The hydrodynamic interactions involved in the self-organisation phenomenon in biological systems are not fully understood and have attracted significant attention. A previous study (Peng et al. 2018 J. Fluid Mech., vol. 853, pp. 587–600) found that, arranged in an unbounded fluid, the largest cluster of self-propelled bodies in tandem, capable of spontaneously forming an ordered configuration, consists of eight swimmers. Here, we numerically investigate the collective behaviour of multiple self-propelled plates in tandem within a channel of width $H$, confined by two parallel walls. These plates are driven by harmonic flapping motions of uniform frequency and amplitude. Results demonstrate for the first time that the channel confinement significantly enhances group cohesion, with up to 72 individuals self-organising into ordered configurations at an optimal channel width. We observe two stable configurations: a hybrid mode with subgroups (typically at smaller channel widths) and a regular mode with sparse configuration. In large regular-mode groups, the vortex fields downstream exhibit spatial periodicity, conforming to Rosenhead’s stability criterion for confined vortex streets (vortex spacing $L_{v\textit{or}} \geqslant 1.419H$). This theoretical alignment explains both the observed upper channel-width limit ($H \approx 4.0{-}4.5$) for large-scale cohesion and the robust order in the regular mode. The plates may adopt spontaneously a ‘vortex-slalom’ path, reducing the drag force and energy consumption while maximising stability. Deviation from this path results in a spring-like restoring force, promptly returning the plate to equilibrium.

This study investigates the dynamics of sequentially released gravity currents in a lock-exchange configuration consisting of two lock fluids using high-resolution numerical simulations and compares them with the classical single-lock exchange. The results demonstrate that, in a two-lock-fluid configuration, the overtaking of the lighter lock current by the heavier lock current alters the current’s front dynamics, leading to complex velocity transitions. Before overtaking occurs, the front propagation is slower than in the classical single-lock-fluid case because of lower density contrast, but after overtaking, the heavier lock fluid accumulates at the head region of the current and enhances its speed. The head of the current is primarily dominated by streamwise velocity vectors, which directly influence the front propagation speed. The body of the current exhibits significant components of streamwise and wall-normal velocities, characterised by large eddies and Kelvin–Helmholtz billows at the interface, enhancing entrainment and mixing. In contrast, the tail region consists of small-scale eddies, which contribute to viscous dissipation, gradually reducing the current’s momentum. A parametric study of the two-lock-fluid configuration, conducted to investigate the effects of non-dimensionalised time of delay in the release of heavier lock fluid, $t_R^*$, the ratio of densities of ambient fluid to heavier lock fluid, $\gamma _2=\rho _a/\rho _2$, and the non-dimensionalised time of overtaking by the heavier lock fluid, $t_O^*$, revealed a nonlinear relationship. As local Reynolds number decreases $(Re_l\lesssim 10{\,}000)$, the relationship becomes nonlinear due to weaker buoyancy forcing of the heavier current travelling in the wake of the lighter current. However, for $Re_l\gtrsim 10{\,}000$, this relationship becomes linear.

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.

The quasi-biennial oscillation (QBO) of Earth’s stratosphere is a slowly reversing, large-scale mean flow that is generated by fast, small-scale waves. The variability of QBO reversals in recent years has triggered significant interests in the intrinsic variability of wave-driven mean flows. In this paper, we show a direct connection between the statistical properties of gravity waves randomly emitted at the bottom of a stably stratified fluid and the statistics of mean-flow reversals. We perform wave-resolved, direct numerical simulations of the two-dimensional Navier–Stokes equations under the Boussinesq approximation. We generate waves monochromatic in space at the bottom of the layer using three different types of temporal forcing: a constant-amplitude monochromatic forcing, a finite band polychromatic forcing and a stochastic forcing. We show that the stochastic forcing scheme consistently generates a mean flow with variable reversals and investigate the dependence of the reversal statistics on the wave Reynolds number and forcing correlation time. In particular, we demonstrate that the mean-flow reversals become increasingly variable as the forcing correlation time approaches the characteristic time scale of the reversals. The monochromatic and polychromatic forcing schemes trigger QBO-type flows that are highly regular for most values of the control parameters considered. Thus, the mean-flow variability under stochastic forcing is not linked to secondary mean-flow instabilities in our simulations, but rather evidence that small-amplitude waves can alter large-scale oscillations when their generation is chaotic. Finally, we demonstrate that the first-order statistics of the mean flow are relatively insensitive to the forcing type.

