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.

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.

Interface-resolved direct numerical simulations are performed to investigate bubble-induced transition from a laminar to elasto-inertial turbulent (EIT) state in a pressure-driven viscoelastic square channel flow. The Giesekus model is used to account for the viscoelasticity of the continuous phase, while the dispersed phase is Newtonian. Simulations are performed for both single- and two-phase flows for a wide range of Reynolds (${Re}$) and Weissenberg (${\textit{Wi}}$) numbers. In the absence of any discrete external perturbations, single-phase viscoelastic flow is transitioned to an EIT regime at a critical Weissenberg number ($Wi_{cr})$ that decreases with increasing ${Re}$. It is demonstrated that injection of bubbles into a laminar viscoelastic flow introduces streamline curvature that is sufficient to trigger an elastic instability leading to a transition to an EIT regime. The temporal turbulent kinetic energy spectrum shows a scaling of $-2$ for this multiphase EIT regime, and this scaling is found to be independent of size and number of bubbles injected into the flow. It is also observed that bubbles move towards the channel centreline and form a string-shaped alignment pattern in the core region at the lower values of ${Re}=10$ and ${\textit{Wi}}=1$. In this regime, there are disturbances in the core region in the vicinity of bubbles while flow remains essentially laminar. Unlike the solid particles, it is found that increasing shear-thinning effect breaks up the alignment of bubbles.

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.

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 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.

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.

Turbulent convection under strong rotation can develop an inverse cascade of kinetic energy from smaller to larger scales. In the absence of an effective dissipation mechanism at the large scales, this leads to the pile up of kinetic energy at the largest available scale, yielding a system-wide large-scale vortex (LSV). Earlier works have shown that the transition into this state is abrupt and discontinuous. Here, we study the transition to the inverse cascade at Ekman number ${Ek}=10^{-4}$ and using stress-free boundary conditions, in the case where the inverse energy flux is dissipated before it reaches the system scale, suppressing the LSV formation. We demonstrate how this can be achieved in direct numerical simulations by using an adapted form of hypoviscosity on the horizontal manifold. We find that, in the absence of the LSV, the transition to the inverse cascade becomes continuous. This shows that it is the interaction between the LSV and the background turbulence that is responsible for the earlier observed discontinuity. We furthermore show that the inverse cascade in absence of the LSV has a more local signature compared with the case with LSV.

Particle motions under nonlinear gravity waves at the free surface of a two-dimensional incompressible and inviscid fluid are considered. The Euler equations are solved numerically using a high-order spectral method based on a Hamiltonian formulation of the water-wave problem. Extending this approach, a numerical procedure is devised to estimate the fluid velocity at any point in the fluid domain given surface data. The reconstructed velocity field is integrated to obtain particle trajectories for which an analysis is provided, focusing on two questions. The first question is the influence of a wave setup or setdown as is typical in coastal conditions. It is shown that such local changes in the mean water level can lead to qualitatively different pictures of the internal flow dynamics. These changes are also associated with rather strong background currents which dominate the particle transport and, in particular, can be an order of magnitude larger than the well-known Stokes drift. The second question is whether these particle dynamics can be described with a simplified wave model. The Korteweg–de Vries equation is found to provide a good approximation for small- to moderate-amplitude waves on shallow and intermediate water depth. Despite discrepancies in severe cases, it is able to reproduce characteristic features of particle paths for a wave setup or setdown.

Motivated by the need for a better understanding of marine plastic transport, we experimentally investigate finite-size particles floating in free-surface turbulence. Using particle tracking velocimetry, we study the motion of spheres and discs along the quasi-flat free-surface above homogeneous isotropic grid turbulence in open channel flows. The focus is on the effect of the particle diameter, which varies from the Kolmogorov scale to the integral scale of the turbulence. We find that particles of size up to approximately one-tenth of the integral scale display motion statistics indistinguishable from surface flow tracers. For larger sizes, the particle fluctuating energy and acceleration variance decrease, the correlation times of their velocity and acceleration increase, and the particle diffusivity is weakly dependent on their diameter. Unlike in three-dimensional turbulence, the acceleration of finite-size floating particles becomes less intermittent with increasing size, recovering a Gaussian distribution for diameters in the inertial subrange. These results are used to assess the applicability of two distinct frameworks: temporal filtering and spatial filtering. Neglecting preferential sampling and assuming an empirical linear relation between the particle size and its response time, the temporal filtering approach is found to correctly predict the main trends, though with quantitative discrepancies. However, the spatial filtering approach, based on the spatial autocorrelation of the free-surface turbulence, accurately reproduces the decay of the fluctuating energy with increasing diameter. Although the scale separation is limited, power-law scaling relations for the particle acceleration variance based on spatial filtering are compatible with the observations.

