We investigate the dynamics, wake instabilities and regime transitions of inertial flow past a transversely rotating angular particle. We first study the transversely rotating cube with a four-fold rotational symmetry axis (RCF4), elucidating the mechanisms of vortex generation and the merging process on the cube surface during rotation. Our results identify novel vortex shedding structures and reveal that the rotation-enhanced merging of streamwise vortex pairs is the key mechanism driving vortex suppression. The flow inertia and particle rotation are demonstrated to be competing factors that influence wake instability. We further analyse the hydrodynamic forces on the rotating cube, with a focus on the Magnus effect, highlighting the influence of sharp edges on key parameters such as lift, drag, rotation coefficients and the shedding frequency. We note that the lift coefficient is independent of flow inertia at a specific rotation rate. We then examine more general angular particles with different numbers of rotational symmetry folds – RTF3 (three-fold tetrahedron), RCF3 (three-fold cube) and ROF4 (four-fold octahedron) – to explore how particle angularity and rotational symmetry affect wake stability, regime transitions and hydrodynamic forces. We show that the mechanisms of vortex generation and suppression observed in RCF4 apply effectively to other angular particles, with the number of rotational symmetry folds playing a crucial role in driving regime transitions. An increased rotational symmetry fold enhances vortex merging and suppression. Particle angularity has a pronounced influence on hydrodynamic forces, with increased angularity intensifying the Magnus effect. Furthermore, the number of effective faces is demonstrated to have a decisive impact on the shedding frequency of the wake structures. Based on the number of effective faces during rotation, we propose a generic model to predict the Strouhal number, applicable to all the angular particles studied. Our results demonstrate that the particle angularity and rotational symmetry can be effectively harnessed to stabilise the wake flow. These findings provide novel insights into the complex interactions between particle geometry, rotation and flow instability, advancing the understanding of the role sharp edges play in inertial flow past rotating angular particles.

This study proposes a machine-learning-based subgrid scale (SGS) model for very coarse-grid large-eddy simulations (vLES). An issue with SGS modelling for vLES is that, because the energy-containing eddies are not accurately resolved by the computational grid, the resolved turbulence deviates from the physically accurate turbulence. This limits the use of supervised machine-learning models commonly trained using pairs of direct numerical simulation (DNS) and filtered DNS data. The proposed methodology utilises both unsupervised learning (cycle-consistency generative adversarial network (GAN)) and supervised learning (conditional GAN) to construct a machine-learning pipeline. The unsupervised learning part of the proposed method first transforms the non-physical vLES flow field to resemble a physically accurate flow field. The second supervised learning part employs super-resolution of turbulence to predict the SGS stresses. The proposed pipeline is trained using a fully developed turbulent channel at the friction Reynolds number of approximately 1000. The a priori validation shows that the proposed unsupervised–supervised pipeline successfully learns to predict the accurate SGS stresses, while a typical supervised-only model shows significant discrepancies. In the a posteriori test, the proposed unsupervised–supervised-pipeline SGS model for vLES using a progressively coarse grid yields good agreement of the mean velocity and Reynolds shear stress with the reference data at both the trained Reynolds number 1000 and the untrained higher Reynolds number 2000, showing robustness against varying Reynolds numbers. A budget analysis of the Reynolds stresses reveals that the proposed unsupervised–supervised-pipeline SGS model predicts a significant amount of SGS backscatter, which results in the strengthened near-wall Reynolds shear stress and the accurate prediction of mean velocity.

Viscous fingering instabilities, common in confined environments such as porous media or Hele-Shaw cells, surprisingly also occur in unconfined, non-porous settings as revealed by recent experiments. These novel instabilities involve free-surface flows of dissimilar viscosity. We demonstrate that such a free-surface flow, involving a thin film of viscous fluid spreading over a substrate that is prewetted with a fluid of higher viscosity, is susceptible to a similar type of novel viscous fingering instability. Such flows are relevant to a range of geophysical, industrial and physiological applications from the small scales of thin-film coating applications and nasal drug delivery to the large scales of lava flows. In developing a theoretical framework, we assume that the intruding layer and the liquid film over which it flows are both long and thin, the effects of inertia and surface tension are negligible, and both layers are driven by gravity and resisted by viscous shear stress so that the principles of lubrication theory hold. We investigate the stability of axisymmetric similarity solutions, describing the base flow, by examining the growth of small-amplitude non-axisymmetric perturbations. We characterise regions of instability across parameter space and find that these instabilities emerge above a critical viscosity ratio. That is, a fluid of low viscosity intruding into another fluid of sufficiently high viscosity is susceptible to instability, akin to traditional viscous fingering in a porous medium. We identify the mechanism of instability, compare with other frontal instabilities and demonstrate that high enough density differences suppress the instability completely.

