This study elucidates the influence of liquid viscosity on the hydrodynamics of simultaneous and non-simultaneous droplet-pair impacts on solid substrates. Using synchronised high-speed imaging and quantitative analysis, the spreading dynamics of droplet lamellae and their interaction-driven central sheet evolution are examined across a range of viscosities from 1.01 to 91.46 mPa s, representing Ohnesorge numbers of 0.002–0.177, under controlled impact Weber numbers in the range of 81–131 and dimensionless inter-droplet spacings in the range of 1.43–1.85. The findings reveal that increasing viscosity results in thicker lamella fronts, reduced spreading and a lower maximum central sheet height. In addition, the central sheet morphology transitions from ‘semilunar’ sheets to ephemeral liquid bumps, accompanied by suppressed capillary waves and reduced rim instabilities. A novel scaling law is derived for the maximum sheet extension, demonstrating its robust applicability to both simultaneous and non-simultaneous impacts of droplet pairs across varying viscosities and impact conditions. Furthermore, distinct morphological differences emerge between simultaneous and non-simultaneous impacts, primarily governed by lamella–lamella interactions and the momentum transfer dynamics. These findings enhance our understanding of the interplay between viscous and inertial forces in droplet-pair impacts, offering valuable insights for optimising spray-based technologies and multiphase fluid systems.

The active-layer model used to account for mixed-size sediment morphodynamic processes may be ill-posed under certain circumstances. Well-posedness guarantees the existence of a unique solution continuously depending on the problem data. When a model becomes ill-posed, infinitesimal perturbations to a solution grow infinitely fast. Apart from the fact that this behaviour cannot represent a physical process, numerical simulations of an ill-posed model continue to change as the grid is refined. For this reason, ill-posed models cannot be used as predictive tools. There exists a regularisation strategy based on a preconditioning method that guarantees that the one-dimensional active-layer model is well-posed. Here, we show that the extension of this strategy to two dimensions does not regularise the model and we propose a different regularisation strategy based on diffusion that guarantees that both the one-dimensional and two-dimensional active-layer models are well-posed. We implement the strategy in Delft3D Flexible Mesh and show an application.

This study investigates convection in a non-isothermal spherical Taylor–Couette flow (sTC) under the influence of the dielectrophoretic (DEP) force. The convective flow is driven by differential rotation of the inner and outer boundaries rotating with $\varOmega$ and $\Delta {\varOmega }$ in combination of an electric tension applied between both shells to induce thermo-electrohydrodynamic (TEHD) convection. To understand the interaction between DEP force-driven and rotation-driven mechanisms, we first analysed TEHD convection and non-isothermal sTC flow independently. For the TEHD case, we establish scaling relations for heat transport by expressing the Nusselt number, ${\textit{Nu}}$, as a function of the electric Rayleigh number, ${\textit{Ra}}_{{E}}$, and the kinetic energy density, $\tilde {E}_k$. These relations are evaluated against classical models of convection to assess consistency and deviations. A similar approach was applied to the non-isothermal sTC flow in the absence of the DEP force, where we identified axisymmetric and non-axisymmetric flow regimes which were classified by ${\textit{Nu}}$, $\tilde {E}_k$ and $\Delta {\varOmega }$, and developed corresponding scaling relations. When both mechanisms were active, ${\textit{Nu}}$ generally increased, however, the DEP force locally suppressed angular momentum transport, especially near the equator. This interplay revealed three distinct regimes: (A) DEP force-dominated TEHD convection, (C) rotation-dominated non-isothermal sTC flow and (B) a transitional regime with reduced heat transport. A decomposition of a derived inflow Nusselt number, ${\textit{Nu}}^q$, based on conductive and convective contributions, further elucidated the underlying heat transport mechanism.