The interaction of near-inertial waves (NIWs) with submesoscale vorticity filaments is explored using theory and simulations. We study three idealised set-ups representative of submesoscale flows allowing for $O(1)$ or greater Rossby numbers. First, we consider the radiation of NIWs away from a cyclonic filament and develop scalings for the decay of wave energy in the filament. Second, we introduce broad anticyclonic regions that separate the cyclonic filaments mimicking submesoscale eddy fields and analyse the normal modes of this system. Third, we extend this set-up to consider the vertical propagation and the radiation of NIW energy. We identify a key length scale $L_m$, dependent on the strength of the filament, stratification and vertical scale of the waves, that when compared with the horizontal scales of the background flow determines the NIW behaviour. A generic expression for the vertical group velocity is derived that highlights the importance of horizontal gradients for vertical wave propagation. An overarching theme of the results is that NIW radiation, both horizontally and vertically, is most efficient when $L_m$ is comparable to the length scales of the background flow.

Identifying self-similarity is key to understanding and modelling a plethora of phenomena in fluid mechanics. Unfortunately, this is not always possible to perform formally in highly complex flows. We propose a methodology to extract the similarity variables of a self-similar physical process directly from data, without prior knowledge of the governing equations or boundary conditions, based on an optimisation problem and symbolic regression. We analyse the accuracy and robustness of our method in five problems which have been influential in fluid mechanics research: a laminar boundary layer, Burger’s equation, a turbulent wake, a collapsing cavity and decaying turbulence. Our analysis considers datasets acquired via both numerical and wind tunnel experiments. The algorithm recovers the known self-similarity expressions in the first four problems and generates new insights into single length scale theories of homogeneous turbulence.

Inertial sedimentation of a cloud of cylinders released within a confined fluid-filled cell is experimentally investigated. Various cylinder numbers, $N_c$, aspect ratios, $\xi$, solid-to-fluid density ratios, $\rho _c / \rho _{\!f}$, and settling velocities corresponding to moderate Reynolds numbers are examined. The parameters correspond to two distinct path regimes for isolated cylinders: oscillatory trajectories for higher-density cylinders and rectilinear sedimentation for lower-density cylinders. In both cases, we observe the formation of subgroups (termed objects of class $N$) composed of $N$ cylinders in contact, as well as their recombination due to splitting or merging. Depending on the parameters, specific distributions of class-$N$ objects are found. In addition, beyond the formation of individual objects, large-scale vertical columnar structures emerge, made of densely packed objects and alternating regions of ascending and descending fluid. These structures, driven by complex interactions between local clustering and global flow organisation, which persist throughout the sedimentation process, are highly sensitive to $\xi$. Despite its inner complex dynamics, the group is observed to sediment as a collective entity, with a constant velocity exceeding that of an isolated cylinder. This velocity may be predicted from multi-scale information. Fluctuating velocities of the objects are further analysed. Different mechanisms for horizontal and vertical components are identified. Horizontal fluctuations are related to intrinsic particle mobility, while vertical fluctuations are attributed to strong wakes and vertical streams. Both fluctuations are mainly influenced by the cylinders’ aspect ratio, which also affects the structural and spatial distribution of the objects.

