The flow around prolate ellipsoids is investigated using large-eddy simulation at a Reynolds number of ReD = 10 000. Five different aspect ratios are considered, with AR = H/D varying from 5 : 1 to 1 : 1, where D and H represent the minor- and major-axes, respectively. The major axes of the ellipsoids are set perpendicular to the free stream, and the influence of body anisotropy on boundary layer separation, shear layer behaviour, enstrophy production and local flow topology is examined. Higher body anisotropy leads to early separation of the boundary layer in the equatorial plane, resulting in a wider wake and a monotonic increase in pressure drag and total drag. Positive enstrophy production reaches a maximum approximately 2.5D downstream of the ellipsoids independently of body anisotropy. High body anisotropy leads to sustained negative enstrophy production in the near-wake, specifically near the poles of the 5 : 1 ellipsoid. Negative production occurs due to the distinct behaviour of streamlines near the high curvature pole, where they undergo strong anisotropic contraction in the cross-stream plane. Interactions between the vorticity vector and the intermediate eigenvector of the strain rate tensor are shown to be the primary source of enstrophy production close to the pole, and the intermediate eigenvalue exhibits negative values in this region. The negative production region is shown to be dominated by the unstable focus/compressing topology, which is consistent with findings from other studies that report negative enstrophy production in turbulent flows.

In this study, experimental deep reinforcement learning (DRL) control of a supersonic cavity flow is conducted for the first time at Mach 2, with the aim of mixing enhancement. A 4 $\times$ 5 pulsed-arc plasma actuator (PAPA) matrix with independently controlled columns and a supersonic hot-wire probe placed at the cavity midline serve as the flow disturber and state observer, respectively. The control law parametrised by a radial basis function network is executed on a field-programmable gate array at 5 kHz loop frequency. Results show that DRL is capable of finding a converged closed-loop control law in less than 10 s, and the resulting cavity velocity fluctuation is three times higher than periodic open-loop control. The control benefits earned by DRL increase with the number of activated columns, yet reduce with the cavity back-wall inclination angle. Using the same number of actuator columns, variable-formation actuation mode allows the DRL to find a more effective control with much less actuator power consumption, when compared with fixed-formation actuation mode. The final control law obtained by DRL can be interpreted as a threshold control conditional on the location of the state vector, and the improvement of total reward is ascribed to both the elevation of occurrence probabilities of high-reward clusters and the ubiquitous increase of the reward expectation at each cluster. Physically, mixing enhancement in the cavity flow is traced back to the thermal bulbs and shock waves produced by the PAPA, which induce a meandering motion of the shear layer.

Simple analytical criteria are derived to determine whether axisymmetric base flows in annuli and pipes are stable or unstable. Both axisymmetric and non-axisymmetric inviscid disturbances are considered. Our sufficient condition for stability improves upon the classical result of Batchelor & Gill (1962) J. Fluid Mech. 14(4), 529–551 following the idea of the second Kelvin–Arnol’d stability theorem. A novel sufficient condition for instability is also derived by extending the recently proposed hurdle theorem for parallel flows (Deguchi et al. 2024 J. Fluid Mech. 997, A25). These analytical criteria are applied to annular and pipe model flows and are shown to effectively predict the neutral parameters obtained from eigenvalue computations of the stability problem.

This study investigates the wake dynamics of a wall-mounted square cylinder with an aspect ratio of 2, subjected to varying inflow turbulence intensities, employing high-fidelity large-eddy simulation complemented by spectral proper orthogonal decomposition. The simulations are conducted at a Reynolds number of 43 000. A synthetic momentum source term is integrated within the Navier–Stokes equations to generate turbulence consistent with the von Kármán spectrum. Four inflow cases, comprising an undisturbed inflow and three disturbed inflows with turbulence intensities of 10 %, 20 % and 30 %, are examined to elucidate their impact on vortex shedding, shear-layer behaviours and coherent structures. Results demonstrate that increased turbulence intensity significantly modifies vortex coherence, suppresses recirculation regions, promotes earlier shear-layer reattachment on the top surface and leads to reattachment of the shear layer on the side surface. Spectral proper orthogonal decomposition analysis, conducted on 17 orthogonal planes in the streamwise (x), wall-normal (y) and spanwise (z) directions, reveals two dominant energetic frequencies: a primary vortex-shedding frequency around a Strouhal number of 0.084, and a secondary high frequency associated with Kelvin–Helmholtz instabilities. The imposed turbulence effectively redistributes spectral energy, diminishing the coherence and altering the spatial organisation of vortical structures. These findings enhance fundamental understanding of turbulent wake dynamics and flow–structure interactions in bluff-body flows.