Dispersion in turbulent flows is of broad interest in engineering and environmental processes, particularly for rivers, lakes and oceanic water bodies. Based on our streamwise dispersion model grounded in a Lagrangian perspective of convection–diffusion dynamics (Guan & Chen, 2024, J. Fluid Mech., vol. 980, A33), this work presents a comprehensive solution that consistently unifies dispersion across the Reynolds number spectrum, bridging laminar and turbulent regimes. The streamwise dispersion mechanism is general across time scales, yet its statistical behaviour cannot be fully described using conventional coarse-grained moments averaged over cross-sections. While classical drift–diffusion models that are effective for long-time asymptotics fail to capture the turbulent dynamics of the pre-asymptotic phase, our analytical model enables a complete spatio-temporal characterisation of concentration, and reveals how local statistics evolve towards their asymptotic, coarse-grained limits. Through asymptotic expansions and eigenfunction analysis, we quantify the time-dependent behaviour of phenomenological dispersion coefficients, and distinguish between local and mean statistics, which diverge significantly during the pre-asymptotic phase. The early regime exhibits robust features, including an overshoot in local dispersivity, asymmetric long tails in mean concentration, and island-shaped solute accumulation near the free surface. Three regimes are identified in the evolution of the local concentration: (i) an initially uniform line source, (ii) a transitional logarithmic profile shaped by vertical shear, and (iii) an emergent Gaussian dispersion regime approaching vertical uniformity. Comparisons of both local and mean concentration demonstrate quantitative agreement with finite difference and Monte Carlo simulations across all regimes. These findings clarify the interplay between shear and turbulent diffusion, laying a foundation for addressing more intricate and physically significant transport problems.

In a previous study, we have proposed a mechanism for simultaneous reduction of drag and lift by half-rotation at moderately low Reynolds numbers. The axis of rotation ($z$) is perpendicular to both the drag ($x$) and lift ($y$) directions, i.e. the rotation is transverse to the incoming flow direction. Under laminar flow conditions, force-element analysis indicates that a partially rotating sphere can significantly reduce both drag and lift with suppression of vortex shedding. This study extends investigation of the same mechanism of half-rotating a sphere to the turbulence regime at a Reynolds number $Re = 1 \times 10^4$. Similar to the laminar case, half-rotation of the sphere introduces a significant negative velocity drag term, which effectively counteracts the rapid increase in the volume- and surface-vorticity drag terms. Numerical simulations with delayed detached eddy simulation, aided by direct numerical simulation, show that the drag coefficient decreases monotonically with increasing the non-dimensional rotational speed $\alpha$, even becoming negative at $\alpha =10$, while the lift and side-force coefficients remain small for all $\alpha$. However, in contrast to laminar conditions, the turbulent regime is characterised by an earlier onset of shear-layer instabilities, which accelerates the transition of the wake into a fully turbulent state. The relative importance of volume- and surface-vorticity contributions to the drag and lift is the most outstanding difference between the laminar and turbulent flows. In turbulent flow, simultaneous reduction of drag and lift is more pronounced as the contributions of volume- and surface-vorticity lift terms almost cancel each other exactly. These mechanisms and characteristics are systematically compared with those observed in the flow around a fully rotating sphere at the same Reynolds number in terms of vorticity structures, force elements, pressure distributions as well as surface-vorticity distributions.

The anomalous scaling of passive scalar fluctuations is experimentally investigated in turbulent pipe flow with a Taylor-microscale Péclet number of $\mathcal{O}(10^5)$, where the turbulence is known to deviate from the homogeneous isotropic turbulence. The scalar structure functions and intermittency in the mixing are examined. The experimental results consolidate that the scaling exponents of scalar structure functions saturate at high-order even moments, evidenced previously in homogeneous isotropic turbulence with a Taylor-microscale Péclet number of $\mathcal{O}(10^3)$. The saturation scaling exponent decreases to approach unity as the Taylor-microscale Péclet number increases. This saturation scaling exponent is further corroborated by the fractal codimension of sharp scalar fronts.