The lift force models for a particle in wall-bounded linear shear flow have been extensively investigated; however, the influence of the curvature of the velocity profile (${\textit{Sg}}$) on the lift force at finite slip Reynolds numbers (${\textit{Re}}$) remains unexplored. In the present work, direct numerical simulations (DNS) are performed to investigate the lift on a spherical particle in unbounded linear shear flow, single-wall-bounded linear shear flow and Poiseuille flow. Based on our DNS data, we first extend the existing unbounded and single-wall-bounded linear shear-slip-induced lift models to higher non-dimensional shear rates ($|Sr|=2.5$) for $0.1\leqslant Re\leqslant 20$. Based on the empirical model for Couette flow or the analytical model for unbounded Poiseuille flow, the lift models are then modified to account for the curvature effect of the parabolic velocity profile, which reduce to the linear shear-slip-induced lift models in the high ${\textit{Re}}$ and low ${\textit{Sg}}$ limits. We also modify the rotation-induced lift model of linear shear flow to account for the parabolic shear effect, which causes lift enhancement for the leading particle and lift attenuation for the lagging particle in the Poiseuille flow, compared to the linear shear case. This lift attenuation may give rise to an inverse Magnus force at low slip Reynolds numbers. In addition, the model for the particle free rotation rate for the Poiseuille flow is established by correcting the one for the linear shear flow, providing a more accurate prediction of the torque on the particle.

A joint experimental–computational investigation was conducted to examine the aerodynamic behaviour of a partially closed cavity model in Mach-6 flow. The model, consisting of a flat plate with a rectangular cavity and a forward-facing hinged door, resulted in a strong 500 Hz fluctuation with a 7.5$^\circ$ door and 25 mm cavity depth. The experiments revealed a recirculation bubble present upstream of the cavity region. The fluctuations, detected by surface pressure sensors on the upper surface, upstream cavity wall and cavity floor, were caused by oscillations of the separation bubble along the streamwise axis. Notably, this phenomenon is not explained by established empirical models for cavity flows, such as the Rossiter mechanism or closed-box acoustic resonance. To further elucidate the flow physics, detached eddy simulations (DESs) of the flow were conducted, providing a detailed understanding of the complex flow phenomena. The DES results complemented the experimental data, offering insights into the unsteady flow behaviour and the mechanisms driving the pressure fluctuations. Additional experiments and simulations were conducted for other door angles to simulate different stages of opening. The strong pressure fluctuations at approximately 500 Hz were only experimentally observed for door angles between 5.0$^\circ$ and 7.5$^\circ$ but were absent at much smaller and larger angles. Additionally, several cavity depths were tested, which demonstrated that a shallower cavity delayed the onset of fluctuations until a higher free-stream Reynolds number was reached. The combination of experimental and numerical results provides valuable initial data on the aerodynamic performance of a hypersonic forward-facing door over a cavity.

In this paper, the transition processes induced by three-dimensional wavy wall roughnesses with two different distribution topologies (staggered type-S and aligned type-A) are studied at Mach 5.92 by direct numerical simulations. For the first time, the effects of the two distribution topologies on transition are investigated. It is found that the type-S roughness can induce transition significantly earlier – about 34.5 % earlier than that of the type-A roughness under the conditions in this paper. Both the type-S and type-A roughnesses can induce counter-rotating pairs of streamwise vortices. A ‘staggered-enhancing’ mechanism for the vortices is discovered in the type-S roughness, which results in significantly stronger vortices than in the type-A case. The enhanced vortices in turn produce stronger shear layers, which is the key factor leading to the stronger transition-induced ability of the type-S roughness. Then, based on the spectral proper orthogonal decomposition, the linear and nonlinear instability characteristics of the two roughnesses are investigated. For type-S roughness, its downstream linear instability is dominated by the low-frequency shear layer instability near 50 kHz. Once the linear fluctuation amplitude saturates, the nonlinear breakdown is triggered from the shear layer. For type-A roughness, its downstream linear instability is co-dominated by two modes: the low-frequency shear layer instability near 23 kHz, and the high-frequency Mack’s second mode above 100 kHz. Both modes exhibit significantly lower growth rates than the dominant shear layer instability in the type-S case, ultimately delaying the transition onset compared to type-S roughness.