We provide a rigorous analysis of the self-similar solution of the temporal turbulent boundary layer, recently proposed by Biau (2023 Comput. Fluids 254, 105795), in which a body force is used to maintain a statistically steady turbulent boundary layer with periodic boundary conditions in the streamwise direction. We derive explicit expressions for the forcing amplitudes which can maintain such flows, and identify those which can hold either the displacement thickness or the momentum thickness equal to unity. This opens the door to the first main result of the paper, which is to prove upper bounds on skin friction for the temporal turbulent boundary layer. We use the Constantin–Doering–Hopf bounding method to show, rigorously, that the skin-friction coefficient for periodic turbulent boundary layer flows is bounded above by a uniform constant which decreases asymptotically with Reynolds number. This asymptotic behaviour is within a logarithmic correction of well-known empirical scaling laws for skin friction. This gives the first evidence, applicable at asymptotically high Reynolds numbers, to suggest that Biau’s self-similar solution of the temporal turbulent boundary layer exhibits statistical similarities with canonical, spatially evolving, boundary layers. Furthermore, we show how the identified forcing formula implies an alternative, and simpler, numerical implementation of periodic boundary layer flows. We give a detailed numerical study of this scheme presenting direct numerical simulations up to a momentum Reynolds number of $\textit{Re}_\theta = 2000$ and implicit large-eddy simulations up to $\textit{Re}_\theta = 8300$, and show that these results compare well with data from canonical spatially evolving boundary layers at equivalent Reynolds numbers.

Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau–Yasuda model, we discovered that linear instability can arise when the power-law index falls below 0.35. This inelastic non-axisymmetric instability can universally arise in generalised Newtonian fluids that extend the power-law model. The viscosity ratio from infinite to zero shear rate can significantly impact instability, even if it is small. Two branches of finite-amplitude travelling-wave solutions bifurcate subcritically from the linear critical point. The solutions exhibit sublaminar drag reduction, a phenomenon not possible in the Newtonian case.

In this work, the correlations between streamwise velocity and temperature fluctuations are investigated in compressible turbulent channel flows from the perspective of coherent structures. The intense fluctuation structures and quadrant-event structures of both velocity and temperature have been identified, extracted separately and compared. Analyses show that although their structure sizes are similar in the whole channel, high correlation only exists in the near-wall region with a high overlapping rate of the instantaneous structures. The hierarchy of the temperature structures are passively formed following the dynamic process of the velocity such as ejections, which contributes to the remaining correlation in the outer layer. However, this passive scalar property cannot provide the production mechanism in the outer layer according to the budget analysis after scale decomposition, and the interscale energy transfer progress is also different from the velocity fluctuation field. Therefore, the temperature structures deviate from the velocity structures in the outer layer and cannot be carried by the following dynamic process of the velocity such as sweeps, passively, which can be found from the conditional averaged structures. All of these findings provide a new perspective for understanding the velocity–temperature relationship in compressible channel flows.

A model for galloping detonations is conceived as a sequence of very fast re-ignitions followed by long periods of evolution with quenched reactions. Numerical simulations of the one-dimensional Euler equations are conducted in this limit. While the mean speed and structure is found in reasonable agreement with Chapman–Jouguet theory, very strong pulsations of the lead shock appear, along with a train of rear-facing N-waves. These dynamics are analysed using characteristics. A closed-form solution for the lead shock dynamics is formulated, which is found in excellent agreement with numerics. The model relies on the presence of a single time scale of the process, the pulsation period, which controls the shock dynamics via the shock change equations and establishes a shock decay with a single time constant. These long periods of shock decay with known dynamics are punctuated by energy release events, with ‘kicks’ in the shocked speed controlled by the pressure increase and resulting lead shock amplification. Model predictions are found in excellent agreement with previous numerical results of pulsating detonations far from the stability limit.

Elastic turbulence can lead to increased flow resistance, mixing and heat transfer. Its control – either suppression or promotion – has significant potential, and there is a concerted ongoing effort by the community to improve our understanding. Here we explore the dynamics of uncertainty in elastic turbulence, inspired by an approach recently applied to inertial turbulence in Ge et al. (J. Fluid Mech., vol. 977, 2023, A17). We derive equations for the evolution of uncertainty measures, yielding insight on uncertainty growth mechanisms. Through numerical experiments, we identify four regimes of uncertainty evolution, characterised by (i) rapid transfer to large scales, with large-scale growth rates of $\tau ^{6}$ (where $\tau$ represents time), (ii) a dissipative reduction of uncertainty, (iii) exponential growth at all scales and (iv) saturation. These regimes are governed by the interplay between advective and polymeric contributions (which tend to increase uncertainty), viscous, relaxation and dissipation effects (which reduce uncertainty) and inertial contributions. In elastic turbulence, reducing Reynolds number increases uncertainty at short times, but does not significantly influence the growth of uncertainty at later times. At late times, the growth of uncertainty increases with Weissenberg number, with decreasing polymeric diffusivity and with the logarithm of the maximum length scale, as large flow features adjust the balance of advective and relaxation effects. These findings provide insight into the dynamics of elastic turbulence, offering a new approach for the analysis of viscoelastic flow instabilities.