An experimental study is conducted investigating the characteristics of tones due to ‘guided jet waves’ in the forward arc of jet noise radiation fields. These spectral peaks disappear in the far acoustic field in the aft and sideline directions, which is why they went unnoticed in decades of jet noise measurements. However, it is clearly shown in the present study that they radiate in the forward arc (shallow upstream polar locations in the approximate range θ < 45°). Jet noise spectra in the forward arc, data on which had been lacking in the literature, are not smooth but are characterised by these peaks. This is found for high subsonic to supersonic jets up to the highest jet Mach number covered in the experiment (MJ ≈ 1.9), for round and rectangular as well as convergent–divergent nozzles. In heated jets, these spectral peaks appear to get weakened especially around transonic conditions, whereas they clearly persist in supersonic conditions.

Elastoviscoplastic (EVP) fluids, characterised by the coexistence of elastic, viscous and yield-stress properties, play a central role in diverse applications, including drug delivery, 3D printing and hydraulic fracturing. These fluids often transport non-spherical particles whose migration dynamics strongly influences flow behaviour. In this work, we employ interface-resolved direct numerical simulations to investigate the migration and orientation dynamics of finite-size spheroidal particles suspended in EVP duct flows across a wide range of governing parameters. Our results show that the equilibrium position and orientation of the particles are influenced significantly by both their aspect ratio and the carrier fluid rheology. In Saramito fluids, spheroidal particles migrate towards the duct centre and align along the duct diagonals in the presence of inertia. At sufficiently high elasticity, they penetrate the central plug and reach the duct core, irrespective of their initial position or shape. At lower elasticities, where larger plug regions persist, interactions with the plug alter the angular dynamics of the particles, leading to unsteady, quasi-periodic tumbling and spinning motions. In contrast, in Saramito–Giesekus fluids, the interplay between inertial forces, shear-thinning plastic viscosity and yield stress drives particles towards the duct corners, aligning them perpendicular to the duct diagonals. In semi-dilute suspensions, flattened particles maintain a greater distance from the walls, whereas their spherical counterparts tend to cluster directly at the corners. These findings reveal complex migration and orientation behaviours unique to EVP media and suggest new opportunities for geometry-based particle separation in microfluidic applications.

The nonlinear evolution of free-stream vortical disturbances entrained in the entrance region of a channel is investigated using asymptotic and numerical methods, building on the linear framework developed by Ricco & Alvarenga (2021 J. Fluid Mech., vol. 927, A18). The focus is on low-frequency disturbances that induce streamwise-elongated structures at Reynolds numbers for which the entrance flow is locally stable according to classical linear stability theory. The perturbation flow along the channel entrance is generated by free-stream vortical disturbances located at the channel inlet. These disturbances are symmetric or antisymmetric with respect to the centreplane and their amplitude is sufficiently intense to provoke nonlinear interactions within the channel. The formation and evolution of the perturbation flow are described by the nonlinear unsteady boundary-region equations. Combined with physically realistic initial conditions, the resulting initial-boundary-value problems are solved numerically using a streamwise integration method. A parametric study is conducted to elucidate how the nonlinear channel flow is influenced by the Reynolds number and the inlet-disturbance properties, i.e. the amplitude and the streamwise, wall-normal and spanwise wavelengths. Nonlinearity is found to stabilise the intense algebraic growth and to drive the formation of elongated channel-entrance structures that span the entire cross-section. These structures, characterised by low- and high-speed regions and streamwise vortices, meander along the streamwise direction and persist even when the base flow is fully developed. They exhibit a half-turn rotational symmetry with respect to the vortex centres. These properties emerge downstream regardless of the symmetry of the initial perturbation flow, provided nonlinear interactions are sufficiently intense. The occurrence of travelling waves is detected sufficiently downstream, and their similarity to those found in the fully developed region by other researchers is discussed. Our results show good agreement with theoretical predictions, numerical results and experimental measurements for both the mean flow and the perturbation flow.

