At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding and unsteady force production. Furthermore, low-aspect-ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading-edge flow separation and a strong, persistent tip vortex over a Reynolds number range of $600 \leq Re \leq 10{\,}000$. In performing this study, we aim to bridge the insight gained from existing low-Reynolds-number studies of separated flow on finite wings ($Re \approx 10^2$) and turbulent flows at higher Reynolds numbers ($Re \approx 10^4$). Our study suggests two primary effects of the Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from $Re = 600$ to $Re = 2500$. Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond $Re = 2500$, an observation attributed to the stabilising impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flow field may be adjusted for higher-Reynolds-number applications.

We present a data-driven feedforward control to attenuate large transient lift experienced by an airfoil disturbed by an extreme level of discrete vortex gust. The current analysis uses a nonlinear machine-learning technique to compress the high-dimensional flow dynamics onto a low-dimensional manifold. While the interaction dynamics between the airfoil and extreme vortex gust are parametrized by its size, gust ratio and position, the wake responses are well captured on this simple manifold. The effect of extreme vortex disturbance about the undisturbed baseline flows can be extracted in a physically interpretable manner. Furthermore, we call on phase-amplitude reduction to model and control the complex nonlinear extreme aerodynamic flows. The present phase-amplitude reduction model reveals the sensitivity of the dynamical system in terms of the phase shift and amplitude change induced by external forcing with respect to the baseline periodic orbit. By performing the phase-amplitude analysis for a latent dynamical model identified by sparse regression, the sensitivity functions of low-dimensionalized aerodynamic flows for both phase and amplitude are derived. With the phase and amplitude sensitivity functions, optimal forcing can be determined to quickly suppress the effect of extreme vortex gusts towards the undisturbed states in a low-order space. The present optimal flow modification built upon the machine-learned low-dimensional subspace quickly alleviates the impact of transient vortex gusts for a variety of extreme aerodynamic scenarios, providing a potential foundation for flight of small-scale air vehicles in adverse atmospheric conditions.

Roughness of the surface underlying the atmospheric boundary layer causes departures of the near-surface scalar and momentum transport in comparison with aerodynamically smooth surfaces. Here, we investigate the effect of $56\times 56$ homogeneously distributed roughness elements on bulk properties of a turbulent Ekman flow. Direct numerical simulation in combination with an immersed boundary method is performed for fully resolved, three-dimensional roughness elements. The packing density is approximately $10\,\%$ and the roughness elements have a mean height in wall units of $10 \lesssim H^+ \lesssim 40$. According to their roughness Reynolds numbers, the cases are transitionally rough, although the roughest case is on the verge of being fully rough. We derive the friction of velocity and of the passive scalar through vertical integration of the respective balances. Thereby, we quantify the enhancement of turbulent activity with increasing roughness height and find a scaling for the friction Reynolds number that is verified up to $Re_\tau \approx 2700$. The higher level of turbulent activity results in a deeper logarithmic layer for the rough cases and an increase of the near-surface wind veer in spite of higher $Re_\tau$. We estimate the von Kármán constant for the horizontal velocity $\kappa _{m}=0.42$ (offset $A=5.44$) and for the passive scalar $\kappa _{h}=0.35$ (offset $\mathbb {A}=4.2$). We find an accurate collapse of the data under the rough-wall scaling in the logarithmic layer, which also yields a scaling for the roughness parameters $z$-nought for momentum ($z_{0{m}}$) and the passive scalar ($z_{0{h}}$).

Previous work suggests that the arrangement of elements in an obstruction may influence the bulk flow velocity through the obstruction, but the physical mechanisms for this influence are not yet clear. This is the motivation for this study, where direct numerical simulation is used to investigate flow through an array of cylinders at a resolution sufficient to observe interactions between wakes of individual elements. The arrangement is altered by varying the gap ratio $G/d$ (1.2 – 18, G is the distance between two adjacent cylinders, d is the cylinder diameter), array-to-element diameter ratio $D/d$ (3.6 – 200, D is the array diameter), and incident flow angle ($0^{\circ} - 30^{\circ}$). Depending on the element arrangement, it is found that the average root-mean-square lift and drag coefficients can vary by an order of magnitude, whilst the average time-mean drag coefficient of individual cylinders ($\overline{C_{d}}$), and the bulk velocity are found to vary by up to $50\,\%$ and a factor of 2, respectively. These arrangement effects are a consequence of the variation in flow and drag characteristics of individual cylinders within the array. The arrangement effects become most critical in the intermediate range of flow blockage parameter $\mathit{\Gamma_{D}^{\prime}} = 0.5-1.5$ ($\mathit{\Gamma_{D}^{\prime}}=\overline{C_{d}}aD/(1-\phi)$, where a is frontal element area per unit volume, and $\phi$ is solid volume fraction), due to the high variability in element-scale flow characteristics. Across the full range of arrangements modelled, it is confirmed that the bulk velocity is governed by flow blockage parameter but only if the drag coefficient incorporates arrangement effects. Using these results, this paper proposes a framework for describing and predicting flow through an array across a variety of arrangements.

