an unstable region right behind the devices, which can be fatal in flow control if transition is triggered, leading to an increase in drag with respect to the reference case without devices. In a previous proof of concept study, numerical simulations were employed to place artificial vortices in the free stream that interact with the boundary layer and accomplish transition delay. In the current study, we present experimental results showing the feasibility of generating free-stream vortices that interact with the boundary layer, creating high- and low-speed boundary layer streaks. This type of streaky base flow can act as stabilizing if introduced properly. We confirm the success of our flow control approach by artificially introducing two-dimensional disturbances that are strongly attenuated in the presence of streaks, leading to a transition delay with respect to the reference case of approximately 40 %.

Wall turbulence consists of various sizes of vortical structures that induce flow circulation around a wide range of closed Eulerian loops. Here we investigate the multiscale properties of circulation around such loops in statistically homogeneous planes parallel to the wall. Using a high-resolution direct numerical simulation database of turbulent channels at Reynolds numbers of $Re_\tau =180$, 550, 1000 and 5200, circulation statistics are obtained in planes at different wall-normal heights. Intermittency of circulation in the planes of the outer flow ($y^+ \gtrsim 0.1Re_\tau$) takes the form of universal bifractality as in homogeneous and isotropic turbulence. The bifractal character simplifies to space-filling character close to the wall, with scaling exponents that are linear in the moment order, and lower than those given by the Kolmogorov paradigm. The probability density functions of circulation are long-tailed in the outer bifractal region, with evidence showing their invariance with respect to the loop aspect ratio, while those in the inner region are closely Gaussian. The unifractality near the wall implies that the circulation there is not intermittent in character.

The aspect ratio effect on side and basal melting in fresh water is systematically investigated across a range of Rayleigh numbers and ambient temperatures using direct numerical simulations. The side mean melt rate follows a ${Ra}^{1/4}\,\gamma ^{-3/8}$ scaling relation in the side-melting dominant regime, where ${Ra}$ is the Rayleigh number, and $\gamma$ is the width-to-height aspect ratio of the ice block. In the basal-melting dominant regime, the basal mean melt rate follows a ${Ra}^{1/4}\gamma ^{3/8}$ scaling relation at low Rayleigh numbers, but transitions to a ${Ra}^{1/3}\gamma ^{1/2}$ scaling relation at higher Rayleigh numbers. This scaling transition is attributed to the formation of a bottom cavity resulting from flow separation at high Rayleigh numbers. The overall mean melt rate exhibits a non-monotonic dependence on the aspect ratio, driven by the competition between side and basal melting. The proposed theoretical model successfully captures the observed non-monotonic behaviour, and accurately predicts the overall mean melt rate over the considered range of Rayleigh numbers and ambient temperatures, especially in the side- and basal-melting dominant regimes. More specifically, the side, basal and overall mean melt rates follow a linear ${St}$ scaling relation for ambient temperatures $T_{w}\geqslant 15^{\,\circ }\textrm {C}$, with ${St}$ being the Stefan number (the ratio between sensible heat and latent heat), but deviations from this scaling relation and a non-monotonic dependence on the ambient temperature are observed at lower ambient temperatures, which can be attributed to the density anomaly effect.

This paper investigates the behaviour of turbulence production in adverse pressure gradient (APG) turbulent boundary layers (TBLs), including the range of pressure gradients from zero-pressure-gradient (ZPG) to separation, moderate and high Reynolds numbers, and equilibrium and non-equilibrium flows. The main focus is on predicting the values and positions of turbulence production peaks. Based on the unique ability of turbulence production to describe energy exchange, the idea that the ratios of the mean flow length scales to the turbulence length scales are locally smallest near peaks is proposed. Thereby, the ratios of length scales are defined for the inner and outer regions, respectively, as well as the ratios of time scales for further consideration of local information. The ratios in the inner region are found to reach the same constant value in different APG TBLs. Like turbulence production in the ZPG TBL, turbulence production in APG TBLs is shown to have a certain invariance of the inner peak. The value and position of the inner peak can also be predicted quantitatively. In contrast, the ratios in the outer region cannot be determined with unique coefficients, which accounts for the different self-similarity properties of the inner and outer regions. The outer time scale ratios establish a link between mean flow and turbulence, thus participating in the discussion on half-power laws. The present results support the existence of a half-power-law region that is not immediately adjacent to the overlapping region.

This article delves into the dynamics of inviscid annular supersonic jets, akin to those exiting converging–diverging nozzles in over-expanded regimes. It focuses on the first azimuthal Fourier mode of flow fluctuations and examines their behaviour with varying mixing layer parameters and expansion regimes. The study reveals that two unstable Kelvin–Helmholtz waves exist in all cases, with the outer-layer wave being more unstable due to differences in the velocity gradient. The inner-layer wave is more sensitive to changes in base flow and extends beyond the jet, potentially contributing to nozzle resonances. The article also investigates upstream propagating guided-jet modes, which are found to be robust and not highly sensitive to changes in base flow, which makes them essential for understanding jet dynamics. A simplified model is used to obtain ideal base flows but with realistic shape in order to study the effects of varying nozzle pressure ratios on the dynamics of the waves supported by the jet.

