We perform numerical simulations of two-dimensional strongly stratified flows in a square periodic domain $(y,z)$ forced by a steady mode with vorticity of the form $\sin (k_{\textit{y f}}y)\sin (k_{\textit{z f}}z)$, where $(k_{\textit{y f}},k_{\textit{z f}})$ are fixed wavenumbers. It is shown that such deterministic forcing can lead to a transition to turbulence and the emergence of horizontal layers (so-called vertically sheared horizontal flows, VSHFs) similarly as for random stochastic forcing. The flow characteristics are studied depending on the Froude and Reynolds numbers. Furthermore, the mechanisms of layers formation are disentangled. Triadic instabilities first lead to the growth of pairs of wavevectors that resonate with each of the four forced wavevectors. Quadratic interactions between these resonant modes and the forcing also drive the growth of several non-resonant modes at the same growth rate. Since the forcing comprises the wavevectors $\pm (k_{\textit{y f}},k_{\textit{z f}})$ and their mirror symmetric with respect to the horizontal $\pm (k_{\textit{y f}},-k_{\textit{z f}})$, there exist enslaved/bound modes with the same horizontal wavenumber and different vertical wavenumbers. Hence, the quadratic interactions between the latter modes force a second generation of modes among which some are VSHFs. Their growth rate is twice the growth rate of the primary resonant modes. Such a mechanism is similar to resonant quartets (Newell, J. Fluid Mech., 1969, vol. 35, no 2, pp. 255–271; Smith & Waleffe, Phys. Fluids, 1999, vol. 11, no 6, pp. 1608–1622). When the forcing is restricted to only the two wavevectors $\pm (k_{\textit{y f}},k_{\textit{z f}})$, the second generation of enslaved/bound modes all have a non-zero horizontal wavenumber. However, further quadratic interactions can force VSHF. Thus, horizontal layers also emerge, but with a growth rate equal to the number of quadratic interactions times the growth rate of the primary instability.

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.

Shock trains compress incoming supersonic flow through a series of shock wave/turbulent boundary layer interactions (STBLIs) that occur in rapid streamwise succession. In this work, the global flow changes across the entire turbulent shock train are analysed as the confluence of local changes imparted by individual STBLIs. For this purpose, wall-resolved large eddy simulations are used on a constant area, back-pressured channel configuration with an entry Mach number of 2.0. Local changes due to individual STBLIs are evaluated in terms of deviations from incoming, near-equilibrium boundary layers, by systematically examining properties of the mean flow structure and turbulent statistics. The first STBLI in the train induces a strongly separated region, which interrupts inner layer dynamics and incites wall-normal deflection of turbulent structures, leading to prominent outer layer Reynolds stress amplification and related transport phenomena. Downstream of the first STBLI, the thickened, turbulent wall layer repeatedly interacts with subsequent shock waves in the train, resulting in cyclic attenuation and amplification of turbulent stresses, localised incipient separations and variations in mean momentum flux gradients. Decreases in mean Mach number along the shock train result in downstream shocks weakening to the point that interactions with the turbulent boundary layer impart negligible changes on the local flow. Consequently, after a sufficient streamwise extent, the boundary layers asymptote towards a new equilibrium state, thus recovering certain classical properties of near-wall turbulence. Among the features that reappear are a self-similar, adverse pressure gradient velocity profile and the restoration of the autonomous roller-streak cycle.

Surface bubbles in the ocean are critical in moderating several fluxes between the atmosphere and the ocean. In this paper, we experimentally investigate the drainage and lifetime of surface bubbles in solutions containing surfactants and salts, subjected to turbulence in the air surrounding them modelling the wind above the ocean. We carefully construct a set-up allowing us to repeatably measure the mean lifetime of a series of surface bubbles, while varying the solution and the wind speed or humidity of the air. To that end, we show that renewing the surface layer is critical to avoid a change of the physical properties of the interface. We show that the drainage of the bubbles is well modelled by taking into account the outwards viscous flow and convective evaporation. The mean lifetime of surface bubbles in solutions containing no salt is controlled by evaporation and independent on surfactant concentration. When salt is added, the same scaling is valid only at high surfactant concentrations. At low concentrations, the lifetime is always smaller and independent of wind speed, owing to the presence of impurities triggering a thick bursting event. When the mean lifetime is controlled by evaporation, the probability density of the lifetime is very narrow around its mean, while when impurities are present, a broad distribution is observed.