The motion of rigid particles in complex fluids is ubiquitous in natural and industrial processes. The most popular toy model for understanding the physics of such systems is the settling of a solid sphere in a viscoelastic fluid. There is general agreement that an elastic wake develops downstream of the sphere, causing the breakage of fore-and-aft symmetry, while the flow remains axisymmetric, independent of fluid viscoelasticity and flow conditions. Using a continuum mechanics model, we reveal that axisymmetry holds only for weak viscoelastic flows. Beyond a critical value of the settling velocity, steady, non-axisymmetric disturbances develop peripherally of the rear pole of the sphere, giving rise to a four-lobed fingering instability. The transition from axisymmetric to non-axisymmetric flow fields is characterized by a regular bifurcation and depends solely on the interplay between shear and extensional properties of the viscoelastic fluid under different flow regimes. At higher settling velocities, each lobe tip is split into two new lobes, resembling fractal fingering in interfacial flows. For the first time, we capture an elastic fingering instability under steady-state conditions, and provide the missing information for understanding and predicting such instabilities in the response of viscoelastic fluids and soft media.

Recently, direct numerical simulations (DNS) of stably stratified turbulence have shown that as the Prandtl number ($Pr$) is increased from 1 to 7, the mean turbulent potential energy dissipation rate (TPE-DR) drops dramatically, while the mean turbulent kinetic energy dissipation rate (TKE-DR) increases significantly. Through an analysis of the equations governing the fluctuating velocity and density gradients we provide a mechanistic explanation for this surprising behaviour and test the predictions using DNS. We show that the mean density gradient gives rise to a mechanism that opposes the production of fluctuating density gradients, and this is connected to the emergence of ramp cliffs. The same term appears in the velocity gradient equation but with the opposite sign, and is the contribution from buoyancy. This term is ultimately the reason why the TPE-DR reduces while the TKE-DR increases with increasing $Pr$. Our analysis also predicts that the effects of buoyancy on the smallest scales of the flow become stronger as $Pr$ is increased, and this is confirmed by our DNS data. A consequence of this is that the standard buoyancy Reynolds number does not correctly estimate the impact of buoyancy at the smallest scales when $Pr$ deviates from 1, and we derive a suitable alternative parameter. Finally, an analysis of the filtered gradient equations reveals that the mean density gradient term changes sign at sufficiently large scales, such that buoyancy acts as a source for velocity gradients at small scales, but as a sink at large scales.

We investigate the dynamics of a gas jet impinging perpendicular to a thin liquid film dragged by a rising vertical substrate. This configuration is relevant to the jet-wiping process in hot-dip galvanization and it is unstable. Previous studies analysed the dynamics of the instability in the case of liquids with low Kapitza numbers (highly viscous liquids), more amenable to experimental and numerical investigations. This work extends the previous investigations by focusing on the wiping at much higher Kapitza numbers, which are more relevant to the galvanizing process. The simulations are carried out by combining volume of fluid and large-eddy simulations, and the dynamics of the gas–liquid interaction is analysed using extended multiscale proper orthogonal decomposition. The simulations allowed for analysing the jet-wiping instability in new flow conditions. Despite the largely different conditions, the results show that the interaction between the gas jet and the liquid film is qualitatively similar, featuring two-dimensional waves in the liquid correlated with oscillations and deflections of the gas jet in all cases. The wave characteristics (e.g. frequency and propagation speed) scale remarkably well using the Shkadov-like scaling based on the liquid, suggesting a dominant role of the liquid film in the coupling, and potentially enabling extrapolation of the results to a broader range of wiping conditions. Finally, we use the numerical results to discuss the limitations of liquid-film models, which constitute currently the only possible approach to study the jet-wiping process in industrial conditions.