This paper investigates the nonlinear dynamics of horizontal shear instability in an incompressible, stratified and rotating fluid in the non-traditional $f$-plane, i.e. with the full Coriolis acceleration, using direct numerical simulations. The study is restricted to two-dimensional horizontal perturbations. It is therefore independent of the vertical (traditional) Coriolis parameter. However, the flow has three velocity components due to the horizontal (non-traditional) Coriolis parameter. Three different scenarios of nonlinear evolution of the shear instability are identified, depending on the non-dimensional Brunt–Väisälä frequency $N$ and the non-dimensional non-traditional Coriolis parameter $\tilde {f}$ (non-dimensionalised by the maximum shear), in the range $\tilde {f}\lt N$ for fixed Reynolds and Schmidt numbers $ \textit{Re}=2000$, $ \textit{Sc}=1$. When the stratification is strong $N\gg 1$, the shear instability generates stable Kelvin–Helmholtz billows like in the traditional limit $\tilde {f}=0$. Furthermore, when $N\gg 1$, the governing equations for any $\tilde {f}$ can be transformed into those for $\tilde {f}=0$. This enables us to directly predict the characteristics of the flow depending on $\tilde {f}$ and $N$. When $N$ is around unity and $\tilde {f}$ is above a threshold, the primary Kelvin–Helmholtz vortex is destabilised by secondary instabilities but it remains coherent. For weaker stratification, $N\leqslant 0.5$ and $\tilde {f}$ large enough, secondary instabilities develop vigorously and destroy the primary vortex into small-scales turbulence. Concomitantly, the enstrophy rises to high values by stretching/tilting as in fully three-dimensional flows. A local analysis of the flow prior to the onset of secondary instabilities reveals that the Fjørtoft necessary condition for instability is satisfied, suggesting that they correspond to shear instabilities.

This work investigates the formation mechanism of the turbulent secondary vortex street (SVS) which appears in the far wake of bluff bodies, when the (primary) Kármán vortex street is absent. The turbulent wakes of four types of highly porous bluff bodies (plates/meshes) are characterised via time-resolved particle image velocimetry and large eddy simulations. The effect of ambient turbulence and initial conditions on SVS development is also examined, by installing a turbulence grid upstream of the bodies, and by varying the homogeneity of the bluff body porosity. Our results indicate that the SVS is a far-wake evolution of near-wake shear-layer vortices which, in the absence of the vortex shedding instability, continually grow and are finally arranged into alternating vortices. Free-stream turbulence and body inhomogeneity are found to significantly influence SVS development by amplifying mixing and attenuating the shear-layer instabilities of the near wake, which in turn lead to the formation of weaker and less coherent SVS structures further downstream.

A data assimilation (DA) strategy based on an ensemble Kalman filter (EnKF) is used to enhance the predictive capabilities of scale-resolving numerical tools for the analysis of flows exhibiting cyclic behaviour. More precisely, an ensemble of numerical runs using large-eddy simulations (LES) for a compressible intake flow rig is augmented via the integration of high-fidelity data. This observation is in the form of instantaneous velocity measurements, which are sampled at localised sensors in the physical domain. Two objectives are targeted. The first objective is the calibration of an unsteady inlet condition suitable to capture the cyclic flow investigated. The second objective is the analysis of the synchronisation of the LES velocity field with the available observations. In order to reduce the computational costs required for this analysis, a hyper-localisation procedure (HLEnKF) is proposed and integrated in the library CONES, tailored to perform fast online DA. The proposed strategy performs a satisfactory calibration of the inlet conditions, and its robustness is assessed using two different prior distributions for the free parameters optimised in this task. The DA state estimation is efficient in obtaining accurate local synchronisation of the inferred velocity fields with the observed data. The modal analysis of the kinetic energy field provides additional insight into the improved reconstruction quality of the velocity field. Thus, the HLEnKF shows promising features for the calibration and synchronisation of scale-resolved turbulent flows, opening perspectives of applications for complex phenomena using advanced tools such as digital twins.

