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.

Microfluidic paper-based analytical devices (${\unicode{x03BC}}$PADs) have gained considerable attention due to their ability to transport fluids without external pumps. Fluid motion in ${\unicode{x03BC}}$PADs is driven by capillary forces through the network of pores within paper substrates. However, the inherently low flow speeds resulting from the small pore sizes in paper often limit the performance of ${\unicode{x03BC}}$PADs. Recent studies have introduced multilayered ${\unicode{x03BC}}$PADs composed of stacked paper sheets, which enable significantly faster fluid transport through inter-layer channels. In this study, we present a combined theoretical and experimental investigation of water imbibition dynamics through channels formed by multiple paper layers. Upon contact with water, the paper layers absorb water and undergo swelling, altering channel geometry and consequently affecting flow dynamics. We develop a mathematical model that extends the classical Washburn equation to incorporate the effects of water absorption and swelling. The model predictions show excellent agreement with experimental observations of water flow through multilayered paper channels. The results elucidate how water absorption and swelling influence capillary imbibition, and suggest potential strategies for regulating flow rates in multilayered ${\unicode{x03BC}}$PADs.

This study introduces a boundary element method to solve the three-dimensional problem of internal tide generation over arbitrary isolated seamounts in a uniformly stratified finite-depth fluid with background rotation, without assumptions on the size or slope of the topography. Focusing on linearly propagating waves with small tidal excursions, the approach employs a vertical mode decomposition to describe the wavefield and the wave energy flux. We apply the model to the generation of internal tides by a unidirectional barotropic tide interacting with an axisymmetric Gaussian seamount. We study the conversion rate and flow field for various topographic configurations. We qualitatively recover some of the two-dimensional results of Papoutsellis et al. (2023 J. Fluid Mech. 964, A20), and find topographies with weak conversion rates, as discussed by Maas (2011 J. Fluid Mech. 684, 5–24). Furthermore, our results reveal the previously underestimated influence of the Coriolis frequency on the wavefield and on the spatial distribution of radiated energy flux. Due to Coriolis effects, the energy fluxes are shifted slightly counter-clockwise in the northern hemisphere. We explain in detail how this shift increases with the magnitude of the Coriolis frequency and the topographic features and why such effects are absent in models based on the weak topography assumption.

This study is concerned with the near-wall flow structure over a NACA 0025 aerofoil at a constant chord-based Reynolds number of 100 000 across various angles of attack, where an array of 12 circular-orifice synthetic jet actuators (SJAs) was used to reattach the flow under conditions of flow separation. The SJAs were operated in burst-mode at two distinct momentum coefficients, a 50 % duty cycle and a modulation frequency of 200 Hz, targeting the separated shear layer frequency. Particle image velocimetry was conducted using three side-by-side cameras to capture the velocity fields along the aerofoil surface at the centreline. At zero angle of attack, the velocity profiles exhibited characteristics of a turbulent boundary layer, following the law of the wall in the inner layer while deviating from the logarithmic law in the outer layer. At higher angles of attack, while some logarithmic behaviour could still be detected close to the wall, a wide region of the velocity profiles became predominantly linear, exhibiting a behaviour differing from both a canonical turbulent boundary layer and a turbulent wall jet. The entire shear flow was decomposed into three regions: the boundary layer, the jet layer and the mixing layer that extended between the two. The mixing layer was analysed by applying several scaling laws to the time-averaged velocity components, where it was revealed that the characteristic velocity of the two velocity components is different. An asymptotic solution was obtained under a low spreading rate at infinite Reynolds number, providing a theoretical basis for the experimental observations.