A theoretical study is made of steady, subcritical (Froude number $F \lt 1$) two-dimensional free-surface flow due to a uniform stream flowing over smooth, locally confined bottom topography of large horizontal extent ($L \gg 1$) and finite peak height ($\varepsilon = O(1)$). In earlier work, this flow was analysed based on the nonlinear shallow-water equations which neglect the effects of dispersion altogether. This so-called hydraulic theory predicts a steady disturbance confined in the vicinity of the topography if $\varepsilon$ is below a critical value $\varepsilon _{\textit{crit}}(F)$. The present asymptotic analysis of the full potential flow equations focuses on how dispersive effects (controlled by $\mu = 1/L \ll 1$) influence this steady state, particularly in regard to a steady short-scale radiating wave downstream that is ignored by hydraulic theory. Utilizing exponential asymptotics, it is shown that as $\varepsilon$ is increased this dispersive wave, whose amplitude is formally exponentially small with respect to $\mu$, grows sharply and ultimately it becomes comparable with the hydraulic wave disturbance when $\varepsilon$ approaches $\varepsilon _{\textit{crit}}$. Thus, the nonlinear shallow-water equations break down in the vicinity of $\varepsilon _{\textit{crit}}$ regardless of $\mu \ll 1$. The asymptotic results are supported by numerical solutions of the full potential flow theory, which also reveal a limiting $\varepsilon$, $\varepsilon _{\textit{lim}} \approx \varepsilon _{{ crit}}$, above which steady wave responses cannot be computed. For $\varepsilon$ just below $\varepsilon _{\textit{lim}}$, the downstream wave resembles a steep steady Stokes periodic wave, while for $\varepsilon$ slightly above $\varepsilon _{\textit{lim}}$ unsteady computations suggest that the downstream disturbance steepens and breaks.

Buoyancy-driven bubbly flows naturally have spatially dependent density fields, which allow for multiple definitions of the scale-dependent (or filtered) energy. A priori, it is not obvious which of these provide the most physically apt scale-by-scale budget. In the present study, we compare two such definitions, based on (i) filtered momentum and filtered velocity (Pandey et al., J. Fluid Mech., 2020, vol. 884, p. R6), and (ii) Favre-filtered energy (Aluie, Phys. D: Nonlinear Phenom., 2013, vol. 247, pp. 54–65; Pandey et al., Phys. Rev. Lett., 2023, vol. 131, p. 114002). We also derive a Kármán–Howarth–Monin relation using the momentum–velocity correlation function and contrast it with the scale-by-scale energy budget obtained in (i). We find that, for the volume fraction and Atwood number explored, irrespective of the definition, energy transfers due to the advective nonlinearity and surface tension are identical. However, discrepancies arise for the buoyancy and pressure contributions. We show that the Favre-filtered definition is the more appropriate choice, within which buoyancy injects energy, pressure transfers energy to large scales and both advective nonlinearity and surface tension transfer energy downscales where it is dissipated by viscosity.

Double-diffusive convection, in which the density of a fluid is dependent on two fields that diffuse at different rates (such as temperature and salinity), has been widely studied in areas as diverse as the oceans and stellar atmospheres. Under the assumption of classical Fickian diffusion for both heat and salt, the evolution of temperature and salinity is governed by parabolic advection–diffusion equations. In reality, there are small additional terms in these equations that render them hyperbolic (the Maxwell–Cattaneo (M–C) effect). Although these corrections are nominally small, they represent a singular perturbation, and hence can lead to significant effects when the underlying differences of salinity and temperature are large. In an earlier paper (Hughes, Proctor & Eltayeb, J. Fluid Mech., vol. 927, 2021, p. A13), we investigated the linear stability of a double-diffusive fluid layer subject to the M–C effect in either the temperature or the salinity equation (but not both). Here we consider the general, and much more complicated, case in which the M–C effect influences both temperature and salinity. We find that, as in the earlier paper, oscillatory instability is indeed facilitated (and in fact made possible when the salinity gradient is destabilising, where the classical problem has no oscillatory instability) when the salinity gradients are sufficiently large. The scalings that emerge from the earlier paper, however, are not necessarily representative of those in the general case, thus justifying the present study. In addition, we have found a remarkable singular situation when the ratio of the M–C effects is equal to the ratio between the heat and salinity diffusivities, near which the critical wavenumber is sharply reduced. In addition to determining the stability boundaries we have also investigated the growth rates of unstable modes and shown that these are on a par with those of classical double-diffusive convection.