Tip leakage noise is one of the least understood noise sources in turbomachinery, arising from the interactions between the tip leakage flow, blade tips and casing boundary layer. This study employs experimental and parametric investigations to systematically identify three key non-dimensional parameters that govern tip leakage noise: the angle of attack $\alpha$, the ratio between the maximum aerofoil thickness and gap size $\tau _{\textit{max}}/e$ and between the gap size and boundary-layer thickness $e/\delta$. These parameters regulate two fluid-dynamic instabilities, vortex shedding and shear-layer roll-up, responsible for the two tip leakage noise sources. Specifically, the first noise source arises when $\tau _{\textit{max}}/e \lt 4$ and with the tip vortex positioned away from the aerofoil surface for $\alpha \geqslant 10^\circ$. The second noise source occurs whenever the tip flow separates at the pressure side edge, with its strength proportional to the lift coefficient, depending on $\alpha$, and diminishing as $e/\delta$ decreases and $\tau _{\textit{max}}/e$ increases. Additionally, a relationship between the first noise source and drag losses is established, demonstrating that these losses are governed by $\alpha$ and $\tau _{\textit{max}}/e$.

While flow confinement effects on a shear layer of an one-sided or submerged vegetation array’s interface have been widely studied, turbulent interactions between shear layers in channels with vegetation on both sides remain unclear. This study presents laboratory experiments investigating flow adjustments and turbulent interaction within a symmetrical vegetation–channel–vegetation system, considering varying array widths and densities. In the outer shear layer, the shear stress is primarily balanced by the pressure gradient. As the array extends laterally, the outer penetration of the shear layer reduces from a fully developed thickness to the half-width of the open region, resulting in flow confinement. Flow confinement enhances the pressure gradient, which increases the interior velocity and shear stress at the interface. Despite the time-averaged shear stress being zero at the centreline when the shear layer is confined, the shear instabilities from both sides interact, producing significant turbulent events at the centreline with equal contributions from each side. Furthermore, the two parallel vortex streets self-organised and created a wave response with a $\pi$-radian phase shift , where alternating vortex cores amplify the pressure gradient, intensifying coherent structures and facilitating momentum exchange across the channel centreline. Although the turbulent intensity is enhanced, the decreased residence time for turbulent flow events may limit transport distance. Overall, the shear layer that develops on one interface acts as an additional resistance to shear turbulence on the other interface, leading to a more rapid decline of shear stress in the open region, despite a higher peak at the interface.

This study connected flow structure and morphological changes in and around a rectangular vegetation patch. The emergent patch was constructed in an 8 cm sand bed. Two patch densities were tested, using a regular configuration of rigid dowels. Near the leading edge of the patch, enhanced turbulence levels produced sediment erosion. Some of the eroded sediment was carried into the patch, forming an interior deposition dune. The denser patch resulted in a smaller dune due to stronger lateral flow diversion and weaker interior streamwise velocity. After the leading-edge dune, in the fully developed region of the patch, vortices formed in the shear layers along the patch lateral edges. Elevated turbulence at the patch edge produced local erosion. For the dense patch, material eroded from the edge was transported into the patch to form a flow-parallel ridge, and there was no net sediment loss/gain by the patch. For the sparse patch, material eroded from the edge was transported away from the patch, resulting in a net loss of sediment from the patch. In the wake of both patches, deposition occurred near the wake edges and not at the wake centreline, which was attributed to the weak lateral transport associated with the weakness of the von Kármán vortex street. Specifically, the lateral transport length scale was less than half the width of the patch. The increasing bedform height within the wake progressively weakened and narrowed the von Kármán vortex street, illustrating an important feedback from morphological evolution to the flow structure. Despite significant local sediment redistribution, the patch did not induce channel-scale sediment transport.

