This article follows on from Scott & Cambon (J. Fluid Mech., vol. 979, 2024, A17) and Scott (Phys. Rev. E, vol. 111, 2025, 035101). Like those articles, it concerns weak, decaying homogeneous turbulence in a rotating, stably stratified fluid with constant Brunt–Väisälä frequency, $N$. The difference is that here we consider the case in which $\beta =2{\varOmega} /N$ is close to $1$, where ${\varOmega}$ is the rotation rate. Because this renders inertial-gravity waves only weakly dispersive, wave-turbulence theory, which played a prominent role in the earlier studies, no longer applies. Indeed, wave-turbulence analysis does not appear here. Nonetheless, much of the analytical framework, based on modal decomposition, carries over, as do many of the conclusions. The flow is expressed as a sum of wave and non-propagating (NP) modes and their weak-turbulence mode-amplitude evolution equations are derived for small $\beta -1$. The NP component is found to evolve independently of the wave one, following an amplitude equation which is precisely that of the previous studies in the limit $\beta \rightarrow 1$. The NP component induces coupling between wave modes and, without it, the wave component has purely linear decay. The mode-amplitude equations are integrated numerically using a scheme similar to that of classical direct numerical simulation and results given. We find an inverse energy cascade of the NP component, whereas the presence of that component induces a forward cascade, hence significant dissipation, of the wave component. Detailed results are given for the energy, energy spectra and energy fluxes of the two components.

Hydrodynamic instability can occur when a viscous fluid is driven rapidly through a flexible-walled channel, including a multiplicity of steady states and distinct families of self-excited oscillations. In this study we use a computational method to predict the stability of flow through a planar finite-length rigid channel with a segment of one wall replaced by a thin pre-tensioned elastic beam of negligible mass. For large external pressures, this system exhibits a collapsed steady state that is unstable to low-frequency self-excited oscillations, where the criticality conditions are well approximated by a long-wavelength one-dimensional (1-D) model. This oscillation growing from a collapsed state exhibits a reduced inlet driving pressure compared with the corresponding steady flow, so the oscillating state is energetically more favourable. In some parameter regimes this collapsed steady state is also unstable to distinct high-frequency normal modes, again predicted by the 1-D model. Conversely, for lower external pressures, the system exhibits an inflated steady state that is unstable to another two modes of self-excited oscillation, neither of which are predicted by the lower-order model. One of these modes becomes unstable close to the transition between the upper and lower steady states, while the other involves small-amplitude oscillations about a highly inflated wall profile with large recirculation vortices within the cavity. These oscillatory modes growing from an inflated steady state exhibit a net increase in driving pressure compared with the steady flow, suggesting a different mechanism of instability to those growing from a collapsed state.

The effectiveness of polymer drag reduction by targeted injection is studied in comparison with that of a uniform concentration (or polymer ocean) in a turbulent channel flow. Direct numerical simulations are performed using a pseudo-spectral code to solve the coupled equations of a viscoelastic fluid using the finitely extensible nonlinear elastic dumbbell model with the Peterlin approximation. Light and heavy particles are used to carry the polymer in some cases, and polymer is selectively injected into specific flow regions in the other cases. Drag reduction is computed for a polymer ocean at a viscosity ratio of $\beta = 0.9$ for simulation validation, and then various methods of polymer addition at $\beta = 0.95$ are compared for their drag-reduction performance and general effect on the flow. It was found that injecting polymer directly into regions of high axial strain inside and around coherent vortical structures was the most effective at reducing drag, while injecting polymer very close to the walls was the least effective. The targeting methods achieved up to 2.5 % higher drag reduction than an equivalent polymer ocean, offering a moderate performance boost in the low drag-reduction regime.

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.

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.

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 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.

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.

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.

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.

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.

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.

Pulsatile fluid flows through straight pipes undergo a sudden transition to turbulence that is extremely difficult to predict. The difficulty stems here from the linear Floquet stability of the laminar flow up to large Reynolds numbers, well above experimental observations of turbulent flow. This makes the instability problem fully nonlinear and thus dependent on the shape and amplitude of the flow perturbation, in addition to the Reynolds and Womersley numbers and the pulsation amplitude. This problem can be tackled by optimising over the space of all admissible perturbations to the laminar flow. In this paper, we present an adjoint optimisation code, based on a GPU implementation of the pseudo-spectral Navier–Stokes solver nspipe, which incorporates an automatic, optimal checkpointing strategy. We leverage this code to show that the flow is susceptible to two distinct instability routes: one in the deceleration phase, where the flow is prone to oblique instabilities, and another during the acceleration phase with similar mechanisms as in steady pipe flow. Instability is energetically more likely in the deceleration phase. Specifically, localised oblique perturbations can optimally exploit nonlinear effects to gain over nine orders of magnitude in energy at a peak Reynolds number of ${\textit{Re}}_{\textit{max}}\approx 4000$. These oblique perturbations saturate into regular flow patterns that decay in the acceleration phase or break down to turbulence depending on the flow parameters. In the acceleration phase, optimal perturbations are substantially less amplified, but generally trigger turbulence if their amplitude is sufficiently large.

Uniform momentum zones (UMZs) are widely used to describe and model the coherent structure of wall-bounded turbulent flows, but their detection has traditionally relied on relatively narrow fields of view which preclude fully resolving features at the scale of large-scale motions (LSMs). We refine and extend recent proposals to detect UMZs with moving-window fields of view by including physically motivated coherency criteria. Using synthetic data, we show how this updated moving-window approach can eliminate noise contamination that is likely responsible for the previously reported, high fractal dimension of UMZ interfaces. By applying the approach to channel flow direct numerical simulation (DNS), we identify a significant number of previously undetected, large-scale UMZ interfaces, including a small fraction of highly linear interfaces with well-defined streamwise inclination angles. We show that the inclination angles vary inversely with the size of the UMZ interfaces and that this relationship can be modelled by the opposing effects of shear-induced inclination and vortex-induced lift-up on hairpin packets. These geometric properties of large-scale UMZ interfaces play an important role in the development of improved stochastic models of wall-bounded turbulence.