We present three-dimensional velocity gradient statistics from turbulent Rayleigh–Bénard convection experiments in a horizontally extended cell of aspect ratio 25, a paradigm for mesoscale convection with its organisation into large-scale patterns. The Rayleigh number ${\textit{Ra}}$ ranges from $3.7 \times 10^5$ to $4.8 \times 10^6$, the Prandtl number ${\textit{Pr}}$ from 5 to 7.1. Spatio-temporally resolved volumetric data are reconstructed from moderately dense Lagrangian particle tracking measurements. All nine components of the velocity gradient tensor from the experiments show good agreement with those from direct numerical simulations, both conducted at ${\textit{Ra}} = 1 \times 10^6$ and ${\textit{Pr}} = 6.6$. As expected, with increasing ${\textit{Ra}}$, the flow in the bulk approaches isotropic conditions in the horizontal plane. The focus of our analysis is on non-Gaussian velocity gradient statistics. We demonstrate that statistical convergence of derivative moments up to the sixth order is achieved. Specifically, we examine the probability density functions (PDFs) of components of the velocity gradient tensor, vorticity components, kinetic energy dissipation and local enstrophy at different heights in the bottom half of the cell. The probability of high-amplitude derivatives increases from the bulk to the bottom plate. A similar trend is observed with increasing ${\textit{Ra}}$ at fixed height. Both indicate enhanced small-scale intermittency of the velocity field. We also determine derivative skewness and flatness. The PDFs of the derivatives with respect to the horizontal coordinates are found to be more symmetric than the ones with respect to the vertical coordinate. The conditional statistical analysis of the velocity derivatives with respect to up-/down-welling regions and the rest did not display significant difference, most probably due to the moderate Rayleigh numbers. Furthermore, doubly logarithmic plots of the PDFs of normalised energy dissipation and local enstrophy at all heights show that the left tails follow slopes of 3 / 2 and 1 / 2, respectively, in agreement with numerical results. In general, the left tails of the dissipation and local enstrophy distributions show higher probability values with increasing proximity towards the plate, in comparison with those in the bulk.

We determine unsteady time-periodic flow perturbations that are optimal for enhancing the time-averaged rate of heat transfer between hot and cold walls (i.e. the Nusselt number Nu), under the constraint of fixed flow power (Pe$^2$, where Pe is the Péclet number). The unsteady flows are perturbations of previously computed optimal steady flows and are given by eigenmodes of the Hessian matrix of Nu, the matrix of second derivatives with respect to amplitudes of flow mode coefficients. Positive eigenvalues of the Hessian correspond to increases in Nu by unsteady flows, and occur at $Pe\geqslant 10^{3.5}$ and within a band of flow periods $\tau \sim Pe^{-1}$. For $\tau {\textit{Pe}}\leqslant 10^{0.5}$, the optimal flows are chains of vortices that move along the walls or along eddies enclosed by flow branches near the walls. At larger $\tau {\textit{Pe}}$, the vorticity distributions are often more complex and extend farther from the walls. The heat flux is enhanced at locations on the walls near the unsteady vorticity. We construct an iterative time-spectral solver for the unsteady temperature field, and find increases in Nu of up to 7 % at moderate-to-large perturbation amplitudes.

Shock-tube experiments are conducted to investigate the Atwood-number dependence of hydrodynamic instability induced by a strong shock with a Mach number exceeding 3.0. The compressible linear theory performs reliably under varying compressibility conditions. In contrast, the impulsive model significantly loses predictive accuracy at high shock intensities and Atwood numbers ($A_t$), particularly when specific heat ratio differences across the interface are pronounced. To address this limitation, we propose a modified impulsive model that offers favourable predictions over a wide range of compressibility conditions while retaining practical simplicity. In the nonlinear regime, increasing $A_t$ enhances both the shock-proximity and secondary-compression effects, which suppress bubble growth at early and late stages, respectively. Meanwhile, spike growth is promoted by the spike-acceleration and shock-proximity mechanisms. Several models reproduce spike growth across a wide range of $A_t$, whether physical or incidental. In contrast, no models reliably describe bubble evolution under all $A_t$ conditions, primarily due to neglecting compressibility effects that persist into the nonlinear regime. Building on these insights, we develop an empirical model that effectively captures bubble evolution over a wide $A_t$ range. Modal evolution is further shown to be strongly affected by compressibility-induced variations in interface morphology. The effect is particularly pronounced at moderate to high $A_t$, where it suppresses the fundamental mode growth while promoting higher-order harmonic generation.