This study experimentally investigates wake recovery mechanisms behind a floating wind turbine subjected to imposed fore-aft (surge) and side-to-side (sway) motions. Wind tunnel experiments with varying free-stream turbulence intensities ($\textit{TI}_{\infty } \in [1.1, 5.8]\,\%$) are presented. Rotor motion induces large-scale coherent structures – pulsating for surge and meandering for sway – whose development critically depends on the energy ratio between the incoming turbulence and the platform motion. The results provide direct evidence supporting the role of these structures in enhancing wake recovery, as previously speculated by Messmer, Peinke & Hölling (J. Fluid Mech., vol. 984, 2024, A66). These periodic structures significantly increase Reynolds shear stress gradients, particularly in the streamwise–lateral direction, which are key drivers of wake recovery. However, their influence diminishes with increasing $\textit{TI}_{\infty }$: higher background turbulence weakens the coherent flow patterns, reducing their contribution to recovery. Beyond a threshold turbulence level – determined by the energy, frequency and direction of motion – rotor-induced structures no longer contribute meaningfully to recovery, which becomes primarily driven by the free-stream turbulence. Finally, we show that the meandering structures generated by sway motion are more resilient in turbulent backgrounds than the pulsating modes from surge, making sway more effective for promoting enhanced wake recovery.

Local shearing motions in turbulence form small-scale shear layers, which are unstable to perturbations at approximately 30 times the Kolmogorov scale. This study conducts direct numerical simulations of passive-scalar mixing layers in a shear-free turbulent front to investigate mixing enhancements induced by such perturbations. The initial turbulent Reynolds number based on the Taylor microscale is $ Re_\lambda = 72$ or 202. The turbulent front develops by entraining outer fluid. Weak sinusoidal velocity perturbations are introduced locally, either inside or outside the turbulent front, or globally throughout the flow. Perturbations at this critical wavelength promote small-scale shear instability, complicating the boundary geometry of the scalar mixing layer at small scales. This increases the fractal dimension and enhances scalar diffusion outward from the scalar mixing layer. Additionally, the promoted instability increases the scalar dissipation rate and turbulent scalar flux at small scales, facilitating faster scalar mixing. The effects manifest locally; external perturbations intensify mixing near the boundary, while internal perturbations affect the entire turbulent region. The impact of perturbations is consistent across different Reynolds numbers when the amplitudes normalised by the Kolmogorov velocity are the same, indicating that even weaker perturbations can enhance scalar mixing at higher Reynolds numbers. The mean scalar dissipation rate increases by up to 50 %, even when the perturbation energy is only 2.5 % of the turbulent kinetic energy. These results underscore the potential to leverage small-scale shear instability for efficient mixing enhancement in applications such as chemically reacting flows.

The broad-band direct combustion noise is an important problem for industrial and domestic burners. The power spectral density (PSD) of this noise is related to the local spectral density of fluctuating heat release rate (HRR) ($\psi _{\dot {q}}$), which is challenging to measure but is readily available from large eddy simulations (LES) results. The behaviour of $\psi _{\dot {q}}$ for a wide range of thermochemical and turbulence conditions is investigated. Three burners are studied, namely a dual-swirl burner, a bluff-body burner and a jet in cross-flow burner, operating at atmospheric conditions with $\textrm {CH}_4$–air and $\textrm {H}_2$–air mixtures. In contrast to the classical $f^{-5/2}$ scaling, the far-field sound pressure level and volume-integrated HRR ($\psi _{\dot {Q}}$) spectra reveal a universal $f^{-5}$ scaling for high frequencies. This differing spectral decay rate for $\psi _{\dot {Q}}$ compared to the classical scaling is due to multi-regime combustion, related to either partial premixing or the local turbulence intensity. The dependence of $\psi _{\dot {q}}$ on the chosen spatial locations, flame configuration and its relation to velocity spectra are studied. A simple model for $\psi _{\dot {q}}$ involving the velocity spectra is found that compares well with LES results. The characteristic frequency involved in this model is related to the time scale of the coherent structures of the flow.

