The mixing mechanism within a single vortex has been a theoretical focus for decades, while it remains unclear especially under the variable-density (VD) scenario. This study investigates canonical single-vortex VD mixing in shock–bubble interactions (SBI) through high-resolution numerical simulations. Special attention is paid to examining the stretching dynamics and its impact on VD mixing within a single vortex, and this problem is investigated by quantitatively characterising the scalar dissipation rate (SDR), namely the mixing rate, and its time integral, referred to as mixedness. To study VD mixing, we first examine single-vortex passive-scalar (PS) mixing with the absence of a density difference. Mixing originates from diffusion and is further enhanced by the stretching dynamics. Under the axisymmetry and zero diffusion assumptions, the single-vortex stretching rate illustrates an algebraic growth of the length of scalar strips over time. By incorporating the diffusion process through the solution of the advection–diffusion equation along these stretched scalar strips, a PS mixing model for SDR is proposed based on the single-vortex algebraic stretching characteristic. Within this framework, density-gradient effects from two perspectives of the stretching dynamics and diffusion process are discovered to challenge the extension of the PS mixing model to VD mixing. First, the secondary baroclinic effect increases the VD stretching rate by the additional secondary baroclinic principal strain, while the algebraic stretching characteristic is still retained. Second, the density source effect, originating from the intrinsic nature of the density difference in the multi-component transport equation, suppresses the diffusion process. By accounting for both the secondary baroclinic effect on stretching and the density source effect on diffusion, a VD mixing model for SBI is further modified. This model establishes a quantitative relationship between the stretching dynamics and the evolution of the mixing rate and mixedness for single-vortex VD mixing over a broad range of Mach numbers. Furthermore, the essential role of the stretching dynamics on the mixing rate is demonstrated by the derived dependence of the time-averaged mixing rate $\overline {\langle \chi \rangle }$ on the Péclet number ${\textit{Pe}}$, which scales as $\overline {\langle \chi \rangle } \sim {\textit{Pe}}^{{2}/{3}}$.

A low-density jet is known to exhibit global self-excited axisymmetric oscillations at a discrete natural frequency. This global mode manifests as large-scale periodic vortex ring structures in the near field. We experimentally investigate the effectiveness of axial and transverse forcing in controlling such global vortical structures. We apply acoustic forcing at a frequency ($f_{\!f}$) around the natural global frequency of the jet ($f_n$) leading up to and beyond lock-in. Using time-resolved stereoscopic particle image velocimetry, we find that the jet synchronises to $f_{\!f}$ when forced sufficiently strongly. When forced purely axially, the jet exhibits in-phase roll-up of the shear layers, producing axisymmetric vortex ring structures. When forced purely transversely, the jet exhibits anti-phase roll-up of the shear layers, producing tilted vortex ring structures. We find that the former produces relatively strong oscillations, while the latter produces oscillations that are even weaker than those of the unforced case due to asynchronous quenching. We show that the transverse forcing breaks the jet axisymmetry by altering the topology of the coherent structures in the near field, leading to global instability suppression. We also find that the wavelength of the applied forcing has a notable influence on the evolution of vortical structures, thereby modifying the forced response of the jet. The efficacy of transverse forcing and the influence of the forcing wavelength in suppressing the global mode of a self-excited low-density jet present new possibilities for the open-loop control of a variety of globally unstable flows.