Jet vortex generators (JVGs) are a promising technique for controlling laminar separation in low-Reynolds-number aerofoils, such as those used in micro air vehicles (MAVs). While previous studies have demonstrated their aerodynamic benefits, the three-dimensional structure of the vortices they generate and their interaction with the boundary layer remain poorly characterised experimentally. In this study, volumetric velocity measurements are performed using the double-pulse Shake-the-Box (STB) technique on an SD7003 aerofoil equipped with skewed and pitched JVGs. Experiments are conducted at Reynolds numbers of 30 000 and 80 000, for angles of attack of 8$^{\circ}$, 10$^{\circ}$ and 14$^{\circ}$. The results provide the first experimental visualisation of the full three-dimensional vortex topology induced by JVGs, revealing asymmetric streamwise vortices that penetrate the separated shear layer and re-energise the near-wall region. In pre-stall conditions, the JVGs reshape the laminar separation bubble into a thinner and more stable structure, reducing its sensitivity to angle of attack. In stall conditions, they induce partial or full flow reattachment, delaying large-scale separation. The evolution of characteristic bubble parameters and the chordwise distribution of the shape factor $H = \delta ^{\ast }/\theta$, where $\delta ^{\ast }$ is the displacement thickness and $\theta$ is the momentum thickness, show a consistent trend of enhanced boundary-layer recovery. These findings offer new insight into the physical mechanisms underlying active separation control at low Reynolds numbers and establish a framework for evaluating vortex-based control strategies using volumetric diagnostics.

Microswimmers and active colloids often move in confined systems, including those involving interfaces. Such interfaces, especially at the microscale, may deform in response to the stresses of the flow created by the active particle. We develop a theoretical framework to analyse the effect of a nearby membrane on the motion of an active particle whose flow fields are generated by force-free singularities. We demonstrate our results on a particle represented by a combination of a force dipole and a mass dipole, while the membrane resists deformation due to tension and bending rigidities. We find that the deformation either enhances or suppresses the motion of the active particle, depending on its orientation and the relative strengths between the fundamental singularities that describe its flow. Furthermore, the deformation can generate motion in new directions.

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.

High Reynolds number effects of wall-bounded flows, involving interscale energy transfers between small and large scales of turbulence within and between the inner and outer regions, challenge the classical description of the structure of these flows and the ensuing turbulence models. The two-scale Reynolds stress model recently proposed by Chedevergne et al. (2024, J. Fluid Mech. vol. 1000), was able to reproduce the small- and large-scale contributions in turbulent channel flows that follow the scale separation performed by Lee & Moser (2019, J. Fluid Mech. vol. 860, pp. 886–938), by partitioning energy spectra at a given wavelength. However, the interscale interactions within the inner region were modelled in an ad hoc manner, but without physical relevance, making the two-scale Reynolds stress model less and less accurate for boundary layer applications as the Reynolds number was increased. In this study, by re-analysing direct numerical simulations data from Lee & Moser (2019), with the objective of modelling these scale interactions, crucial observations on energy transfers between large and small scales could be made. In particular, the analysis reveals the important role played by the spanwise component of the Reynolds stress in the logarithmic region. From the analysis undertaken, a revisited version of the two-scale model was thus proposed, focusing efforts on interscale transfer modelling. The resulting model is then successfully tested on high Reynolds number boundary layer configurations without pressure gradient, up to $\textit{Re}_{\tau }=20\,000$. The excellent agreement reflects the good prediction capabilities of the proposed model, and above all, the relevance of the modelling of the energy transfers within and between the inner and outer regions of wall-bounded flows.

The flow in a rapidly rotating cylinder forced by the harmonic oscillations of a small sphere along the rotation axis is explored numerically. For oscillation frequencies less than twice the cylinder rotation frequency, the forced response flows feature conical shear layers emitted from the critical latitudes of the sphere. These latitudes are where the characteristics of the hyperbolic system, arrived at by ignoring nonlinear, viscous and forcing terms in the governing equations, are tangential to the sphere. These conical shear layers vary continuously with the forcing frequency so long as it remains inertial. At certain values of the forcing frequency, linear inviscid inertial modes of the cylinder are resonated. Of all possible inertial modes, only those whose symmetries are compatible with the symmetry of the forced system are resonated. This all occurs even in the linear limit of vanishingly small forcing amplitude. As the forcing amplitude is increased, nonlinearity leads to non-harmonic oscillations and a non-zero mean flow which features a Taylor columnar structure extending from the sphere to the two endwalls in an axially invariant fashion.