Droplet coalescence is an essential multiphase flow process in nature and industry. For the inviscid coalescence of two spherical droplets, our experiment shows that the classical 1/2 power-law scaling for equal-size droplets still holds for the unequal-size situation of small size ratios, but it diverges as the size ratio increases. Employing an energy balance analysis, we develop the first theory for asymmetric droplet coalescence, yielding a solution that collapses all experimental data of different size ratios. This confirms the physical relevance of the new set of length and time scales given by the theory. The functionality of the solution reveals an exponential dependence of the bridge’s radial growth on time, implying a scaling-free nature. Nevertheless, the small-time asymptote of the model is able to recover the classical power-law scaling, so that the actual bridge evolution still follows the scaling law asymptotically in a wide parameter space. Further analysis suggests that the scaling-free evolution behaviour emerges only at late coalescence time and large size ratios.

An experimental study is conducted to compare droplet generation in a deep-water plunging breaker in filtered tap water and in the presence of low and high bulk concentrations of the soluble surfactant Triton X-100. The breakers are generated by a programmable wave maker that is set with a single motion profile that produces a highly repeatable dispersively focused two-dimensional (2-D) wave packet with a central wavelength of $\lambda _0=1.18\,\rm m$. The droplets are measured with an in-line cinematic holographic system. It is found that the presence of surfactants significantly modifies the overall droplet number and the distributions of droplet diameter and velocity components produced by the four main droplet producing mechanisms of the breaker as identified by Erinin et al. ( J. Fluid Mech., vol. 967, 2023, p. A36). These modifications are due to both surfactant-induced changes in the flow structures that generate droplets and changes in the details of droplet production mechanisms in each flow structure.

Thermo-responsive hydrogels are smart materials that rapidly switch between hydrophilic (swollen) and hydrophobic (shrunken) states when heated past a threshold temperature, resulting in order-of-magnitude changes in gel volume. Modelling the dynamics of this switch is notoriously difficult and typically involves fitting a large number of microscopic material parameters to experimental data. In this paper, we present and validate an intuitive, macroscopic description of responsive gel dynamics and use it to explore the shrinking, swelling and pumping of responsive hydrogel displacement pumps for microfluidic devices. We finish with a discussion on how such tubular structures may be used to speed up the response times of larger hydrogel smart actuators and unlock new possibilities for dynamic shape change.

Bubble bursting and subsequent collapse of the open cavity at free surfaces of contaminated liquids can generate aerosol droplets, facilitating pathogen transport. After film rupture, capillary waves focus at the cavity base, potentially generating fast Worthington jets that are responsible for ejecting the droplets away from the source. While extensively studied for Newtonian fluids, the influence of non-Newtonian rheology on this process remains poorly understood. Here, we employ direct numerical simulations to investigate the bubble cavity collapse in viscoelastic media, such as polymeric liquids. We find that the jet and drop formations are dictated by two dimensionless parameters: the elastocapillary number $Ec$ (the ratio of the elastic modulus and the Laplace pressure) and the Deborah number $De$ (the ratio of the relaxation time and the inertio-capillary time scale). We show that, for low values of $Ec$ and $De$, the viscoelastic liquid adopts a Newtonian-like behaviour, where the dynamics is governed by the solvent Ohnesorge number $Oh_s$ (the ratio of visco-capillary and inertio-capillary time scales). In contrast, for large values $Ec$ and $De$, the enhanced elastic stresses completely suppress the formation of the jet. For some cases with intermediate values of $Ec$ and $De$, smaller droplets are produced compared with Newtonian fluids, potentially enhancing aerosol dispersal. By mapping the phase space spanned by $Ec$, $De$ and $Oh_s$, we reveal three distinct flow regimes: (i) jets forming droplets, (ii) jets without droplet formation and (iii) absence of jet formation. Our results elucidate the mechanisms underlying aerosol suppression versus fine spray formation in polymeric liquids, with implications for pathogen transmission and industrial processes involving viscoelastic fluids.

The Cahn–Hilliard–Navier–Stokes (CHNS) partial differential equations (PDEs) provide a powerful framework for the study of the statistical mechanics and fluid dynamics of multiphase fluids. We provide an introduction to the equilibrium and non-equilibrium statistical mechanics of systems in which coexisting phases, distinguished from each other by scalar order parameters, are separated by an interface. We then introduce the coupled CHNS PDEs for two immiscible fluids and generalisations for (i) coexisting phases with different viscosities, (ii) CHNS with gravity, (iii) three-component fluids and (iv) the CHNS for active fluids. We discuss mathematical issues of the regularity of solutions of the CHNS PDEs. Finally we provide a survey of the rich variety of results that have been obtained by numerical studies of CHNS-type PDEs for diverse systems, including bubbles in turbulent flows, antibubbles, droplet and liquid-lens mergers, turbulence in the active-CHNS model and its generalisation that can lead to a self-propelled droplet.