Chiral fluids – such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids – flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional (3-D) anisotropic chiral fluid, we predict counterintuitive phenomena such as motion at an angle to the direction of applied forces and spinning under the force of gravity.

Thin-film equations are utilised in many different areas of fluid dynamics when there exists a direction in which the aspect ratio can be considered small. We consider thin free films with Marangoni effects in the extensional flow regime, where velocity gradients occur predominantly along the film. In practice, because of the local deposition of surfactants or input of energy, asymmetric distributions of surfactants or surface tension more generally, are possible. Such examples include the surface of bubbles and the rupture of thin films. In this study, we consider the asymmetric thin-film equations for extensional flow with Marangoni effects. Concentrating on the case of small Reynolds number $ Re $, we study the deposition of insoluble surfactants on one side of a liquid sheet otherwise at rest and the resulting thinning and rupture of the sheet. The analogous problem with a uniformly thinning liquid sheet is also considered. In addition, the centreline deformation is discussed. In particular, we show analytically that if the surface tension isotherm $\sigma = \sigma (\varGamma )$ is nonlinear (surface tension $\sigma$ varies with surfactant concentration $\varGamma$), then accounting for top–bottom asymmetry leads to slower (faster) thinning and pinching if $\sigma = \sigma (\varGamma )$ is convex (concave). The analytical progress reported in this paper allows us to discuss the production of satellite drops from rupture via Marangoni effects, which, if relevant to surface bubbles, would be an aerosol production mechanism that is distinct from jet drops and film drops.

The effects of thermal convection on turbulence in accretion discs, and particularly its interplay with the magnetorotational instability (MRI), are of significant astrophysical interest. Despite extensive theoretical and numerical studies, such an interplay has not been explored experimentally. We conduct linear analysis of the azimuthal version of MRI (AMRI) in the presence of thermal convection and compare the results with our experimental data published before. We show that the critical Hartmann number ($Ha$) for the onset of AMRI is reduced by convection. Importantly, convection breaks symmetry between $m = \pm 1$ instability modes ($m$ is the azimuthal wavenumber). This preference for one mode over the other makes the AMRI wave appear as a ‘one-winged butterfly’.

Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae that coalesce due to molecular diffusion. Owing to the linearity of the advection–diffusion equation, coalescence can be envisioned as an aggregation process. Here, we demonstrate that in smooth two-dimensional chaotic flows, mixing obeys a correlated aggregation process, where the spatial distribution of the number of lamellae in aggregates is highly correlated with their elongation, and is set by the fractal properties of the advected material lines. We show that the presence of correlations makes mixing less efficient than a completely random aggregation process because lamellae with similar elongations and scalar levels tend to remain isolated from each other. We show that correlated aggregation is uniquely determined by a single exponent that quantifies the effective number of random aggregation events. These findings expand aggregation theories to a larger class of systems, which have relevance to various fundamental and applied mixing problems.

In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where the contact line is almost perpendicular to the cylinder wall whereas a small angle forms between the contact line and the substrate, and the film size is smaller than the cylinder radius. The film stability, which depends on the film size and the wall wettability, is first predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and postinstability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and volume-of-fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighbouring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighbouring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.

Turbulence can have a strong effect on the fall speed of snowflakes and ice crystals. In this experimental study, the behaviour of thin disks falling in homogeneous turbulence is investigated, in a range of parameters relevant to plate crystals. Disks ranging in diameter from 0.3 to 3 mm, and in Reynolds number $Re = 10\unicode{x2013}435$, are dispersed in two air turbulence levels, with velocity fluctuations comparable to the terminal velocity. For each case, thousands of trajectories are captured and reconstructed by high-speed laser imaging, allowing for statistical analysis of the translational and rotational dynamics. Air turbulence reduces the disk terminal velocities by up to 35 %, with the largest diameters influenced most significantly, which is primarily attributed to drag nonlinearity. This is evidenced by large lateral excursions of the trajectories, which correlate with cross-flow-induced drag enhancement as reported previously for falling spheres and rising bubbles. As the turbulence intensity is increased, flat-falling behaviour is progressively eliminated and tumbling becomes prevalent. The rotation rates of the tumbling disks, however, remain similar to those displayed in still air. This is due to their large moment of inertia compared to the surrounding fluid, in stark contrast with studies conducted in water. In fact, the observed reduction of settling velocity is opposite to previous findings on disks falling in turbulent water. This emphasizes the importance of the solid-to-fluid density ratio in analogous experiments that aim to mimic the behaviour of frozen hydrometeors.

