Acoustic resonance is a critical issue in turbomachinery that induces noise and structural vibrations. The resonant mechanism for stator blade rows was first revealed more than half a century ago, along with the well-known concept of stationary Parker modes. However, despite various efforts based on this mechanism, previous studies have failed to explain the experimental Parker-type resonance results observed in rotor blade rows. This study establishes a theoretical model to elucidate acoustic resonance phenomena in rotating annular cascades, with focus on the effects of inlet distortion. The results demonstrate that the present model captures the experimental trends for Parker-type rotor acoustic resonances, which also implies that the conventional stationary Parker modes no longer exist in rotor blade rows due to rotation and the frequency scattering effect. Meanwhile, theoretical predictions on inlet-distortion–rotor interaction reveal that the unsteady blade loading is significantly higher at resonance frequencies compared to the cut-on frequency in duct acoustics. Accordingly, a modified Campbell diagram incorporating acoustic natural frequencies is proposed to aid in avoiding resonance-induced blade vibrations during the design stage. It is shown that the acoustic resonance frequencies intersect with the synchronous excitation frequencies across a wide speed range. High-amplitude unsteady blade loading is induced at these frequency crossings, due to the Parker-type acoustic resonance eigenmodes being excited by inlet-distortion–rotor interactions.

Flocculation of suspended cohesive particles in turbulence plays a crucial role in various natural and industrial processes. In this study, we carry out direct numerical simulations with a cohesive discrete element method to investigate the evolution of cohesive particle flocs in homogeneous isotropic turbulence. We focus on how particle flocs are formed and destructed in turbulence, and the influences of cohesive strength, particle inertia, particle volume fraction and turbulence intensity. The statistics show that the formation and destruction of cohesive particle flocs vary across different flocculation stages and conditions. At the early developing stage, flocs primarily form through coagulation, where individual primary particles collide and adhere together. As the system approaches equilibrium, floc formation may also proceed via separation, where small flocs detach from larger ones under the conditions of strong cohesive strength, low particle inertia or weak turbulent shear. Under these same conditions, floc destruction occurs predominantly through absorption across all stages, in which smaller flocs are incorporated into larger ones. In contrast, under the opposite conditions, floc destruction shifts to disintegration, where a floc breaks apart into primary particles or two-particle flocs. The probability distribution of the floc lifetime follows an exponential decay. Furthermore, flocs exhibit shorter lifetimes under stronger turbulent shear, larger particle inertia or weaker cohesion, as these conditions promote more frequent destruction. A higher particle volume fraction leads to more frequent floc formation and destruction, thus producing shorter lifetimes. Meanwhile, cohesion between particles markedly extends the floc lifetime compared to lifetimes of non-cohesive particle clusters. Moreover, floc compactness is positively correlated with its lifetime. These findings advance our understanding of the flocculation dynamics of cohesive particles in turbulent flow.

Transient growth analysis has been extensively studied in asymptotically stable flows to identify their short-term amplification of perturbations. Generally, in global transient growth analyses, matrix-free methods are adopted, requiring the construction of adjoint equations, either in the discrete or continuous form. This paper introduces a data-driven algorithm that circumvents the adjoint equations by extracting the optimal initial perturbation and its energy growth over a specified time horizon from transient snapshots of perturbations. This method is validated using data from the linearised complex Ginzburg–Landau equation, backward-facing step flow and the Batchelor vortex. Unlike model-based methods, which require $S$ sets of integrations of the linearised governing equation and its adjoint for $S$ time horizons, the proposed approach collects the snapshots of $S$ time horizons in one integration of the linearised equation. Furthermore, this study provides a robust framework for utilising proper orthogonal decomposition modes to synthesise optimal modes. The developed capacity to conduct transient growth analyses without solving the adjoint equations is expected to significantly reduce the barriers to transient dynamics research.

