Time-varying flow-induced forces on bodies immersed in fluid flows play a key role across a range of natural and engineered systems, from biological locomotion to propulsion and energy-harvesting devices. These transient forces often arise from complex, dynamic vortex interactions and can either enhance or degrade system performance. However, establishing a clear causal link between vortex structures and force transients remains challenging, especially in high-Reynolds-number nominally three-dimensional flows. In this study, we investigate the unsteady lift generation on a rotor blade that is impulsively started with a span-based Reynolds number of 25 500. The lift history from this direct-numerical simulation reveals distinct early-time extrema associated with rapidly evolving flow structures, including the formation, evolution and breakdown of leading-edge and tip vortices. To quantify the influence of these vortical structures on the lift transients, we apply the force partitioning method (FPM) that quantifies the surface pressure forces induced by vortex-associated effects. Two metrics – $Q$-strength and vortex proximity – are derived from FPM to provide a quantitative assessment of the influence of vortices on the lift force. This analysis confirms and extends qualitative insights from prior studies, and offers a simple-to-apply data-enabled framework for attributing unsteady forces to specific flow features, with potential applications in the design and control of systems where unsteady aerodynamic forces play a central role.

Tip leakage noise is one of the least understood noise sources in turbomachinery, arising from the interactions between the tip leakage flow, blade tips and casing boundary layer. This study employs experimental and parametric investigations to systematically identify three key non-dimensional parameters that govern tip leakage noise: the angle of attack $\alpha$, the ratio between the maximum aerofoil thickness and gap size $\tau _{\textit{max}}/e$ and between the gap size and boundary-layer thickness $e/\delta$. These parameters regulate two fluid-dynamic instabilities, vortex shedding and shear-layer roll-up, responsible for the two tip leakage noise sources. Specifically, the first noise source arises when $\tau _{\textit{max}}/e \lt 4$ and with the tip vortex positioned away from the aerofoil surface for $\alpha \geqslant 10^\circ$. The second noise source occurs whenever the tip flow separates at the pressure side edge, with its strength proportional to the lift coefficient, depending on $\alpha$, and diminishing as $e/\delta$ decreases and $\tau _{\textit{max}}/e$ increases. Additionally, a relationship between the first noise source and drag losses is established, demonstrating that these losses are governed by $\alpha$ and $\tau _{\textit{max}}/e$.

We investigate the shape of a tin sheet formed from a droplet struck by a nanosecond laser pulse. Specifically, we examine the dynamics of the process as a function of laser beam properties, focusing on the outstanding puzzle of curvature inversion: tin sheets produced in experiments and state-of-the-art extreme ultraviolet (EUV) nanolithography light sources curve in a direction opposite to previous theoretical predictions. We resolve this discrepancy by combining direct numerical simulations with experimental data, demonstrating that curvature inversion can be explained by an instantaneous pressure impulse with low kurtosis. Specifically, we parametrise a dimensionless pressure width, $ W$, using a raised cosine function and successfully reproduce the experimentally observed curvature over a wide range of laser-to-droplet diameter ratios, $ 0.3 \lt d/D_0 \lt 0.8$. The simulation process described in this work has applications in the EUV nanolithography industry, where a laser pulse deforms a droplet into a sheet, which is subsequently ionised by a second pulse to produce EUV-emitting plasma.

We study the two-dimensional steady-state creeping flow in a converging–diverging channel gap formed by two immobile rollers of identical radius. For this purpose, we analyse the Stokes equation in the streamfunction formulation, i.e. the biharmonic equation, which has homogeneous and particular solutions in the roll-adapted bipolar coordinate system. The analysis of existing works, investigating the particular solutions allowing arbitrary velocities at the two rollers, is extended by an investigation of homogeneous solutions. These can be reduced to an algebraic eigenvalue problem, whereby the associated discrete but infinite eigenvalue spectrum generates symmetric and asymmetric eigenfunctions with respect to the centre line between the rollers. These represent nested viscous vortex structures, which form a counter-rotating chain of vortices for the smallest unsymmetrical eigenvalue. With increasing eigenvalue, increasingly complex finger-like structures with more and more layered vortices are formed, which continuously form more free stagnation points. In the symmetrical case, all structures are mirror-symmetrical to the centre line and with increasing eigenvalues, finger-like nested vortex structures are also formed. As the gap height in the pressure gap decreases, the vortex density increases, i.e. the number of vortices per unit length increases, or the length scales of the vortices decrease. At the same time the rate of decay between subsequent vortices increases and reaches and asymptotic limit as the gap vanishes.