The evolution of the flow structure around an impulsively stopped sphere is investigated in an incompressible viscous fluid under a transverse magnetic field. The study focuses on the wake structure and drag force over the range of Reynolds numbers $60 \leqslant {\textit{Re}}_{\!D} \leqslant 300$ and $ {\textit{Re}}_{\!D}=1000$, with the interaction parameters $0 \leqslant N \leqslant 10$, where $N$ characterises the strength of the magnetic field. The wake is fully developed before the impulsive stop, after which it moves downstream and interacts with the sphere under the influence of a transverse magnetic field. The complex flow structures are characterised by skin friction lines on the downstream side of the sphere and categorised into five regimes in the $\{N, {\textit{Re}}_{\!D}\}$ phase diagram based on nearly 200 cases. The drag force generally decays over time following the impulsive stop. A drag decomposition model based on the vorticity diffusion scale is proposed, attributing the drag decay to three components: the original Stokes contribution, an inertia correction at high Reynolds numbers and a magnetohydrodynamic (MHD) correction, where the inertia and MHD effects both contribute a temporal power-law decay with an exponent of $-1/6$. Temporal scaling laws of the drag decay are derived by coupling these three different effects, considering flow structures at short and long time scales, as well as the dependence on ${\textit{Re}}_{\!D}$ and $N$. The prediction results are consistent with present simulations. Furthermore, the proposed drag decomposition model is successfully extended to complex vortex flow past a sphere at ${\textit{Re}}_{\!D}=1000$, to an anisotropic ellipsoidal particle and to different magnetic field orientations.

Recent theoretical and experimental investigations have revealed that flapping compliant membrane wings can significantly enhance propulsive performance (e.g. Tzezana & Breuer J. Fluid Mech., 2019, vol. 862, pp. 871–888) and energy harvesting efficiency (e.g. Mathai et al. J. Fluid Mech., 2022, vol. 942, p. R4) compared with rigid foils. Here, we numerically investigate the effects of the in-plane stretching stiffness (or aeroelastic number), $K_{\!S}$, the flapping frequency, ${\textit{St}}_c$, and the pitching amplitude, $\theta _0$, on the propulsive performance of a compliant membrane undergoing combined heaving and pitching in uniform flow. Distinct optimal values of $K_{\!S}$ are identified that respectively maximise thrust and efficiency: thrust can be increased by 200 %, and efficiency by 100 %, compared with the rigid case. Interestingly, these optima do not occur at resonance but at frequency ratios (flapping to natural) below unity, and this ratio increases with flapping frequency. Using a force decomposition based on the second invariant of the velocity gradient tensor $Q$, which measures the relative strength between the rotation and deformation of fluid elements, we show that thrust primarily arises from $Q$-induced and body-acceleration forces. The concave membrane surface can trap the leading-edge vortex (LEV) generated during the previous half-stroke, generating detrimental $Q$-induced drag. However, moderate concave membrane deformation weakens this LEV and enhances body-acceleration-induced thrust. Thus, the optimal $K_{\!S}$ for maximum thrust occurs below resonance, balancing beneficial deformation against excessive drag. Furthermore, by introducing the membrane’s deformation into a tangential angle at the leading edge and substituting it into an existing scaling law developed for rigid plates, we obtain predictive estimates for the thrust and power coefficients of the membrane. The good agreement confirms the validity of this approach and offers insights for performance prediction.

We integrate a discrete vortex method (DVM) with complex network analysis to strategise dynamic stall mitigation over aerofoils with active flow control. The objective is to inform the actuator placement and the timing to introduce control inputs during the highly transient process of dynamic stall. To this end, we treat a massively separated flow as a network of discrete vortical elements and quantify the interactions among the vortical nodes by tracking the spread of displacement perturbations between each pair of vortical elements using a DVM. This allows us to perform network broadcast mode analysis to identify an optimal set of discrete vortices, the critical timing and the direction to seed perturbations as control inputs. Motivated by the objective of dynamic stall mitigation, the optimality is defined as maximising the reduction of total circulation of the free vortices generated from the leading edge over a prescribed time horizon. We demonstrate the use of the analysis on a two-dimensional flow over a flat plate aerofoil and a three-dimensional turbulent flow over an SD$7003$ aerofoil. The results from the network analysis reveal that the optimal timing for introducing disturbances occurs slightly after the onset of flow separation, before the shear layer rolls up and forms the core of the dynamic stall vortex. The broadcast modes also show that the vortical nodes along the shear layer are optimal for introducing disturbances, hence providing guidance to actuator placement. Leveraging these insights, we perform nonlinear simulations of controlled flows by introducing flow actuation that targets the shear layer slightly after the separation onset. We observe that the network-guided control results in a $21 \,\%$ and $14\,\%$ reduction in peak lift for flows over the flat plate and SD$7003$ aerofoil, respectively. A corresponding decrease in vorticity injection from the aerofoil surface under the influence of control is observed from simulations, which aligns with the objective of the network broadcast analysis. The study highlights the potential of integrating the DVMs with the network analysis to design an effective active flow control strategy for unsteady aerodynamics.