This work focuses on the intensity variation mechanisms in the mean inner and outer shear layers of a premixed swirling flame. In order to close the gap between the Lagrangian vorticity transport and the Eulerian shear layer intensity ($\gamma$), we propose a combined Reynolds-vorticity transport approach to obtain the streamwise variation of $\gamma$ as the integrals of vorticity generation terms, including tilting, baroclinic torque, diffusion and dilatation. However, different from the classical vorticity (transport) equation, the vortex stretching vanishes, and the original dilatation is replaced by a shear-layer dilatation in the new model. It enables the quantitative evaluation of how the different vorticity transport terms affect the shear layer intensity; in particular, we have identified vortex tilting and baroclinic torque as the main cause of the inner shear layer enhancement in the swirling flame’s near field. Although this model is initially developed to study the flame-attached shear layers, the broader significance lies in its applicability to general axisymmetric shear flows.

Small-scale shear layers arising from the turbulent motion of viscoelastic fluids are investigated through direct numerical simulations of statistically steady, homogeneous isotropic turbulence in a fluid described by the FENE-P model. These shear layers are identified via a triple decomposition of the velocity gradient tensor. The viscoelastic effects are examined through the Weissenberg number ($\textit{Wi}$), representing the ratio of the longest polymer relaxation time scale to the Kolmogorov time scale. The mean flow around these shear layers is analysed within a local reference frame that characterises shear orientation. In both Newtonian and viscoelastic turbulence, shear layers appear in a straining flow, featuring stretching in the shear vorticity direction and compression in the layer normal direction. Polymer stresses are markedly influenced by the shear and strain, which enhance kinetic energy dissipation due to the polymers. The shear layers in viscoelastic turbulence exhibit a high aspect ratio, undergoing significant characteristic changes once $\textit{Wi}$ exceeds approximately 2. As $\textit{Wi}$ increases, the extensive strain weakens, diminishing vortex stretching. This change coincides with an imbalance between extension and compression in the straining flow. In the shear layer, the interaction between vorticity and polymer stress causes the destruction and production of enstrophy at low and high $\textit{Wi}$ values, respectively. Enstrophy production at high $\textit{Wi}$ is induced by normal polymer stress oriented along the shear flow, associated with the diminished extensive strain. The $\textit{Wi}$-dependent behaviour of these shear layers aligns with the overall flow characteristics, underscoring their pivotal roles in vorticity dynamics and kinetic energy dissipation in viscoelastic turbulence.

Compound flows consist of two or more parallel compressible streams in a duct and their theoretical treatment has gained attention for the analysis and modelling of ejectors. Recent works have shown that these flows can experience choking upstream of the geometric throat. While it is well known that friction can push the sonic section downstream of the throat, no mechanism has been identified yet to explain its displacement in the opposite direction. This study extends the existing compound flow theory and proposes a one-dimensional (1-D) model, including friction between the streams and the duct walls. The model captures the upstream and downstream displacements of the sonic section. Through an analytical investigation of the singularity at the sonic section, it is demonstrated that friction between the streams is the primary driver of upstream displacement. The 1-D formulation is validated against axisymmetric Reynolds averaged Navier–Stokes simulations of a compound nozzle for various inlet pressures and geometries. The effect of friction is investigated using an inviscid simulation for the isentropic case and viscous simulations with both slip and no-slip conditions at the wall. The proposed extension accurately captures the displacement of the sonic section, offering a new tool for in-depth analysis and modelling of internal compound flows.

Three-dimensional vortex dynamics around two pitching foils arranged in side-by-side (parallel) configurations is numerically examined at a range of separation (gap) distances ($0.5c \leqslant y^* \leqslant 1.5c$). In-phase ($\phi =0$) and out-of-phase ($\phi ={\rm \pi}$) motions are considered for Strouhal numbers of $0.3$ and $0.5$ at a Reynolds number of $8000$. In this work, we show that the foil proximity effect, defined as the influence of one foil on the flow characteristics around the other, induces a spanwise instability in the braids of trailing-edge vortices (TEVs) during their roll-up. This is a newly identified instability that manifests itself in the form of secondary vortical structures with opposite circulation compared with the TEVs formed on the foils, which leads to the formation of double necking on the braids of the TEVs. We provide quantitative evidence linking the formation of these secondary structures to the braid instability. The first neck merges with the TEV, while the second neck detaches from the braid region and moves downstream independently. As the foil proximity effect intensifies (spacing between the foils decreases), secondary vortical structures, as well as the necks, become more prominent, leading to the emergence of three-dimensional wake features. Lastly, the influence of kinematics of the foils on three-dimensionality of the wake is investigated. At higher Strouhal numbers, broader regions of high strain are developed near the trailing edge, associated with the detachment of stronger structures from the braids of TEVs. The characterized instability demonstrates consistent properties for in-phase and out-of-phase motions, albeit with specific differences in dynamics of leading-edge vortices.