The present work numerically investigates the dynamics of inclined thin flexible plates in oscillatory flows to assess the effects of bending stiffness, wave orbital excursion and inclination angle on plate deflection, reconfiguration, drag force and energy conversion. Four distinct structural response modes are identified, together with their transition conditions. An analytical expression for the lift coefficient of inclined rigid plates in the oscillatory flow is derived. By combining the drag and lift coefficients, we propose a modified Cauchy number, which quantitatively reveals the inclination effect from both geometric and mechanical perspectives. The dynamic behaviours of the plate deflection can be separated into two states. In the fully reconfigured state, a balance is achieved between elastic restoring force and hydrodynamics-driven force. Based on moment and energy balance, we derive a scaling law incorporating the modified Cauchy number, which accurately predicts the variation of tip deflection. In the passive movement state, the flexible plate moves passively along the flow, and its tip deflection saturates to the order of wave orbital excursions. A pronounced drag reduction is induced by the plate reconfiguration, following a $-1$ scaling law with a combined parameter, which is explained by the model of effective plate length. The energy conversion from fluid kinetic energy to structural elastic strain energy first increases and then decreases with increasing flexibility, yielding an optimal energy conversion efficiency. The modified Cauchy-number-based scaling law accurately predicts the averaged elastic energy growth and critical conditions for optimal energy conversion through a time scale competition mechanism.

Birds extend their flight envelope and adapt to time-varying aerodynamic demands by actuating the shoulder and wrist joints to morph the local sweep angles of the inner and outer wings. However, the local sweep morphing may cause unfavourable unsteady lift on the lifting surface. We investigate these unsteady lift responses using an avian-inspired wing with local sweep morphing under different morphing strategies. The unsteady lift is computed through numerically solving the incompressible Navier–Stokes equations. The results show that the local sweep morphing wing experiences a substantial maximum lift overshoot when forward sweeping and a notable maximum lift undershoot when backward sweeping. These lift over/undershoot phenomena can be alleviated by three measures: adopting smooth nonlinear morphing kinematics, initiating morphing from lift extrema opposite to the over/undershoot direction and prolonging the morphing duration. For the lift over/undershoot, the component obtained by subtracting the extended pre-morphing lift is attributed to the modification induced by local sweep morphing. To predict such lift over/undershoot, we develop a reduced-order unsteady model for the sweeping-modification lift coefficient, where Prandtl’s lifting-line theory is extended to the regime of variable translational velocity. The proposed model captures the symmetry of the sweeping-modification lift coefficient, dominated by the horizontal morphing velocity. Additionally, the vertical morphing velocity is found to correlate with the asymmetry of the sweeping-modification lift coefficient by modulating the leading-edge vortices. This study is expected to improve the understanding of surging-wing flow physics and support the design of bio-inspired multifunctional aircraft.

Variational data assimilation and machine-learning based super-resolution are two alternative approaches to state estimation in turbulent flows. The former is an optimisation problem featuring a time series of coarse observations, the latter usually requires a library of high-resolution ‘ground truth’ data. We show that the classic ‘4DVar’ data assimilation algorithm can be used to train neural networks for super-resolution in three-dimensional isotropic turbulence without the need for high-resolution reference data. To do this, we adapt a pseudo-spectral version of the fully differentiable JAX-CFD solver (Kochkov et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 21, 2021, e2101784118) to three-dimensional flows and combine it with a convolutional neural network for super-resolution. As a result, we are able to include entire trajectories in our loss function, which is minimised with gradient-based optimisation to define the neural network weights. We show that the resulting neural networks outperform 4DVar for state estimation at initial time over a wide variety of metrics, though 4DVar leads to more robust predictions towards the end of its assimilation window. We also present a hybrid approach in which the trained neural network output is used to initialise 4DVar. The resulting performance is more than twice as accurate as other state estimation strategies for all times and performs well even beyond known limiting length scales, all without requiring access to high-resolution measurements at any point.

Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent, capturing the shear layer. The Oldroyd-B model discretised with Chebyshev polynomials is employed, and energy budget analysis is used to interpret underlying mechanisms. At low Weber numbers, the jet evolves axisymmetrically and the instability is governed by interfacial gas-pressure fluctuations; as the Weber number increases, the growing inertia drives a transition of the predominant mode from axisymmetric to helical. At weak elasticity, the instability is also primarily governed by gas-pressure fluctuations. As elasticity increases, the predominant mode transitions from axisymmetric to helical. This transition is accompanied by a migration of disturbance structures from the interface toward the jet interior and an enhanced coupling between velocity perturbation and the basic flow. These trends reveal a new predominant instability mechanism – the elasticity-enhanced shear-driven instability – which is distinct from capillary or Kelvin–Helmholtz instabilities in Newtonian jets. A $\textit{We}$–$El$ phase diagram delineates the boundary between predominant modes and experimental results obtained in a flow-focusing configuration validate the theoretical predictions. Compared with temporal stability results, the spatial framework – by directly resolving the convective downstream amplification of disturbances – achieves quantitative agreement with experiments and highlights the superiority of spatial instability analysis in capturing the dynamics of strongly convective, non-parallel jet flows. These findings provide mechanistic insight into viscoelastic jet instabilities and offer guidance for applications involving droplet and fibre formation in co-flow systems.

Camassa et al. (J. Fluid Mech. 745, 2014, 682–715) demonstrated excellent agreement between the theoretical predictions using the longwave equation and experimental observations for the absolute instability-induced plug formation in the gravity-driven flow of a liquid coating the inner surface of a tube. A similar flow of airway surface liquid (ASL) exists in the proximal airways, driven by the turbulent airflow in addition to gravity. Motivated by the conclusions of previous studies, we probe for the existence of absolute instability in the proximal airways in the present study to determine plug formation and subsequent airway closure by considering ASL elasticity, cylindrical flow geometry and the effect of inhaled air temperature. To accomplish this, we derive a longwave evolution equation, which is then used to obtain the dispersion relation. In contradistinction to the distal airways, the analysis predicts the absence of absolute instability-induced airway closure in the proximal airways for a healthy lung. However, an increased ASL thickness and/or elasticity due to excessive secretion of mucus and mucins in a diseased lung could lead to airway closure due to ASL plugs. Furthermore, inhaling colder air (than body temperature) enhances the absolute instability region, and the opposite is true for inhaling warmer air (than body temperature). For lungs with increased ASL thickness (due to diseases), plug formation is aggravated by colder air inhalation, thus demonstrating that inhaling colder (warmer) air is detrimental (beneficial) for diseased lungs. The predictions of the present analysis are in agreement with clinical observations.

Acoustic resonance is a critical issue in turbomachinery that induces noise and structural vibrations. The resonant mechanism for stator blade rows was first revealed more than half a century ago, along with the well-known concept of stationary Parker modes. However, despite various efforts based on this mechanism, previous studies have failed to explain the experimental Parker-type resonance results observed in rotor blade rows. This study establishes a theoretical model to elucidate acoustic resonance phenomena in rotating annular cascades, with focus on the effects of inlet distortion. The results demonstrate that the present model captures the experimental trends for Parker-type rotor acoustic resonances, which also implies that the conventional stationary Parker modes no longer exist in rotor blade rows due to rotation and the frequency scattering effect. Meanwhile, theoretical predictions on inlet-distortion–rotor interaction reveal that the unsteady blade loading is significantly higher at resonance frequencies compared to the cut-on frequency in duct acoustics. Accordingly, a modified Campbell diagram incorporating acoustic natural frequencies is proposed to aid in avoiding resonance-induced blade vibrations during the design stage. It is shown that the acoustic resonance frequencies intersect with the synchronous excitation frequencies across a wide speed range. High-amplitude unsteady blade loading is induced at these frequency crossings, due to the Parker-type acoustic resonance eigenmodes being excited by inlet-distortion–rotor interactions.