We study natural convection in porous media using a lattice Boltzmann method that recovers the incompressible Navier–Stokes–Fourier dynamics. The porous structure consists of a staggered two-dimensional cylinder array with half-cylinders at the walls, forming a Darcy continuum at the domain scale. Hydrodynamic reference simulations reveal distinct flow regimes: laminar (Darcy), steady inertial (Forchheimer) and vortex shedding. We then analyse the effects of porosity and solid-to-fluid conductivity ratio ($k_s/k_{\!f}$) on natural convection. At low porosity ($\varphi = 33\,\%$), convection is highly sensitive to thermal coupling, particularly for insulating solids, whereas conductive matrices buffer this effect through lateral diffusion. Increasing porosity ($\varphi = 43\,\%$) smooths the transition as solid and fluid phases become more balanced. Across the explored range, two inertial regimes emerge governed by plume-scale confinement. The transition from Darcy to inertia-driven convection begins once the dynamics resembles the Forchheimer regime of the reference simulations. Based on our data, the system is governed by the confinement parameter $\varLambda$, which relates the plume-neck width, equivalent to the thermal boundary-layer thickness, to the pore scale: for $\varLambda \gtrsim 1$, the dynamics follows Forchheimer scaling, while for $\varLambda \lt 1/2$ it shifts toward Rayleigh–Bénard behaviour. Comparison with experimental data shows the same trend: the nominal Darcy–Rayleigh-to-porous-Prandtl ratio, $Ra^*/\textit{Pr}_{\!p} \approx 1$, holds for $\varLambda \gt 10$, but weaker confinement causes earlier departure. Finally, we revise benchmark Nusselt numbers for a cavity with square obstacles, showing that the reference by Merrikh & Lage (2005 Intl J. Heat Transfer 48(7), 1361–1372) misrepresents trends due to improper normalisation.

For decades, it has been established that there are two distinct types of instability waves leading to rotating stall in compressors, known as modes and spikes. Modal-type stall inception can be explained by conventional stability theory; however, spike-type instabilities are inherently nonlinear, whose exploration requires a different theoretical approach. For this problem, a two-dimensional point vortex instability model is developed in this paper. This simple model represents a cascade of blades by a row of bound vortices and large-scale shed vortices by point vortices. It assumes that lift on an overloaded blade abruptly drops as local incidence exceeds a critical value, analogous to leading edge stall of an isolated aerofoil, such that local cascade characteristic can be expressed as a discontinuous function. The nonlinearity thus introduced precludes the possibility of modal-type inception. As the results show, a localised stall cell will be formed in the cascade once a local perturbation triggers a discontinuous drop in blade loading, which is bounded by the stall and starting vortices shed respectively from the stalling and unstalling blades. Accordingly, a spike appears in the calculated velocity or pressure trace, directly growing into rotating stall. With this model, the experimentally observed features of spike stall are qualitatively reproduced. Moreover, the temporal variation of the stall cell size is predicted for the first time, showing qualitative agreement with existing experiments. Finally, a new prediction is made that the spike amplitude increases approximately linearly with time, in contrast to the exponential growth of linear modes.

We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that capture the small-scale dynamics. This framework is consistent with high-Reynolds-number asymptotic theory and offers a promising approach to constructing time-periodic finite-amplitude solutions in a broad class of spatially developing shear flows. As a first application, we consider a non-uniformly curved channel flow, assuming that a finite-amplitude travelling-wave solution of plane Poiseuille flow is sustained at the inlet. The method allows for the estimation of momentum transport and highlights the impact of the inlet condition on both the transport properties and the overall flow structure. We then consider a case with gradually decreasing curvature, starting with Dean vortices at the inlet. In this setting, small external oscillatory disturbances can give rise to subcritical self-sustained states that persist even after the curvature vanishes.

