Dynamic stall on aerofoils is an undesirable and potentially dangerous phenomenon. The motto for aerodynamic systems with unsteadily moving wings, such as helicopters or wind turbines, is that prevention beats recovery. In case prevention fails or is not feasible, we need to know when recovery starts, how long it takes, and how we can improve it. This study revisits dynamic stall reattachment to identify the sequence of events during flow and load recovery, and to characterise key observable features in the pressure, force and flow field. Our analysis is based on time-resolved velocity field and surface pressure data obtained experimentally for a two-dimensional, sinusoidally pitching thin aerofoil. Stall recovery is a transient process that does not start immediately when the angle of attack falls below the critical stall angle. The onset of recovery is delayed to angles below the critical stall angle, and the duration of the reattachment delay decreases with increasing unsteadiness of the pitching motion. An angle of attack below the critical angle is a necessary but not sufficient condition to initiate the stall recovery process. We identified a critical value of the leading-edge suction parameter, independent of the pitch rate, that is a threshold beyond which reattachment consistently initiates. Based on prominent changes in the evolution of the shear layer, the leading-edge suction, and the lift deficit due to stall, we divided the reattachment process into three stages: the reaction delay, wave propagation and the relaxation stage, and extracted the characteristic features and time scales for each stage.

The nonlinear free-surface response of moonpools with recesses is investigated through both experimental and theoretical analyses. A theoretical model is developed to compute the natural frequencies using linearised potential flow theory and eigenfunction expansions. Four moonpool configurations with varying recess lengths are examined experimentally. The analysis reveals that larger recess lengths correspond to increasingly pronounced nonlinear responses. It is also shown that, for an incident wave group with suitable frequency content, the linear moonpool response can be significantly smaller than the second- and third-harmonic components. This effect is attributed to super-harmonic secondary resonance, characterised by $n \omega =\omega _{pq}$ ($n\geqslant 2$ and $p+q\geqslant 1$), where $n$ denotes the super-harmonic order, $\omega$ is the excitation frequency, and $p$ and $q$ are the longitudinal and transverse mode numbers, respectively. Here, $\omega_{pq}$ represents the sloshing frequency of the three-dimensional moonpool. Furthermore, it is found that, as the primary responses increase, cross-flow instability can lead to secondary resonance in non-symmetric modes. This occurs because the double and triple frequencies of the base mode approach the transverse or diagonal sloshing frequencies. Additionally, hard-spring Duffing effects for secondary resonance induced by super-harmonics are observed in cases with recesses, becoming more pronounced as the recess length increases, particularly when $h/l\lt 0.3368$, where $h$ is the water depth above the recess and $l$ is the moonpool length.

Active deformable filaments exhibit a large range of qualitatively different three-dimensional dynamics, depending on their flexibility, the strength and nature of the active forcing, and the surrounding environment. We investigate the dynamic behaviour of elastic, chemically propelled phoretic filaments, combining two existing models; a local version of slender phoretic theory, which determines the resulting slip flows for chemically propelled filaments with a given shape and chemical patterning, is paired with a computationally efficient method for capturing the elastohydrodynamics of a deformable filament in viscous flow to study the chemoelastohydrodynamics of filaments. As the activity increases, or equivalently the filament stiffness decreases, these filaments undergo buckling instabilities that alter their behaviour from rigid rods. We follow their behaviour well beyond the buckling threshold to find a rich array of dynamics. Through two illustrative examples, we conduct initial-value simulations that show that as the stiffness of the filament is decreased, the dynamic behaviour moves from rigid motion to planar buckling, through an out-of-plane transition, eventually reaching diffusive-like behaviours for very deformable filaments.

The inertial migration of a neutrally buoyant sphere in pipe Poiseuille flow is examined using numerical simulations. Three migration regimes are observed with increasing Reynolds number (${\textit{Re}}$): monotonic convergence to the equilibrium position, overshooting convergence and damped oscillations. The critical Reynolds numbers separating these regimes decrease with the sphere-to-pipe diameter ratio, $d/D$. The axial entry length, $L_{p}$, required for the sphere to reach equilibrium decreases with both ${\textit{Re}}$ and $d/D$ in the monotonic regime, but increases in the oscillatory regime. These results elucidate the dynamics of inertial migration and inform strategies for manipulating particles in confined, particle-laden flows.

We derive a self-consistent hydrodynamic theory of coupled binary fluid–surfactant systems from the underlying microscopic physics using Rayleigh’s variational principle. At the microscopic level, surfactant molecules are modelled as dumbbells that exert forces and torques on the fluid and interface while undergoing Brownian motion. We obtain the overdamped stochastic dynamics of these particles from a Rayleighian dissipation functional, which we then coarse-grain to derive a set of continuum equations governing the surfactant concentration, orientation, fluid density and velocity. This approach introduces a polarisation field $\boldsymbol{p}(\boldsymbol{r},t)$, representing the average orientation of surfactants, which plays a central role in suppressing droplet coalescence. The remaining hydrodynamic equations are consistently obtained from a mesoscopic free energy functional. The resulting model accurately captures key surfactant phenomena, including surface tension reduction and droplet stabilisation, as confirmed by both perturbation theory and numerical simulations, and is thermodynamically consistent with both the Gibbs adsorption isotherm and Henry’s law for adsorbed surfactant concentration.