The forward leaning inclination angle, $\gamma$, of coherent turbulent structures is a well-known feature of wall-bounded turbulent flows. Although invariant across friction Reynolds numbers within the range $\textit{Re}_\tau =10^3{-}10^6$, $\gamma$ can vary significantly across turbulent scales within a high-Reynolds-number flow. Very-large-scale motions (VLSMs) are known to induce significant changes in the instantaneous shear profile, which is a conditioning event that could trigger variability in the inclination angle of smaller coherent turbulent structures. Although this aspect has been extensively studied via numerical and laboratory experiments, few studies have explored this feature for a very-high-Reynolds-number atmospheric flow. In this work, the inclination angle of turbulent structures within the atmospheric surface layer at a very high Reynolds number ($\textit{Re}_\tau =7.9\times 10^5$) is investigated by deploying a scanning Doppler light detection and ranging and a super large particle image velocimetry (SLPIV) apparatus. The inclination angle of wall-attached eddies is inferred either from the two-point correlation of streamwise velocity ($\gamma =41.1^\circ$) or with a scale-dependent approach through the spectral linear stochastic estimator (SLSE). The SLSE (and, thus, the scale-dependent inclination angle) is conditionally evaluated based on the high- and low-momentum events induced by VLSMs, both in the streamwise ($u'_{\textit{VLSM}}$) and in the vertical ($w'_{\textit{VLSM}}$) velocity components. As a result, lower inclination angles ($\gamma =30^\circ {-}50^\circ$) are found for $u'_{\textit{VLSM}}\gt 0$ ($w'_{\textit{VLSM}}\lt 0$), while higher values ($50^\circ {-}85^\circ$) are ascribed to $u'_{\textit{VLSM}}\lt 0$ ($w'_{\textit{VLSM}}\gt 0$). This result emphasises the primary role that VLSMs play in shaping the wall-attached eddy geometry, which, in turn, is crucial to determine the Reynolds stress balance within the wall-attached eddy range.

Systematic deflection of microparticles off of initial streamlines is a fundamental task in microfluidics, aiming at applications including sorting, accumulation or capture of the transported particles. In a large class of set-ups, including deterministic lateral displacement and porous media filtering, particles in non-inertial (Stokes) flows are deflected by an array of obstacles. We show that net deflection of force-free particles passing an obstacle in Stokes flow is possible solely by hydrodynamic interactions if the flow and obstacle geometry break fore–aft symmetries. The net deflection is maximal for certain initial conditions and we analytically describe its scaling with particle size, obstacle shape and flow geometry, confirmed by direct trajectory simulations. For realistic parameters, separation by particle size is comparable to what is found assuming contact (roughness) interactions. Our approach also makes systematic predictions on when short-range attractive forces lead to particle capture or sticking. In separating hydrodynamic effects on particle motion strictly from contact interactions, we provide novel, rigorous guidelines for elementary microfluidic particle manipulation and filtering.

The spatial structure of advective transport in two-dimensional homogeneous Rayleigh–Bénard (HRB) convection is investigated by means of direct numerical simulations. The convective driving leads to the emergence of thermal plumes. These create dynamically changing pathways characterised by localised mean flows. The resulting large-scale anisotropy of the system diminishes with increasing nominal Rayleigh number (Ra). The key components of advective transport are extracted via a network-based analysis of Lagrangian trajectories. This reveals a coherent structure based on plume-related pathways that governs the transport of heat and matter. A reduced description of the structure is given by the zero isoline of scale-filtered vorticity. While its essential large-scale characteristics display only a weak dependency on Ra, geometric analysis shows that the decrease of large-scale anisotropy with increasing Ra is due to a reduction of the length of vertical transport paths. Mean profiles with respect to the transport paths suggest that this reduction is caused by an enhanced turbulent transfer of temperature fluctuations into adjacent shear layers and vortices. This process leads to a spatial decorrelation of temperature and velocity and, consequently, to a reduced structural impact of the thermal driving on the flow. Spatially resolved nonlinear fluxes indicate that shear layers and vortices next to the transport paths are associated with a spectrally inverse flux of enstrophy. The observed structure of advective transport in HRB convection also displays asymptotically scale-invariant characteristics, contrasting the structural properties of wall-bounded classical Rayleigh–Bénard convection.

A nonlinear stability analysis entirely in the Lagrangian frame is conducted, revealing the fundamental role of the wave-induced mean flow in modifying further wave growth and providing new insight into the classic problem of wave generation by wind. The prevailing theory, a critical-layer resonance mechanism proposed by Miles (J. Fluid Mech., 1957, vol. 3, no. 2, pp. 185–204), has seen numerous refinements; yet, the role of Lagrangian drift – the velocity a fluid parcel actually experiences – in wave growth was not understood. Our analysis first recovers the classic Miles growth rate from linear theory before extending it to third order in the wave slope to derive a modified growth rate. The leading-order wave-induced mean flow alters the higher-order instability, manifesting as a suppression of growth with increasing wave steepness for the realistic wind profiles considered. This modified growth rate shows good agreement with experimental observations, explaining the observed steepness-dependent suppression via a single physical mechanism. An integral momentum budget clarifies this mechanism, revealing that the wave-induced current alters the coupling between the total phase speed and the total Lagrangian mean flow at the critical level (as defined in the linear theory), thereby acting to reduce the efficiency of momentum transfer. Notably, this Lagrangian drift is precisely what Doppler-shift-based remote sensing of upper ocean currents measure, providing a direct observational pathway to account for this wave-induced feedback in studies of air–sea coupling. More broadly, this approach can be generalised to analyse other shear instabilities and provides a direct path towards refining wind-stress parametrisations.