For a perturbed trefoil vortex knot evolving under the Navier–Stokes equations, a sequence of $\nu$-independent times $t_m$ are identified that correspond to a set of scaled, volume-integrated vorticity moments $\nu ^{1/4}\mathcal{O}_{\textit{Vm}}$, with this hierarchy $t_\infty \leqslant \ldots \leqslant t_m\ldots t_1=t_x\approx 40$ and $\mathcal{O}_{\textit{Vm}}=(\int _{V\ell }|\omega |^{2m}\,{\rm d}V)^{1/2m}$. For the volume-integrated enstrophy $Z(t)$, convergence of $\sqrt {\nu }Z(t)=\bigl (\nu ^{1/4}\mathcal{O}_{\textit{V}\text{1}}(t)\bigr )^2$ at $t_x=t_1$ marks the end of reconnection scaling. Physically, reconnection follows from the formation of a double vortex sheet, then a knot, which splits into spirals. Meanwhile $Z$ accelerates, leading to approximate finite-time $\nu$-independent convergence of the energy dissipation rate $\epsilon (t)=\nu Z(t)$ at $t_\epsilon \sim 2t_x$. This is sustained over a finite temporal span of at least $\Delta T_\epsilon \searrow 0.5 t_\epsilon$, giving Reynolds number independent finite-time, temporally integrated dissipation, $\Delta E_\epsilon =\int _{\Delta T_\epsilon }\epsilon \,{\rm d}t$, and thus satisfies one definition for a dissipation anomaly, with enstrophy spectra that are consistent with transient $k^{1/3}$ Lundgren-like inertial scaling over some of the $\Delta T_\epsilon$ time. A critical factor in achieving these temporal convergences is how the computational domain $V_\ell =(2\ell \pi )^3$ is increased as $\ell \sim \nu ^{-1/4}$, for $\ell =2$ to 6, then to $\ell =12$, as $\nu$ decreases. Appendix A shows compatibility with established $(2\pi )^3$ mathematics where $\nu \equiv 0$ Euler solutions bound small $\nu$ Navier–Stokes solutions. Two spans of $\nu$ are considered. Over the first factor of 25 decrease in $\nu$, most of the $\nu ^{1/4}\mathcal{O}_{\textit{Vm}}(t)$ converge to their respective $t_m$. For the next factor of 5 decrease (125 total) in $\nu$, with increased $\ell$ to $\ell =12$, there is initially only convergence of $\nu ^{1/4}\varOmega _{V\infty }(t)$ to $t_\infty$, without convergence for $9\gt m\gt 1$. Nonetheless, there is later $\sqrt {\nu }Z(t)$ convergence at $t_1=t_x$ and $\epsilon (t)=\nu Z$ over $t\sim t_\epsilon \approx 2t_x$.

Whilst surface-stress integration remains the standard approach for fluid force evaluation, control-volume integral methods provide deeper physical insights through functional relationships between the flow field and the resultant force. In this work, by introducing a second-order tensor weight function into the Navier–Stokes equations, we develop a novel weighted-integral framework that offers greater flexibility and enhanced capability for fluid force diagnostics in incompressible flows. Firstly, in addition to the total force and moment, the weighted integral methods establish, for the first time, rigorous quantitative connections between the surface-stress distribution and the flow field, providing potential advantages for flexible body analyses. Secondly, the weighted integral methods offer alternative perspectives on force mechanisms, through vorticity dynamics or pressure view, when the weight function is set as divergence-free or curl-free, respectively. Thirdly, the derivative moment transformation (DMT)-based integral methods (Wu et al., J. Fluid Mech. vol. 576, 2007, 265–286) are generalised to weighted formulations, by which the interconnections among the three DMT methods are clarified. In the canonical problem of uniform flow past a circular cylinder, weighted integral methods demonstrate advantages in yielding new force expressions, improving numerical accuracy over original DMT methods, and enhancing surface-stress analysis. Finally, a force expression is derived that relies solely on velocity and acceleration at discrete points, without spatial derivatives, offering significant value for experimental force estimation. This weighted integral framework holds significant promise for flow diagnostics in fundamentals and applications.