The generation and propagation of acoustic-gravity–Scholte wave fields produced by different types of nonlinear interactions between ocean surface waves and shallow, non-uniform depth contours of an elastic seafloor are investigated. Specifically, nonlinear interactions between surface waves and the seafloor, surfacewaves themselves and the seafloor, and acoustic-gravity-waves and the seafloor are shown to produce resonantly strong bottom pressures. Whereas the interaction between shoreward-propagating surface waves and seafloor depth contours (and the resulting seafloor waves and microseisms) has been discussed in the literature, not much is known about the compression wave–seafloor wave groups forming an important component of the overall energy transfer process in shallow water. Forcing due to the different wave interactions involving the seafloor depth contours and the dispersion relations for the coupled ocean–seafloor system are derived, providing estimates of the energy transfer that results at resonance when the interaction produces a wavenumber–frequency combination that lies on one of the dispersion surfaces for the two-media system. Wavenumber spectra and their temporal evolution are found analytically for stationary random surface-wave fields, and the acoustic-gravity wave potentials, seafloor pressure amplitudes, seafloor power densities and Scholte wave amplitudes are computed, and their sensitivity to critical parameters is estimated. The nonlinear interactions derived here may account for some of the 200 % increase of low-frequency ($0.01\leqslant f\leqslant 0.03$ Hz) spectral densities of bottom pressure observed between 25 and 8 m water depths in the Atlantic Ocean at a site off Duck, NC. Further, subject to experimental validation, the power densities estimated here could contribute energy for sensing operations.

Quantifying the rate at which a stratified turbulent flow mixes a density field is of crucial importance for many environmental and industrial applications. In the absence of molecular diffusion $\kappa$ (i.e. in the absence of irreversible mixing), a stratified turbulent flow forced so as to have a constant kinetic energy will converge towards a statistical steady state whose density field geometric properties depend on the Richardson number $Ri$ (defined as the ratio of the kinetic energy in the flow to the amount of energy required to overturn the full water column). This statistical steady state is reached after vertically disturbed fluid parcels have explored the depth that is accessible energetically and have returned to their neutrally buoyant position, i.e. after a ‘resetting time’ $t_{R}$. The magnitude of $t_{R}$ is controlled by stratification strength $N$ and the buoyancy Reynolds number $Re_{b}$, quantifying the ratio between the Kolmogorov and Ozmidov scales, and hence the range of scales effectively unaffected by stratification. When $\kappa \neq 0$, a second time scale needs to be considered: the mixing time scale $t_{M}$. Within a mixing time, diffusion smooths the density field. We show that the ratio of the mixing and resetting times $t_{M}/t_{R}$, as well as $Ri$, control how fast stratified turbulent flows mix a density field into a fully homogeneous state and, hence, the history of mixing in such flows. In particular, we identify three regions in the $(Ri,t_{M}/t_{R})$ parameter space for which the time evolution of measures of mixing is controlled by different algebraic combinations of $t_{M}/t_{R}$ and $Ri$. These scaling laws are compared with idealised direct numerical simulations. Using these findings, we propose a simple model for the time evolution of the density histogram in stratified turbulent flows.

We perform analytical and numerical analyses of the propulsion of a rigid body in a viscous fluid subjected to a periodic force with zero average over a period. This general formulation specifically addresses the significant case where propulsion is generated by the oscillation of a mass located in an internal cavity of the body. We provide a rigorous proof of the necessary and sufficient conditions for propulsion at the second order of magnitude of the force. These conditions are implemented and confirmed by numerical tests for bodies without fore-and-aft symmetry, while they are silent for bodies with such symmetry, like round ellipsoids. Consequently, in this case, propulsion can only occur at an order higher than the second. This problem is investigated by numerically integrating the entire set of equations, and the result shows that, in fact, propulsion does occur, thus opening new avenues for further analytical studies.

The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a linear arbitrary Lagrangian–Eulerian method to solve the fluid–structure linear problem as well as a forced problem where a harmonic motion of the bodies is imposed. We then propose a low computational-cost impedance-based criterion to predict the instability thresholds. A global stability analysis of the fluid–structure system is then performed for a tandem of cylinders and the instability thresholds obtained are found to be in perfect agreement with the predictions of the impedance-based criterion. An extensive parametric study is then performed for a tandem of cylinders and the effects of mass, damping and spacing between the bodies are investigated. Finally we also apply the impedance-based method to a three-body system to show its validity to a higher number of bodies.