In this study, we experimentally investigate the stress field around a gradually contaminated bubble as it moves straight ahead in a dilute surfactant solution with an intermediate Reynolds number ($20 \lt {{\textit{Re}}} \lt 220$) and high Péclet number. Additionally, we investigate the stress field around a falling sphere unaffected by surface contamination. A newly developed polarisation measurement technique, highly sensitive to the stress field in the vicinity of the bubble or the sphere, was employed in these experiments. We first validated this method by measuring the flow around a solid sphere sedimenting in a quiescent liquid at a terminal velocity. The measured stress field was compared with established numerical results for ${{\textit{Re}}} = 120$. A quantitative agreement with the numerical results validated this technique for our purpose. The results demonstrated the ability to determine the boundary layer. Subsequently we measured a bubble rising in a quiescent surfactant solution. The drag force on the bubble, calculated from its rise velocity, was set to transiently vary from that of a clean bubble to a solid sphere within the measurement area. With the intermediate drag force between clean bubble and solid sphere, the stress field in the vicinity of the bubble front was observed to be similar to that of a clean bubble, and the structure near the rear was similar to that of a solid sphere. Between the front and rear of the bubble, the phase retardation exhibited a discontinuity around the cap angle at which the boundary conditions transitioned from no slip to slip, indicating an abrupt change in the flow structure. A reconstruction of the axisymmetric stress field from the phase retardation and azimuth obtained from polarisation measurements experimentally revealed that stress spikes occur around the cap angle. The cap angle (stress jump position) shifted as the drag on the bubble increased owing to surfactant accumulation on its surface. Remarkably, the measured cap angle as a function of the normalised drag coefficient quantitatively agreed with the numerical results at intermediate ${{\textit{Re}}} = 100$ of Cuenot et al. (1997 J. Fluid Mech. 339, 25–53), exhibiting only a slight deviation from the curve predicted by the stagnant cap model at low ${\textit{Re}}$ (creeping flow) proposed by Sadhal & Johnson (1983 J. Fluid Mech. 126, 237–250).

This numerical investigation focuses on the mechanisms, flow topology and onset of Kelvin–Helmholtz instabilities (KHIs), that drive the leading-edge shear-layer destabilisation in the wake of wall-mounted long prisms. Large-eddy simulations are performed at ${\textit{Re}} = 2.5\times 10^3, 5\times 10^3$ and $1\times 10^4$ for prisms with a range of aspect ratio (AR, height-to-width) between $0.25$ and $1.5$, and depth ratios (DR, length-to-width) of $1{-}4$. Results show that shear-layer instabilities enhance flow irregularity and modulate spanwise vortex structures. The onset of KHI is strongly influenced by depth ratio, such that long prisms (${\textit{DR}}= 4$) experience earlier initiation compared with shorter ones (${\textit{DR}}= 1$). At higher Reynolds numbers, the onset of KHI shifts upstream towards the leading-edge, intensifying turbulence kinetic energy and increasing flow irregularity, especially for long prisms. The results further show that in this configuration, energy transfer from the secondary recirculation region contributes to the destabilisation of the leading-edge shear layer by reinforcing low-frequency modes. A feedback mechanism is identified wherein energetic flow structures propagate upstream through reverse boundary-layer flow, re-energising the leading-edge shear layer. Quantification using probability density functions reveals rare, intense upstream energy convection events, driven by this feedback mechanism. These facilitate the destabilisation process regardless of Reynolds number. This study provides a comprehensive understanding of the destabilisation mechanisms for leading-edge shear layers in the wake of wall-mounted long prisms.