We present a back-in-time analysis for the origin of vorticity in viscous separated flows over immersed bodies, using the adjoint-vorticity framework recently introduced by Xiang et al. (2025 J. Fluid Mech. vol. 1011, A33. The solution of the adjoint-vorticity equations yields the volume density of mean deformation, which captures the stretching and tilting of the earlier vorticity that leads to the terminal value. The analysis also takes into account the boundary contributions of vorticity and its flux. Three examples are considered. Steady, axisymmetric separation in the flow over a sphere at Reynolds number $Re=200$ is shown to be established due to wall flux from both upstream and downstream of separation, the latter contribution being absent from the classical description by Lighthill. For unsteady separation at higher $Re=300$, the streamwise vorticity within the wake hairpin vortex is traced back, quantitatively, to the azimuthal vorticity on the sphere. The third configuration is the flow over a prolate spheroid at $Re=3000$. The null vorticity at three-dimensional separation originates from the cancellation of opposite interior contributions adjacent to the separation surface. The contribution from the downstream side migrates across the separation surface into the upstream region due to a tilting effect – a fundamental distinction between two- and three-dimensional separation. We also examine the detached vortical structures. The streamwise vorticity in the primary vortex originates from tilting of near-wall azimuthal vorticity, differing from Lighthill’s conjecture that the origin is streamwise near-wall vorticity that arises due to the reduced Coriolis force. Finally, a necklace vortex in the turbulent wake is traced back in time, and is shown to have contributions from the spheroid trailing-edge shed shear layer and the large-scale counter-rotating primary vortices.

The interaction between a coherent vortex ring and an inertial particle is studied through a combination of experimental and numerical methods. The vortex ring is chosen as a model flow ubiquitous in various geophysical and industrial flows. A detailed description of the vortex properties together with the evolution of the particle kinematics during the interaction is addressed thanks to time-resolved particle image velocimetry and three-dimensional shadowgraphy visualisations. Complementary, direct numerical simulations are realised with a one-way coupling model for the particle, allowing for the identification of the elementary forces responsible for the interaction behaviours. The experimental and numerical results unequivocally demonstrate the existence of three distinct interaction regimes in the parameter range of the present study: simple deviation, strong deviation and capture. These regimes are delineated as functions of key controlled dimensionless parameters, namely, the Stokes number and the initial radial position of the particle relative to the vortex ring axis of propagation.

A large-scale parametric study of the flow over the prolate spheroid is presented to understand the effect of Reynolds number and angle of attack on the separation, the wake formation and the loads. Large-eddy simulation is performed for six Reynolds numbers ranging from ${\textit{Re}} = 0.15\times 10^6$ to $4 \times 10^6$ and for eight angles of attack ranging from $\alpha = 10^\circ$ to $\alpha = 90^\circ$. For all the cases considered, the boundary layer separates symmetrically and forms a recirculation region. Several distinct flow topologies are observed that can be grouped into three categories: proto-vortex, coherent vortex and recirculating wake. In the proto-vortex state, the recirculation does not have a distinct centre of rotation, instead, a two-layer detached flow structure is formed. In the coherent vortex state, the separated shear layer rolls into a three-dimensional vortex that is aligned with the axis of the spheroid. This vortex has a clear centre of rotation corresponding to a minimum of pressure and transforms the transverse momentum from the separated shear layer into axial momentum. In the recirculating wake regime, the recirculation is incoherent and the primary separation forms a dissipative shear layer that is convected in the direction of the free stream. This symmetric pair of shear layers bounds a low-momentum recirculating cavity on the leeward side of the spheroid. The properties of these states are not constant, but evolve along the axis of the spheroid and are dictated by the characteristics of the boundary layer at separation. The variation of the flow with Reynolds number and angle of attack is described, and its connection to the loads on the spheroid are discussed.