We present an experimental and theoretical investigation of steady Taylor cone-jetting of highly viscous liquids at the minimum flow rate required for steady jetting. To achieve a steady cone-jet, the viscous liquid is flown through a conducting needle under the action of a strong electric field acting between the needle and a flat collector plate. Experiments reveal that the minimum flow rate and the corresponding jet diameter depend on both the needle diameter and the electrical conductivity of the liquid. Subsequently, we used the experimental measurements to formulate correlations among the minimum flow rate, the needle diameter and the physical properties of the liquid, including the electrical conductivity. To elucidate the underlying physics and experimental observations, we performed an order-of-magnitude analysis. The scaling analysis reveals that in the cone region, the viscous and interfacial tension forces are of comparable magnitude, while in the current transfer region, the viscous and electrostatic suction forces are the dominant resisting and driving forces, respectively. Subsequently, we theoretically derived the scaling relations for the minimum flow rate and the corresponding jet diameter by considering the balance of forces at the cone-tip and in the current transfer region. The empirical and theoretical scaling laws for the minimum flow rate and the corresponding jet diameter agree well for highly viscous liquids with electrical conductivity spanning over four orders of magnitude. Lastly, we present the limits that describe the regime for which the minimum flow rate depends on the needle diameter, and the derived scaling laws are applicable.

Heat transfer in fractured media results from the interplay between advective transport within the fracture and conductive heat exchange with the surrounding rock matrix. Aperture heterogeneity structures this interplay by generating preferential flow channels and quasi-stagnant zones, leading to early-time anomalous transport dominated by advective channelling and to late-time non-Fickian dynamics controlled by matrix conduction. This study develops a physics-based stochastic framework that couples a time-domain random walk (TDRW) representation of in-fracture advection and conduction with a semi-analytical description of matrix–fracture heat exchange, enabling a unified characterisation of both short- and long-time anomalous heat-transport regimes. Matrix trapping times follow a Lévy–Smirnov distribution derived from first-passage theory, and the interfacial heat flux is evaluated through a non-local Duhamel kernel that rigorously captures the temporal non-locality imposed by heat-conduction theory. Monte Carlo simulations over stochastic aperture fields elucidate the roles of fracture closure, correlation length and Péclet number in shaping heat transport. Increasing fracture closure enhances channelisation and accelerates early-time heat transport, whereas larger correlation lengths amplify anomalous spreading. Higher Péclet numbers strengthen advective dominance, but do not suppress the long-time subdiffusive tail induced by matrix conduction. Breakthrough curves exhibit heavy-tailed decay consistent with Lévy–Smirnov trapping induced by semi-infinite matrix diffusion. Results reveal a transition from superdiffusive to subdiffusive transport governed by advective channelling, aperture-induced dispersion and matrix conduction. The framework provides a predictive and computationally efficient route for modelling heat transport in heterogeneous fractures, with relevance to geothermal energy extraction, subsurface thermal storage and engineered thermal systems.

Because of the high dimensionality and geometric complexity of the circular-pipe problem, formulating and implementing boundary conditions are challenging, and most existing theoretical studies either neglect boundary effects or impose purely specular-reflection boundary conditions. To address this gap, we devise and explore an analytical model for microswimmer dispersion in a cylindrical pipe flow under a diffuse-reflection boundary condition, extending our earlier studies (Jiang & Chen, J. Fluid Mech., vol. 899, 2020, A18; Zeng et al., J. Fluid Mech., 1018, 2025, A27). We derive a well-posed Laplacian eigenvalue problem under diffuse reflection and obtain a complete basis formed by products of Bessel functions and spherical harmonics. The moment equations are solved by the Galerkin spectral method, and the computation is simplified by decomposing the operator and basis functions, together with an analytical treatment of the orientational integrals. The study follows the entire transport process by examining the local and radial distributions, the drift velocity and the dispersivity, and we assess the effects of key parameters with comparisons to the specular reflection conditions. Our results show that diffuse reflection drives microswimmers away from the wall more efficiently and promotes downstream alignment and cross-stream migration. When swimming is strong, non-gyrotactic microswimmers can develop centre accumulation, whereas gyrotaxis promotes near-wall accumulation that counteracts the effect of diffuse reflection, in contrast to classical behaviour. Distinct mechanisms dominate different stages of the transient evolution, leading to different temporal trends in the radial distribution and dispersivity. Overall, diffuse reflection yields a larger drift velocity and a smaller dispersivity, while both gyrotaxis and elongation increase dispersivity.