Vortex–magnetic interactions shape magnetohydrodynamic (MHD) turbulence, influencing energy transfer in astrophysical, geophysical and industrial systems. In the solar atmosphere, granular-scale vortex flows couple strongly with magnetic fields, channelling energy into the corona. At high Reynolds numbers, vorticity and magnetic fields are nearly frozen into the charged fluid, and MHD flows emerge from the Lorentz force mediated interactions between coherent vortex structures in matter and the field. To probe this competition in a controlled setting, we revisit the canonical problem of two antiparallel flux tubes. By varying the magnetic flux threading each tube – and thus sweeping the interaction parameter $N_i$, which gauges Lorentz-to-inertial force balance – we uncover three distinct regimes: vortex-dominated joint reconnection, instability-triggered cascade, and Lorentz-induced vortex disruption. At low $N_i$, classical vortex dynamics dominates, driving joint vortex–magnetic reconnection, and amplifying magnetic energy via a dynamo effect. At moderate $N_i$, the system oscillates between vorticity-driven attraction and magnetic damping, triggering instabilities and nonlinear interactions that spawn secondary filaments and drive an energy cascade. At high $N_i$, Lorentz forces suppress vortex interactions, aligning the tubes axially while disrupting vortex cores and rapidly converting magnetic to kinetic energy. These findings reveal how the inertial–Lorentz balance governs energy transfer and coherent structure formation in MHD turbulence, offering insight into vortex–magnetic co-evolution in astrophysical plasmas.

The effects of Reynolds number across ${\textit{Re}}=1000$, $2500$, $5000$ and $10\,000$ on separated flow over a two-dimensional NACA0012 airfoil at an angle of attack of $\alpha =14^\circ$ are investigated through biglobal resolvent analysis. We identify modal structures and energy amplifications over a range of frequencies, spanwise wavenumbers, and values of the discount parameter, providing insights across various time scales. Using temporal discounting, we find that the shear-layer dynamics dominates over short time horizons, while the wake dynamics becomes the primary amplification mechanism over long time horizons. Spanwise effects also appear over long time horizons, sustained by low frequencies. The low-frequency and high-wavenumber structures are found to be dominated by elliptic mechanisms within the recirculation region. At a fixed angle of attack and across the Reynolds numbers, the response modes shift from wake-dominated structures at low frequencies to shear-layer-dominated structures at higher frequencies. The frequency at which the dominant mechanism changes is independent of the Reynolds number. Comparisons at a different angle of attack ($\alpha =9^\circ$) show that the transition from wake to shear-layer dynamics with increasing frequency only occurs if the unsteady flow is three-dimensional. We also study the dominant frequencies associated with wake and shear-layer dynamics across the angles of attack and Reynolds numbers, and confirm characteristic scaling laws from the literature.

The effects of high-intensity, large-scale free stream turbulence on the aerodynamic loading and boundary layer flow field development on a NACA 0018 aerofoil model were studied experimentally using direct force measurements and particle image velocimetry at a chord Reynolds number of $7\times 10^4$. An active turbulence grid was used to generate free stream turbulence intensities of up to $16\,\%$ at integral length scales of the order of the aerofoil chord length. Relative to the clean flow condition with a free stream turbulence intensity of $0.1\,\%$, elevated levels of free stream turbulence intensity decrease the lift slope at low angles of attack, and increase the stall angle and maximum lift coefficient. At moderate angles of attack, high-intensity free stream turbulence causes large variations in the location of transition, with laminar flow occasionally persisting over $90\,\%$ of the chord length. At pre-stall angles of attack, high-intensity free stream turbulence causes intermittent massive separation. Variations in the extent of turbulence in the suction surface boundary layer are linked to fluctuations in effective angle of attack, suggesting that the observed variability in transition location is related to large-scale incoming flow disturbances impinging on the aerofoil model. A comparative analysis of the present results and those in previous studies for predominantly smaller integral length scales shows the importance of both the intensity and length scale of free stream turbulence on the flow development over the aerofoil.

Flag flutter frequently features a marked difference between the onset speed of flutter and the speed below which flutter stops. The hysteresis tends to be especially large in experiments as opposed to simulations. This phenomenon has been ascribed to inherent imperfections of flatness in experimental samples, which are thought to inhibit the onset of flutter but have a lesser effect once a flag is already fluttering. In this work, we present an experimental confirmation for this explanation through motion tracking. We also visualize the wake to assess the potential contribution of discrete vortex shedding to hysteresis. We then mould our understanding of the mechanism of bistability and additional observations on flag flutter into a novel, observation-based, semiempirical model for flag flutter in the form of a single ordinary differential equation. Despite its simplicity, the model successfully reproduces key features of the physical system such as bistability, sudden transitions between non-fluttering and fluttering states, amplitude growth and frequency growth.