Single-cell tornado-like vortices (TLVs) exhibit periodic wandering fluctuations around the time-averaged vortex core, a phenomenon known as vortex wandering, which constitutes the most prominent periodic behaviour in such flows. The coupling between vortex motion and wandering creates complex swirl dynamics, posing significant analytical challenges. However, the limited availability of experimental studies on vortex wandering decomposition hampers a deeper understanding of this phenomenon. To address this gap, a tornado simulator was designed to generate a controllable single-cell TLV, and high-frequency velocity data were obtained using particle image velocimetry. A sparsity-promoting dynamic mode decomposition (sp-DMD) method was developed to decouple coherent structures and analyse dynamic characteristics. Results show that as the swirl ratio increases, the vortex structure becomes more diffuse, with significant reductions in intensity. Vortex wandering is present across all swirl conditions, with its periodicity strongly modulated by the swirl ratio. Importantly, sp-DMD identified two primary modes, the time-averaged mode (first mode), representing the dominant rotational vortex motion, and the vortex-wandering-dominated modes (second and third conjugate modes), which correspond to persistent periodic velocity fluctuations and contribute the most significant pulsations. These modes exhibit a pair of oppositely rotating vortices symmetrically revolving around the central flow axis. Visualisations of the Q criterion reveal a symmetric dipole pattern. This suggests that rotational and shear effects are likely responsible for the periodic movement of the vortex core. Furthermore, as the swirl ratio increases, the energy of the vortex-wandering-dominated modes diminishes, and motion transitions from high-energy, organised dynamics to low-energy, disordered behaviour.

We investigate the effectiveness of linear optimal perturbation (LOP) for the flow past a finite span wing in reducing the lifespan of its trailing vortex system. Two approaches, referred to as local and model analysis, are introduced and used for our investigation. Both analyses assume that the baseflow is parallel. Local analysis is suited for intermediate distance from the wing where both tip vortices (TVs) and trailing edge wake (TEW) are present. Its results suggest that the unperturbed baseflow is stable. The separation between TVs and TEW increases downstream and their dynamics appear to be uncoupled at large distance from the wing. When perturbation corresponding to LOP is added to the baseflow, the vortices are displaced forming a helical twist. With time, the maximum displacement initially increases and then saturates. The perturbation retains its compact wavepacket-like structure, and perturbation energy within the tip vortex remains nearly constant. In the model analysis, the far wake is modelled as a pair of counter-rotating $q$-vortices. For low Reynolds number, the flow is stable. However, for higher Reynolds number, the trailing vortices develop Crow instability. Its growth rate is found to be in good agreement with earlier studies. Instability leads to contact of vortices, resulting in the formation of vortex rings. The time for vortex contact decreases with increase in the strength of the initial perturbation. The results suggest that LOP is effective in reducing the lifespan of trailing vortices.

A backward swept shape is one of the common features of the wings and fins in animals, which is argued to contribute to leading-edge vortex (LEV) attachment. Early research on delta wings proved that swept edges could enhance the axial flow inside the vortex. However, adopting this explanation to bio-inspired flapping wings and fins yields controversial conclusions, in that whether and how enhanced spanwise flow intensifies the vorticity convection and vortex stretching is still unclear. Here, the flapping wings and fins are simplified into revolving plates with their outboard 50 $\%$ span swept backward in either linear or nonlinear profiles. The local spanwise flow is found to be enhanced by these swept designs and further leads to stronger vorticity convection and vortex stretching, thus contributing to local LEV attachment and postponing bursting. These results further prove that a spanwise gradient of incident velocity is sufficient to trigger a regulation of LEV intensity, and a concomitant gradient of incident angle is not necessary. Moreover, an attached trailing-edge vortex is generated on a swept wing and induces an additional low-pressure region on the dorsal surface. The lift generation of swept wings is inferior to that of the rectangular wing because the extended stable LEV along the span and the additional suction force near the trailing edge are not comparable to the lift loss due to the reduced LEV intensity. Our findings evidence that a swept wing can enhance the spanwise flow and vorticity transport, as well as limit excessive LEV growth.