A coupled computational-fluid-dynamics/finite-element methodology is implemented to investigate the free aerodynamic separation of clusters of equally sized spheres arranged in regular configurations in Mach-20 flow, representing an idealized meteoroid-fragmentation scenario. The regular nature of the initial agglomeration geometries – touching sphere pairs, tetrahedral four-sphere arrangements and face-centred-cubic 13-sphere configurations – allows a systematic exploration of both individual sphere motions and bulk cluster dynamics as the initial orientation is varied. For sphere pairs, a stable lifting configuration arises when the spheres are in contact in a skewed configuration, a phenomenon that can also emerge in the more populous clusters. In the tetrahedral survey, comprising 38 initial orientations, shock surfing of downstream bodies is found to play a significant role in driving the separation dynamics. Despite substantial variations in detailed sphere motions with initial orientation, the trajectory type and final lateral velocity collapse reasonably well with the initial polar angle of the sphere within the cluster. Indices describing the bluntness and asymmetry of the initial configuration are introduced and correlate well with the collective cluster dynamics, though not always in an intuitive way. For the 13-sphere clusters, the dependency of individual sphere lateral velocities follows a similar trend with initial polar angle to the four-sphere case, suggesting that a simplified separation model may be possible for such configurations. The influence of the initial cluster bluntness on the bulk dynamics is somewhat reduced, however, indicating a tendency towards more homogeneous separation as the cluster population is increased.

We present a combined theoretical and numerical investigation of the inertial exit dynamics of a long horizontal circular cylinder vertically lifted out of a finite-size liquid bath at constant velocity. The various steps of the exit dynamics are studied in detail: from the formation of a bulge on the surface ahead of the cylinder to the coating of the cylinder by a liquid film while crossing the interface. We focus on inertial dynamics, a regime characteristic of large exit velocities, i.e. large Reynolds numbers ($500 \lt \textit{Re} \lt 10\,000$) and negligible interfacial effects. The dynamics is investigated through two-dimensional computations of the Navier–Stokes equations using a finite element method with moving boundaries. We describe in detail the exit dynamics while emphasising the effect of various parameters on surface deformation and resistive force. We identify subtle effects and interplay, such as initial free-surface response after impulsive start-up, the important role of the lateral bounding of the reservoir, and the close relationship between wake size and surge amplitudes as revealed by comparing with free-slip cylinder simulations. All these aspects are shown to be crucial to accurately predict the coated film thickness and the exit force.

This study presents a novel extension of the Onsager variational principle to incorporate inertial and thermal effects in fluid dynamics, thereby establishing a unified variational framework for modelling non-isothermal two-phase flows with liquid–vapour phase transitions and wetting effects on solid substrates. From this framework, we naturally derive a thermodynamically consistent model for the fluid system, comprising two-phase Navier–Stokes equations, an equation for the total energy, and dynamic boundary conditions that account for thermal and wetting effects. The derivation is independent of the equation of state, and generalises the dynamic van der Waals theory. To address the computational complexity of the resulting dynamic system, we propose a lattice Boltzmann method based on double distribution functions, which enables accurate and robust simulations of coupled fluid and thermal transport. Numerical experiments – including droplet evaporation, bubble nucleation and departure, and Leidenfrost droplet impact – demonstrate good agreement with theoretical predictions and experimental data, indicating that the proposed numerical method can effectively capture complex thermohydrodynamic phenomena.

Wavy topography can exert a significant influence on gravity-driven flows in porous media. Building on the low-dimensional theoretical framework for a wavy topography of height $f(x) = A[1 - \cos (\lambda x)]$, where $A$ is the amplitude and $\lambda$ is the wavenumber of the topography, under small-slope conditions ($A\lambda \ll 1$) Di et al. (2025 J. Fluid Mech., vol. 1016, A16), we extend the framework to constant-flux injection while incorporating uniform drainage and localised leakage through low-permeability substrates. A key dimensionless topographic intensity, emerges as the ratio of the pressure gradient required to overcome topographic slopes to the characteristic viscous gradient driving the flow, thereby quantifying topographic resistance. Our results show that a larger topographic intensity retards current advancement, while drainage, governed by the drainage intensity, imposes an upper bound on propagation distance. Leakage proves highly sensitive to the along-slope position of fissured zones. Comparisons with a macroscopic sharp-interface flow model indicate that the low-dimensional model simplifies the two-phase dynamics in substrates via a Darcy’s sink term, yielding underestimates of propagation during drainage and leakage. Applied to the field of carbon dioxide sequestration, our low-dimensional model reveals how injection flux modulates the early-stage flow dynamics over wavy cap rocks, offering theoretical insights into sequestration performance.

In this work, we will present evidence for the incompatibility of smoothed particle hydrodynamics (SPH) methods and eddy viscosity models. Taking a coarse-graining perspective, we physically argue that SPH methods operate intrinsically as Lagrangian large eddy simulations for turbulent flows with strongly overlapping discretisation elements. However, these overlapping elements in combination with numerical errors cause a significant amount of implicit subfilter stresses (SFS). Considering a Taylor–Green flow at $Re=10^4$, the SFS will be shown to be relevant where turbulent fluctuations are created, explaining why turbulent flows are challenging even for current SPH methods. Although one might hope to mitigate the implicit SFS using eddy viscosity models, we show a degradation of the turbulent transition process, which is rooted in the non-locality of these methods.