We consider numerically a Lagrangian view of turbulent mixing in two-layer stably stratified parallel shear flow. By varying the ratio of shear layer depth to density interface thickness, these flows are prone to either a primary Kelvin–Helmholtz instability (KHI) or to a primary Holmboe wave instability (HWI). These instabilities are conventionally thought to mix qualitatively differently; by vortical ‘overturning’ of the density interface induced by KHI, or by turbulent ‘scouring’ on the edges of the density interface induced by HWI. By tracking Lagrangian particles in direct numerical simulations, so that the fluid buoyancy sampled along particle paths provides a particular Lagrangian measure of mixing, we investigate the validity of this overturning/scouring classification. The timing of mixing events experienced by particles inside and outside the interface is qualitatively different in simulations exhibiting KHI and HWI. The root mean square (r.m.s.) buoyancy for particles that start with the same buoyancy is actually larger for HWI-associated flows than for KHI-associated flows for the same bulk Richardson number $Ri_b$, implying heterogeneous mixing along particle paths for HWI. The number of particles starting close to the mid-plane of the interface which experience a change in sign in the local fluid buoyancy (and hence end up on the opposite side of the mid-plane after mixing) is compared for KHI and HWI in flows with various $Ri_b$. Perhaps surprisingly, for HWI with a large $Ri_b$, more than half of the particles that start near the mid-plane end up on the opposite side of the mid-plane.

The reconfiguration of flexible aquatic vegetation and the associated forces have been extensively studied under two-dimensional flow conditions – such as unidirectional currents, pure waves and co-directional wave–current flows. However, behaviour under more complex, orthogonal wave–current flows remains largely unexplored. In coastal environments, such orthogonal flows arise when waves propagate perpendicular to a longshore current. To improve understanding of how aquatic vegetation helps protect coastlines and attenuates waves, we extended existing effective-length scaling laws that were validated in pure currents, pure waves, and co-directional waves and currents to orthogonal wave–current conditions by introducing new definitions of the Cauchy number. Experiments were conducted in a wave–current basin, where cylindrical rubber stems were mounted on force transducers to measure hydrodynamic forces. Stem velocities were extracted from video recordings to compute the relative velocity between the flow and the stems. Incorporating the phase shift between flow and stem velocities into the force models significantly improved predictions. Comparison of predicted and measured forces showed good agreement for both pure wave and wave–current scenarios, underscoring the importance of phase shifts and velocity reduction for force estimation. Our hypothesised effective-length scaling parameters under wave–current conditions were validated, but with a higher scaling coefficient due to inertial effects from the larger material aspect ratio. These findings offer new insights into the hydrodynamics of flexible structures under complex coastal flow conditions.

Using direct numerical simulations, we systematically investigate the inner-layer turbulence of a turbulent vertical buoyancy layer (a model for a vertical natural convection boundary layer) at a constant Prandtl number of $0.71$. Near-wall streaky structures of streamwise velocity fluctuations, synonymous with the buffer layer streaks of canonical wall turbulence, are not evident at low and moderate Reynolds numbers (${\textit{Re}}$) but manifest at high ${\textit{Re}}$. At low ${\textit{Re}}$, the turbulent production in the near-wall region is negligible; however, this increases with increasing ${\textit{Re}}$. By using domains truncated in the streamwise, spanwise and wall-normal directions, we demonstrate that the turbulence production in the near-wall region at moderate and high ${\textit{Re}}$ is largely independent of large-scale motions and outer-layer turbulence. On a fundamental level, the near-wall turbulence production is autonomous and self-sustaining, and a well-developed bulk is not needed to drive the inner-layer turbulence. Near-wall streaks are also not essential for this autonomous process. The type of thermal boundary condition only marginally influences the velocity fluctuations, revealing that the turbulence dynamics are primarily governed by the mean-shear induced by the buoyancy field and not by the thermal fluctuations, despite the current flow being solely driven by buoyancy. In the inner layer, the spanwise wavelength of the eddies responsible for positive shear production is remarkably similar to that of canonical wall turbulence at moderate and high ${\textit{Re}}$ (irrespective of near-wall streaks). Based on these findings, we propose a mechanistic model that unifies the near-wall shear production of vertical buoyancy layers and canonical wall turbulence.