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.

We derive a mathematical model for the overflow fusion glass manufacturing process. In the limit of zero wedge angle, the model leads to a canonical fluid mechanics problem in which, under the effects of gravity and surface tension, a free-surface viscous flow transitions from lubrication flow to extensional flow. We explore the leading-order behaviour of this problem in the limit of small capillary number, and find that there are four distinct regions where different physical effects control the flow. We obtain leading-order governing equations, and determine the solution in each region using asymptotic matching. The downstream behaviour reveals appropriate far-field conditions to impose on the full problem, resulting in a simple governing equation for the film thickness that holds at leading order across the entire domain.

Induced diffusion (ID), an important mechanism of spectral energy transfer due to interacting internal gravity waves (IGWs), plays a significant role in driving turbulent dissipation in the ocean interior. In this study, we revisit the ID mechanism to elucidate its directionality and role in ocean mixing under varying IGW spectral forms, with particular attention to deviations from the standard Garrett–Munk spectrum. The original interpretation of ID as an action diffusion process, as proposed by McComas et al., suggests that ID is inherently bidirectional, with its direction governed by the vertical-wavenumber spectral slope $\sigma$ of the IGW action spectrum, $n \propto m^\sigma$. However, through the direct evaluation of the wave kinetic equation, we reveal a more complete depiction of ID, comprising both a diffusive and a scale-separated transfer rooted in the energy conservation within wave triads. Although the action diffusion may reverse direction depending on the sign of $\sigma$ (i.e. red or blue spectra), the net transfer by ID consistently leads to a forward energy cascade at the dissipation scale, contributing positively to turbulent dissipation. This supports the viewpoint of ID as a dissipative mechanism in physical oceanography. This study presents a physically grounded overview of ID, and offers insights into the specific types of wave–wave interactions responsible for turbulent dissipation.

We analyse the long-time dynamics of trajectories within the stability boundary between laminar and turbulent square duct flow. If not constrained to a symmetric subspace, the edge trajectories exhibit a chaotic dynamics characterised by a sequence of alternating quiescent phases and intense bursting episodes. The dynamics reflects the different stages of the well-known near-wall streak–vortex interaction. Most of the time, the edge states feature a single streak with a number of flanking vortices attached to one of the four surrounding walls. The initially straight streak undergoes a linear instability and eventually breaks in an intense bursting event. At the same time, the downstream vortices give rise to a new low-speed streak at one of the neighbouring walls, thereby causing the turbulent activity to ‘switch’ from one wall to the other. If the edge dynamics is restricted to a single or twofold mirror-symmetric subspace, the bursting and wall-switching episodes become self-recurrent in time, representing the first periodic orbits found in square duct flow. In contrast to the chaotic edge states in the non-symmetric case, the imposed symmetries enforce analogue bursting cycles to simultaneously appear at two parallel opposing walls in a mirror-symmetric configuration. Both the localisation of turbulent activity to one or two walls and the wall-switching dynamics are shown to be common phenomena in marginally turbulent duct flows. We argue that such episodes represent transient visits of marginally turbulent trajectories to some of the edge states detected here.

Symmetry-based analyses of multiscale velocity gradients highlight that strain self-amplification (SS) and vortex stretching (VS) drive forward energy transfer in turbulent flows. By contrast, a strain–vorticity covariance mechanism produces backscatter that contributes to the bottleneck effect in the subinertial range of the energy cascade. We extend these analyses by using a normality-based decomposition of filtered velocity gradients in forced isotropic turbulence to distinguish contributions from normal straining, pure shearing and rigid rotation at a given scale. Our analysis of direct numerical simulation (DNS) data illuminates the importance of shear layers in the inertial range and (especially) the subinertial range of the cascade. Shear layers contribute significantly to SS and VS and play a dominant role in the backscatter mechanism responsible for the bottleneck effect. Our concurrent analysis of large-eddy simulation (LES) data characterizes how different closure models affect the flow structure and energy transfer throughout the resolved scales. We thoroughly demonstrate that the multiscale flow features produced by a mixed model closely resemble those in a filtered DNS, whereas the features produced by an eddy viscosity model resemble those in an unfiltered DNS at a lower Reynolds number. This analysis helps explain how small-scale shear layers, whose imprint is mitigated upon filtering, amplify the artificial bottleneck effect produced by the eddy viscosity model in the inertial range of the cascade. Altogether, the present results provide a refined interpretation of the flow structures and mechanisms underlying the energy cascade and insight for designing and evaluating LES closure models.

Transonic buffet presents time-dependent aerodynamic characteristics associated with shock, turbulent boundary layer and their interactions. Despite strong nonlinearities and a large degree of freedom, there exists a dominant dynamic pattern of a buffet cycle, suggesting the low dimensionality of transonic buffet phenomena. This study seeks a low-dimensional representation of transonic airfoil buffet at a high Reynolds number with machine learning. Wall-modelled large-eddy simulations of flow over the OAT15A supercritical airfoil at two Mach numbers, $M_\infty = 0.715$ and 0.730, respectively producing non-buffet and buffet conditions, at a chord-based Reynolds number of ${Re} = 3\times 10^6$ are performed to generate the present datasets. We find that the low-dimensional nature of transonic airfoil buffet can be extracted as a sole three-dimensional latent representation through lift-augmented autoencoder compression. The current low-order representation not only describes the shock movement but also captures the moment when the separation occurs near the trailing edge in a low-order manner. We further show that it is possible to perform sensor-based reconstruction through the present low-dimensional expression while identifying the sensitivity with respect to aerodynamic responses. The present model trained at ${Re} = 3\times 10^6$ is lastly evaluated at the level of a real aircraft operation of ${Re} = 3\times 10^7$, exhibiting that the phase dynamics of lift is reasonably estimated from sparse sensors. The current study may provide a foundation towards data-driven real-time analysis of transonic buffet conditions under aircraft operation.

We explore the mechanisms and regimes of mixing in yield-stress fluids by simulating the stirring of an infinite, two-dimensional domain filled with a Bingham fluid. A cylindrical stirrer moves along a circular path at constant speed, with the path radius fixed at twice the stirrer diameter; the domain is initially quiescent and marked by a passive dye in the lower half. We first examine the mixing process in Newtonian fluids, identifying three key mechanisms: interface stretching and folding around the stirrer’s path, diffusion across streamlines and dye advection and interface stretching due to vortex shedding. Introducing yield stress leads to notable mixing localisation, manifesting through three mechanisms: advection of vortices within a finite distance of the stirrer, vortex entrapment near the stirrer and complete suppression of vortex shedding at high yield stresses. Based on these mechanisms, we classify three distinct mixing regimes: (i) regime SE, where shed vortices escape the central region, (ii) regime ST, where shed vortices remain trapped near the stirrer and (iii) regime NS, where no vortex shedding occurs. These regimes are quantitatively distinguished through spectral analysis of energy oscillations, revealing transitions and the critical Bingham and Reynolds numbers. The transitions are captured through effective Reynolds numbers, supporting the hypothesis that mixing regime transitions in yield-stress fluids share fundamental characteristics with bluff-body flow dynamics. The findings provide a mechanistic framework for understanding and predicting mixing behaviours in yield-stress fluids, suggesting that the localisation mechanisms and mixing regimes observed here are archetypal for stirred-tank applications.