The $k^{-23/6}$ wave action spectrum with an inverse cascade is one of the fundamental Kolmogorov–Zakharov solutions for gravity wave turbulence, which is part of the citation for the Dirac Medal in 2003. Instead of confirming this solution, however, several existing simulations and experiments suggest a spectrum of $k^{-3}$ in set-ups corresponding to the inverse cascade. We provide a theoretical explanation for the latter, considering the condensate that naturally forms in finite domains of experiments/simulations. Our new theory hinges on: (1) derivation of a spectral diffusion equation when non-local interactions with the condensate become dominant, for the first time systematically formulated for quartet-interaction systems; and (2) careful analysis of the asymptotics of interaction coefficient with a remarkable cancellation of all leading-order terms.

A high-resolution simulation of a thermal vortex ring is analysed from the point of view of the vortex dynamics. A power-spectrum analysis of vortex-ring sections suggests that the simulated flows are overall ‘two dimensional’ in the large-scale limit, being dominated by axisymmetric components, but with a substantial contribution from the non-axisymmetric component at small scales. Contribution of the non-axisymmetric components is negligible in budgets of volume integrals of the vorticity and potential vorticity as well as the impulse (moments of the vorticity weighted by $s^n$ with $n=-1$, 0, 1, where $s$ is the distance from the vertical axis of the vortex ring). A concise description of the dynamics is obtained as a function of geometrical factors together with these three integral variables. Analysis shows that the geometrical factors are fairly close to constant with time, and thus, a redundant closed description of the system is obtained in the similarity regime after spin up of the vortex ring. This redundancy leads to a constraint on the geometrical factors, which is reasonably satisfied by the simulation. A closed description is also obtained over the initial spin-up period of the vortex ring by adding a phenomenologically derived prognostic equation for the source for the volume integral of the potential vorticity (with $n=-1$). Analysis of the budget supports this description.

Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as $Re$ is increased from weakly chaotic flow at $Re=40$ to a chaotic state dominated by a domain-filling vortex pair at $Re=400$. ‘Latent Fourier analysis’ (Page et al., Phys. Rev. Fluids 6, 2021, p. 034402) reveals a detached class of bursting dynamics at $Re=40$ which merge with the low-dissipation dynamics as $Re$ is increased to $100$ and provides an efficient representation within which to find unstable periodic orbits (UPOs) using recurrent flow analysis. Focusing on initial guesses with energy in higher latent Fourier wavenumbers allows a significant number of high-dissipation-rate UPOs associated with the bursting events to be found for the first time. At $Re=400$, the UPOs discovered at lower $Re$ move away from the attractor, and an entirely different embedding structure is formed within the network devoid of small-scale vortices. Here latent Fourier projections identify an associated ‘large-scale’ UPO which we believe to be a finite-$Re$ continuation of a solution to the Euler equations.

The linear stability of plane Couette–Poiseuille flow (CPF) is studied with the physical effects of stratification, rotation and viscosity all included for the first time together. With no stratification, two instability mechanisms are present due to the shear and rotation which, for the most part, do not interact as they favour different forms of two-dimensionality. However, there are some small parts of parameter space where new three-dimensional instability appears indicating that Rayleigh's criterion is also violated in parameter space beyond where shear instability is expected. No fully localised centrifugal instabilities can be found for CPF, but they are shown to exist if the base flow shear has a maximum in the domain (the base flow needs to be at least cubic in the cross-stream variable rather than just quadratic as in CPF). With stable stratification present, new instabilities are found due to the combined effects of stratification and rotation, but only some appear to be of the resonance-type associated with the strato-rotational instability. The other unstable branches are more accurately interpreted as a stratification-modified centrifugal instability. Three-dimensional versions of this violate Rayleigh's criterion even when this is extended to include stratification. When stratification is stronger than rotation, the resonance-type instabilities are only dominant for cyclonic flows.