We propose a simple method to identify unstable parameter regions in general inviscid unidirectional shear flow stability problems. The theory is applicable to a wide range of basic flows, including those that are non-monotonic. We illustrate the method using a model of Jupiter's alternating jet streams based on the quasi-geostrophic equation. The main result is that the flow is unstable if there is an interval in the flow domain for which the reciprocal Rossby Mach number (a quantity defined in terms of the zonal flow and potential vorticity distribution), surpasses a certain threshold or ‘hurdle’. The hurdle height approaches unity when we can take the hurdle width to greatly exceed the atmosphere's intrinsic deformation length, as holds on gas giants. In this case, the Kelvin–Arnol’d sufficient condition of stability accurately detects instability. These results improve the theoretical framework for explaining the stable maintenance of Jupiter and Saturn's jets over decadal time scales.

Scale dependence of local shearing motion is investigated experimentally in decaying homogeneous isotropic turbulence generated through multiple-jet interaction. The turbulent Reynolds number, based on the Taylor microscale, is between approximately 900 and 400. Velocity fields, measured using particle image velocimetry, are analysed through the triple decomposition of a low-pass filtered velocity gradient tensor, which quantifies the intensities of shear and rigid-body rotation at a given scale. These motions manifest predominantly as layer and tubular vortical structures, respectively. The scale dependence of the moments of velocity increments, associated with shear and rigid-body rotation, exhibits power-law behaviours. The scaling exponents for shear are in quantitative alignment with the anomalous scaling of the velocity structure functions, suggesting that velocity increments are influenced predominantly by shearing motion. In contrast, the exponents for rigid-body rotation are markedly smaller than those predicted by Kolmogorov scaling, reflecting the high intermittency of rigid-body rotation. The mean flow structure associated with shear at intermediate scales is investigated with conditional averages around locally intense shear regions in the filtered velocity field. The averaged flow field exhibits a shear layer structure with aspect ratio approximately 4.5, surrounded by rotating motion. The analysis at different scales reveals the existence of self-similar structures of shearing motion across various scales. The mean velocity jump across the shear layer increases with the layer thickness. This relationship is well predicted by Kolmogorov's second similarity hypothesis, which is useful in predicting the mean characteristics of shear layers across a wide range of scales.

Comprehensive coherent structures around a surface-mounted low aspect ratio square cylinder in uniform flow with an oblique angle of $45^{\circ }$ were investigated for cylinder-width-based Reynolds numbers of 3000 and 10 000 by direct numerical simulation based on a topology-confined mesh refinement framework. High-resolution simulations and the critical-point concept were scrutinized to reveal for the first time the reasonable and compatible topologies of flow separation and complete near-wall structures, due to their extensive impact on various engineering applications. Large-scale horseshoe vortices are observed at two notable foci in the viscous sublayer. Within this layer, a wall-parallel jet is formed by downflow intruding into the bottom surface at the half-saddle point, then deflecting in the upstream direction and finally penetrating the bottom surface until the half-saddle point. A pair of conical vortices on the cylinder's top surface switch themselves on two sides of the square cylinder, where the switching frequency is identical with that of the sway of the side shear layer. The undulation of the Kelvin–Helmholtz instability is identified in the instantaneous development of a conical vortex and side shear layer, where the scaling of the ratio of the Kelvin–Helmholtz and von Kármán frequencies follows the power-law relation obtained by Lander et al. (J. Fluid Mech., vol. 849, 2018, pp. 1096–1119). Large-scale arch-shaped vortex is often detected in the intermediate wake region of a square cylinder, involving two interconnected portions, such as the leg portion separated from leeward surfaces and head portion rolled up from the top surface. The leg portion of the arch-shaped vortex was rooted by two foci near the bottom-surface plane.