We analyse the process of convective mixing in two-dimensional, homogeneous and isotropic porous media with dispersion. We considered a Rayleigh–Taylor instability in which the presence of a solute produces density differences driving the flow. The effect of dispersion is modelled using an anisotropic Fickian dispersion tensor (Bear, J. Geophys. Res., vol. 66, 1961, pp. 1185–1197). In addition to molecular diffusion ($D_m^*$), the solute is redistributed by an additional spreading, in longitudinal and transverse flow directions, which is quantified by the coefficients $D_l^*$ and $D_t^*$, respectively, and it is produced by the presence of the pores. The flow is controlled by three dimensionless parameters: the Rayleigh–Darcy number $\textit{Ra}$, defining the relative strength of convection and diffusion, and the dispersion parameters $r=D_l^*/D_t^*$ and $\varDelta =D_m^*/D_t^*$. With the aid of numerical Darcy simulations, we investigate the mixing dynamics without and with dispersion. We find that in the absence of dispersion ($\varDelta \to \infty$) the dynamics is self-similar and independent of $\textit{Ra}$, and the flow evolves following several regimes, which we analyse. Then we analyse the effect of dispersion on the flow evolution for a fixed value of the Rayleigh–Darcy number ($\textit{Ra}=10^4$). A detailed analysis of the molecular and dispersive components of the mean scalar dissipation reveals a complex interplay between flow structures and solute mixing. We find that the dispersion parameters $r$ and $\varDelta$ affect the formation of fingers and their dynamics: the lower the value of $\varDelta$ (or the larger the value of $r$), the wider, more convoluted and diffused the fingers. We also find that for strong anisotropy, $r=O(10)$, the role of $\varDelta$ is crucial: except for the intermediate phases of the flow dynamics, dispersive flows show more efficient (or at least comparable) mixing than in non-dispersive systems. Finally, we look at the effect of the anisotropy ratio $r$, and we find that it produces only second-order effects, with relevant changes limited to the intermediate phase of the flow evolution, where it appears that the mixing is more efficient for small values of anisotropy. The proposed theoretical framework, in combination with pore-scale simulations and bead packs experiments, can be used to validate and improve current dispersion models to obtain more reliable estimates of solute transport and spreading in buoyancy-driven subsurface flows.

Turbulence exhibits a striking duality: it drives concentrated substances apart, enhancing mixing and transport, while simultaneously drawing particles and bubbles into collisions. Little experimental data exist to clarify the latter process due to challenges in techniques for resolving bubble pairs from afar to coalescence via turbulent entrainment, film drainage and rupture. In this work, we tracked pairs of bubbles across nearly four orders of magnitude in spatial resolution, capturing the entire dynamics of collision and coalescence. The resulting statistics show that critical variables exhibit scalings with bubble size in ways that are different from some classical models, which were developed based on assumptions that bubble collision and coalescence only mirror the key scales of the surrounding turbulence. Furthermore, contrary to classical models which suggest that coalescence favours slow collision velocity, we find a ‘Goldilocks zone’ of relative velocities for bubble coalescence, where there is an optimal coalescence velocity that is neither too high nor too low. This zone arises from the competition between bubble–bubble and bubble–eddy interactions. Incorporating this zone into the new model yields excellent agreement with experimental results, laying a foundation for better predictions for many multiphase flow systems.