We investigate Lighthill’s proposed turbulent mechanism for near-wall concentration of spanwise vorticity by calculating mean flows conditioned on motion away from or toward the wall in an (friction Reynolds number) ${\textit{Re}}_\tau =1000$ database of plane-parallel channel flow. Our results corroborate Lighthill’s proposal throughout the entire logarithmic layer, but extended by counter-flows that help explain anti-correlation of vorticity transport by advection and by stretching/tilting. We present evidence also for Lighthill’s hypothesis that the vorticity transport in the log layer is a ‘cascade process’ through a scale hierarchy of eddies, with intense competition between transport outward from and inward to the wall. Townsend’s model of attached eddies of hairpin-vortex type accounts for half of the vorticity cascade, whereas we identify necklace type or ’shawl vortices’ that envelop turbulent sweeps as supplying the other half.

High-resolution particle image velocimetry (PIV) particle-to-velocity analyses using small interrogation areas (IAs) often require substantial processing time. To overcome this limitation, a generative adversarial network (GAN)-based model is proposed to achieve spatio-temporal super-resolution (SR) reconstruction from low-resolution PIV data with large IAs, thereby significantly reducing post-processing time. Time-resolved PIV measurements of plasma-induced vortex flows, covering vortex formation, growth, transition and breakdown stages, are employed to train and evaluate the model with multi-scale vortical structures. By sequentially constructing spatial and temporal datasets, the GAN-based model enables reliable SR reconstruction at different scaling factors. Reconstruction accuracy is systematically assessed using time-averaged, instantaneous and phase-averaged velocity fields. At SR factors of $\times$4 and $\times$8, the reconstructed fields closely match high-resolution references, effectively capturing both fluctuating velocities and small-scale vortical structures. In contrast, $\times$16 reconstructions exhibit diminished accuracy due to the loss of fine-scale information from highly downsampled inputs. For time-averaged fields, high-resolution reconstructions reliably capture plasma jet characteristics at all SR factors. To enhance generalisation, transfer learning is introduced to fine tune the parameters of SR-related layers in the generator, enabling accurate reconstructions under varying vortex dynamics. In addition, the efficiency gains in PIV particle-to-velocity analysis and the fundamental limitations on achievable SR factors imposed by spatio-temporal data correlations are discussed. This study demonstrates that GAN-based spatio-temporal SR models offer a promising approach to accelerate PIV analyses while maintaining high reconstruction fidelity with diverse flow conditions.

Amphibious unmanned vehicles promise next-generation water-based missions by eliminating the need for multiple vehicles to traverse water and air separately. Existing research-grade quadrotors can navigate in water and air and cross the water–air boundary, but it remains unclear how their transition is affected by rotor kinematics and geometry. We present here experimental results from isolated small rotors (diameters $\sim 10\,\mathrm{cm}$) dynamically transitioning from water to air. We discovered that rotors experience an abrupt change in frequency, lift and torque before reaching the interface, and the change is linked to the surface depression caused by a free surface vortex. We explored how the surface dynamics are affected by advance ratio, rotor diameter, number of rotor blades and input throttle. Free surface vortices above rotating objects have been studied in the context of unbaffled stirred tanks, but not in the field of small amphibious rotorcraft. We show that existing free surface vortex models can be adapted to explain water-to-air rotor performance. A better understanding of water–air rotor transitions helps to (i) assess the amphibious capability of existing aerial rotors, and (ii) suggest efficient water–air transition strategies for next-generation amphibious vehicles.

Quantum turbulence is characterised by the collective motion of mutually interplaying thin and discrete vortex filaments of fixed circulation which move in two mutually interacting fluid components. Despite this very peculiar nature determined by quantum-mechanical effects, turbulence in quantum fluids may exhibit very similar features to classical turbulence in terms of the vortex dynamics, energy spectrum and decay and intermittency. The recent work by Blaha et al. (2025 J. Fluid. Mech. 1015, A57) reveals an additional classical behaviour of quantum turbulence, by showing that the trajectories of starting vortices shed by accelerating airfoils in a quantum fluid are almost indistinguishable from their counterpart in classical viscous flows. These results strongly support the suggestive idea that turbulent flows, both classical and quantum, may be described by the collective dynamics of interacting, thin and discrete filaments of fixed circulation.