We derive effective Boussinesq and Korteweg–de Vries equations governing nonlinear wave propagation over a structured bathymetry using a three-scale homogenization approach. The model captures the anisotropic effects induced by the bathymetry, leading to significant modifications in soliton dynamics. Homogenized parameters, determined from elementary cell problems, reveal strong directional dependencies in wave speed and dispersion. Our results provide new insights into nonlinear wave propagation in structured shallow-water environments, and consequently motivate further fundamental and applied studies in wave hydrodynamics and coastal engineering.

In this paper, we consider the flow of a nematic liquid crystal in the domain exterior to a small spherical particle. We work within the framework of the $\unicode{x1D64C}$-tensor model, taking into account the orientational elasticity of the medium. Under a suitable regime of physical parameters, the governing equations can be reduced to a system of linear partial differential equations. Our focus is on precise far-field asymptotics of the flow velocity with an emphasis on its anisotropic behaviour. We are able to analytically characterize the flow pattern and compare it with that of the classical isotropic Stokes flow. The expression for velocity away from the particle can be computed numerically or symbolically.

To address the possible occurrence of a finite-time singularity during the oblique reconnection of two vortex rings, (Moffatt and Kimura 2019, J. Fluid Mech., vol. 870, R1) developed a simplified model based on the Biot–Savart law and claimed that the vorticity amplification $\omega _{{max}}/\omega _0$ becomes very large for vortex Reynolds number $Re_{\varGamma } \geqslant 4000$. However, with direct numerical simulations (DNS), Yao and Hussain (2020a, J. Fluid Mech.vol. 888, pp. R2) were able to show that the vorticity amplification is in fact much smaller and increases slowly with $Re_{\varGamma }$. This suppression of vorticity was linked to two key factors – deformation of the vortex core during approach, and formation of hairpin-like bridge structures. In this work, a recently developed numerical technique called log-lattice (Campolina & Mailybaev, 2021, Nonlinearity, vol. 34, 4684), where interacting Fourier modes are logarithmically sampled, is applied to the same oblique vortex ring interaction problem. It is shown that the log-lattice vortex reconnection displays core compression and formation of bridge structures, similar to the actual reconnection seen with DNS. Furthermore, the sparsity of the Fourier modes allows us to probe very large $Re_{\varGamma } = 10^8$ until which the peak of the maximum norm of vorticity, while increasing with $Re_{\varGamma }$, remains finite, and a blow-up is observed only for the inviscid case.

Turbulence is an out-of-equilibrium flow state that is characterised by non-zero net fluxes of kinetic energy between different scales of the flow. These fluxes play a crucial role in the formation of characteristic flow structures in many turbulent flows encountered in nature. However, measuring these energy fluxes in practical settings can present a challenge in systems other than the case of unrestricted turbulence in an idealised periodic box. Here, we focus on rotating Rayleigh–Bénard convection, being the canonical model system to study geophysical and astrophysical flows. Owing to the effect of rotation, this flow can yield a split cascade, where part of the energy is transported to smaller scales (direct cascade), while another fraction is transported to larger scales (inverse cascade). We compare two different techniques for measuring these energy fluxes throughout the domain: one based on a spatial filtering approach and an adapted Fourier-based method. We show how one can use these methods to measure the energy flux adequately in the anisotropic, aperiodic domains encountered in rotating convection, even in domains with spatial confinement. Our measurements reveal that in the studied regime, the bulk flow is dominated by the direct cascade, while significant inverse cascading action is observed most strongly near the top and bottom plates, due to the vortex merging of Ekman plumes into larger flow structures.

This paper presents an experimental investigation focusing on the impact of structural damping on the flow-induced vibration (FIV) of a set of generic three-dimensional bodies, in this case, elastically mounted oblate spheroids. The objective is to identify and analyse the two primary FIV responses: vortex-induced vibration (VIV) and galloping, and how these vary with structural damping ratio. The VIV response has similarities to that observed for a sphere, reaching a maximum amplitude of approximately one major diameter. However, and not seen in the sphere case, a galloping-like response exhibits a linear amplitude growth as the reduced velocity is increased beyond the normal resonant range, akin to the transverse galloping response seen for a D-section or elliptical cross-section cylinder. By increasing the damping ratio, this aerodynamic-instability-driven response is effectively suppressed. However, increased damping also significantly reduces the VIV response, decreasing its maximum amplitude and contracting the VIV synchronisation, or lock-in, region. These results suggest that three-dimensional spheroids, as for two-dimensional cylindrical bodies such as D-section and elliptical cylinders, can encounter asymmetric aerodynamic forces that support movement-induced vibration, resulting in substantial body oscillation – beyond that expected under VIV alone. The study indicates that modifying the structural damping ratio can facilitate a transition between the VIV and galloping responses. These findings offer novel insights into the dynamics of fluid–structure interactions and have potential implications for designing structures and devices that can experience resonant flow conditions. Additionally, the energy harvesting performance of oblate spheroids has been evaluated, revealing that the afterbody significantly influences energy harvesting capabilities. Notably, an oblate spheroid can extract up to $50\,\%$ more power from the fluid flow than a sphere.