Turbulence is often treated as memoryless. Once the forcing and control parameters are fixed and after any transients have decayed, the system settles into a unique, statistically stable turbulent state. A growing body of work shows that this paradigm does not have to be true. Even under identical forcing and boundary conditions, turbulent flows may sustain multiple long-lived structures, each with its own characteristic transport properties and fluctuations. The paper by Yao et al. (2026 J. Fluid Mech., vol. 1030, R4) demonstrates this phenomenon particularly clearly for centrifugal convection, where the flow self-organises into different numbers of coherent rolls depending on the initial conditions. Beyond reporting the observation of multiple flow states, they provide a theoretical explanation as to why only certain flow states can exist and why the range of possible multiple states shrinks as turbulence intensifies.

A comprehensive set of experiments were performed to document the separated flow over a three-dimensional (3-D) bump with the purpose of generating a benchmark experimental database useful in validating computational fluid dynamics flow simulations and improving model development. The emphasis of this manuscript is on the 3-D topographical and topological features of the separated flow that forms downstream of the bump and its sensitivity to upstream flow conditions. The bump model geometry was designed to provide well-defined and repeatable smooth-body flow separation conditions that were suitable for both experiments and simulations. The bump had a Gaussian streamwise profile with a constant maximum height equal to 8.5 % of its width over the central 60 % of its span. The remaining 40 % were outboard spanwise portions that gradually taper to zero using an error function profile to minimize tunnel sidewall boundary layer interaction effects. The model was immersed in a canonical turbulent boundary layer that was developed on a suspended flat plate in the Notre Dame Mach 0.6 closed-circuit wind tunnel. To document the effect of the incoming boundary layer thickness on the flow separation, the bump model could be located at two streamwise positions. The measurements of the flow separation region included fluorescent surface flow visualization, wall shear stress using oil-film interferometry, mean and dynamic surface pressure, hot-wire anemometry and planar and stereoscopic particle image velocimetry. It is shown that the surface flow separation topology is characterized by the `owl-face pattern of the first kind’. This flow topology consists of four singular points – two saddle points at the bump centrespan and two foci located at a spanwise-symmetric position. It is shown that the spanwise separation of the twin foci increases with Reynolds number indicating a corresponding increase in the spanwise extent of the flow separation. The two surface foci represent the footprint of vortices that lift off the ramp surface and form an arch vortex time-mean off-surface flow topology aft of the bump.

To facilitate the rapid approximate prediction of the oscillation characteristics of a fluidic oscillator featuring a mixing chamber and two feedback channels, this study develops a nonlinear reduced-order model based on its underlying oscillation mechanism. By analysing the horizontal momentum of fluid parcels in the main jet, the feedback mechanism and jet attachment within the mixing chamber are separately modelled, resulting in a reduced-order equation analogous to the van der Pol equation. The model parameters are categorised into two types: shape parameters, which are derived directly from the oscillator geometry, and characteristic parameters, which are obtained from simulations or experimental data. Based on the reduced-order model, a theoretical formula of the Strouhal number (St) is proposed for fluidic oscillators with a mixing chamber and dual-feedback channels. This formula predicts St values of approximately 0.0150 and 0.0189 for typical curved and angled fluidic oscillators, respectively, showing close agreement with experimental values of 0.015 and 0.019, respectively. It also accurately captures the linear relationship between frequency and jet velocity under incompressible conditions. In addition, the model satisfactorily predicted the variation in the jet sweeping angle over time. This study offers further insights into the oscillation mechanism of fluidic oscillators and establishes a foundation for developing more accurate reduced-order models in the future.