It is known that the dispersion of colloidal particles in porous media is determined by medium structure, pore-scale flow variability and diffusion. However, much less is known about how diffusiophoresis, that is, the motion of colloidal particles along salt gradients, impacts large-scale particle dispersion in porous media. To shed light on this question, we perform detailed pore-scale simulations of fluid flow, solute transport and diffusiophoretic particle transport in a two-dimensional hyper-uniform porous medium. Particles and solute are initially uniformly distributed throughout the medium. The medium is flushed at constant flow rate, and particle breakthrough curves are recorded at the outlet to assess the macroscopic effects of diffusiophoresis. Particle breakthrough curves show non-Fickian behaviour manifested by strong tailing that is controlled by the diffusiophoretic mobility. Although diffusiophoresis is a short-time, microscopic phenomenon owing to the fast attenuation of salt gradients, it governs macroscopic colloid dispersion through the partitioning of particles into transmitting and dead-end pores. We quantify these behaviours by an upscaled analytical model that describes both the retention and release of colloids in dead-end pores and the observed long-time tailings. Our results suggest that diffusiophoresis is an efficient tool to control particle dispersion and filtration through porous media.

Motivated by contradicting or insufficient information regarding the large-scale flow dynamics around surface-mounted finite-height square prisms of small aspect ratio, the present study investigates the dominant vortex shedding and low-frequency dynamics around a surface-mounted cube. These flow modes were obtained from the spectral proper orthogonal decomposition of large-eddy simulation results, at a Reynolds number of $\textit {Re}=1\times 10^4$ and two different types of boundary layer: a thin and laminar boundary layer with thickness $\delta /D=0.2$ and a thick and turbulent boundary layer with $\delta /D=0.8$. The main antisymmetric mode pair revealed a new flow pattern with the alternate shedding of streamwise flow structures, indicating a transition from the half-loops of taller prisms to only streamwise strands (i.e. no vertical core) for smaller aspect ratio. The formation process of the streamwise structures is due to a reorientation of the vorticity of the arch vortex in the streamwise direction characteristic of the shed structures. The low-frequency drift mode affected the length of the recirculation region, the strength of vortex shedding, and the near-wall flow field and pressure distribution on the cube's faces, leading to low-frequency variations in the fluctuating drag and normal force coefficients. These large-scale flow dynamics were similar for both boundary layers, but minor differences were identified, related mostly to the occurrence of flow attachment and the formation of a headband vortex for the thicker boundary layer.

A theory of incompressible turbulent plane jets (TPJs) is proposed by advancing an improved boundary layer approximation over the limiting classical – retaining more terms in the momentum balance equations. A pressure deficit inside the jet (with respect to the ambient) must exist due to transverse turbulence (Miller & Comings, J. Fluid Mech., vol. 3, 1957, pp. 1–16; Hussain & Clarke, Phys. Fluids, vol. 20, 1977, pp. 1416–1426). Contrary to the universally accepted invariance of the total momentum flux $J_T(x)$ (non-dimensionalized by its inlet value) as a function of the streamwise distance $x$, we prove that $J_T(x) >1$ – a condition that all TPJs must satisfy; surprisingly, prior theories and most experiments do not satisfy this condition. This motivated us to apply Lie symmetry analysis with translational and dilatational transformations of the modified equations (incorporating $J_T>1$), which yields scaling laws for key jet measures: the mean streamwise and transverse velocities $U(x,y)$ and $V(x,y)$, the turbulence intensities, the Reynolds shear stress $-\rho \,\overline {u'v'}(x,y)$, the mean pressure $P(x,y)$, etc. Experiments satisfying $J_T(x)>1$ validate our predictions for all jet measures, including, among others, the profiles of $U$, $V$ and $-\rho \,\overline {u'v'}$. We further predict $U \sim x^{-0.24}$, $V \sim x^{-0.45}$, $-\rho \,\overline {u'v'}\sim x^{-0.69}$, the mass flux $Q_m \sim x^{0.55}$, and $J_T$ increases to approximately 1.5. Contrary to the classical linear jet spread, we find sublinear spread, with the jet half-width growing like $b(x)\sim x^{0.79}$, indicating a narrower jet. Our predictions differ notably from most results reported in the literature. These contradictions demand revisiting jet studies involving carefully designed facilities and boundary conditions, and highly resolved simulations.