The scattering of surface waves by structures intersecting liquid surfaces is fundamental in fluid mechanics, with prior studies exploring gravity, capillary and capillary–gravity wave interactions. This paper develops a semi-analytical framework for capillary–gravity wave scattering by a fixed, horizontally placed, semi-immersed cylindrical barrier. Assuming linearised potential flow, the problem is formulated with differential equations, conformal mapping and Fourier transforms, resulting in a compound integral equation framework solved numerically via the Nyström method. An effective-slip dynamic contact line model accounting for viscous dissipation links contact line velocity to deviations from equilibrium contact angles, with fixed and free contact lines of no dissipation as limiting cases. The framework computes transmission and reflection coefficients as functions of the Bond number, slip coefficient and barrier radius, validating energy conservation and confirming a $90^\circ$ phase difference between transmission and reflection in specific limits. A closed-form solution for scattering by an infinitesimal barrier, derived using Fourier transforms, reveals spatial symmetry in the diffracted field, reduced transmission transitioning from gravity to capillary waves and peak contact line dissipation when the slip coefficient matches the capillary wave phase speed. This dissipation, linked to impedance matching at the contact lines, persists across a range of barrier sizes. These results advance theoretical insights into surface-tension-dominated fluid mechanics, offering a robust theoretical framework for analysing wave scattering and comparison with future experimental and numerical studies.

Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching modelling framework is absent. This paper provides a unified framework for N-phase incompressible Navier–Stokes Cahn–Hilliard Allen–Cahn mixture models with a single momentum equation. The framework emerges naturally from continuum mixture theory, exhibits an energy-dissipative structure, and is invariant to the choice of fundamental variables. This opens the door to exploring connections between existing N-phase models and facilitates the computation of N-phase flow models rooted in continuum mixture theory.

The interaction between the dynamics of a flame front and the acoustic field within a combustion chamber represents an aerothermochemical problem with the potential to generate hazardous instabilities, which limit burner performance by constraining design and operational parameters. The experimental configuration described here involves a laminar premixed flame burning in an open–closed slender tube, which can also be studied through simplified modelling. The constructive coupling of the chamber acoustic modes with the flame front can be affected via strategic placement of porous plugs, which serve to dissipate thermoacoustic instabilities. These plugs are lattice-based, 3-D-printed using low-force stereolithography, allowing for complex geometries and optimal material properties. A series of porous plugs was tested, with variations in their porous density and location, in order to assess the effects of these variables on viscous dissipation and acoustic eigenmode variation. Pressure transducers and high-speed cameras are used to measure oscillations of a stoichiometric methane–air flame ignited at the tube’s open end. The findings indicate that the porous medium is effective in dissipating both pressure amplitude and flame-front oscillations, contingent on the position of the plug. Specifically, the theoretical fluid mechanics model is developed to calculate frequency shifts and energy dissipation as a function of plug properties and positioning. The theoretical predictions show a high degree of agreement with the experimental results, thereby indicating the potential of the model for the design of dissipators of this nature and highlighting the first-order interactions of acoustics, viscous flow in porous media and heat transfer processes.

Waves propagating over oscillating periodic structures can be reflected and attenuated either by Bragg scattering or by local resonance. In this work, we focus on the interplay between surface gravity waves and submerged resonators, investigating the effect of the local resonance on wave propagation. The study is performed using a state of the art numerical simulation of the Navier–Stokes equation in two-dimensional form with free boundary and moving bodies. A volume of fluid interface technique is employed for tracking the free surface, and an immersed boundary method for the fluid–structure interaction. A wave maker is placed at one end of the flume and an absorbing beach at the other. The evolution in space of a monochromatic wave interacting with up to four resonators coupled only fluid mechanically is presented. We evaluate the efficiency of the system in terms of wave amplitude attenuation and energy transfers between the fluid and the solid phase. The results indicate that, near resonance conditions, both wave reflection and energy dissipation increase significantly. Conversely, far from resonance, waves can propagate through the system with minimal dissipation, even in the presence of numerous resonators. Moreover, when the time scale associated with the resonator’s restoring force is longer than the wave period, the resonators tend to follow the wave motion, oscillating with an amplitude comparable to that of the wave. In contrast, when the two time scales are similar, the resonator motion becomes amplified, resulting in stronger velocity gradients and enhanced viscous dissipation.

The dynamics of ice basal melting in seawater is one of the key factors in understanding and modelling the ice–seawater interaction in the polar oceans. In this work we study the basal melting of solid ice in seawater, and focus on the interaction between the melting process and the double diffusive convection developed in the seawater layer. Different temperatures and salinity differences are systematically simulated, and two different flow regimes are identified. For a relatively weak salinity difference, the convection layer occupies most of the liquid layer and grows in height as the ice melts. When the salinity difference is strong enough, the convection layer shrinks with time and a stably stratified layer grows between the ice layer and convection layer. When the dynamics is dominated by the convection layer, the global heat and salinity transfer rates follow a power-law scaling. Theoretical models are developed for the local mean salinity at the ice–water interface and the melting rates, and the critical density ratio corresponding to the transition between the two regimes, which all agree with the numerical results. Density inversion happens consistently adjacent to the ice–seawater interface, which has a profound influence on the ice surface shape. All these findings provide useful insights into the detailed dynamics of ice basal melting in oceans.

Riblets are a well-known passive drag reduction technique with the potential for as much as $9\, \%$ reduction in the frictional drag force in laboratory settings, and proven benefits for large-scale aircraft. However, less information is available on the applicability of these textures for smaller air/waterborne vehicles where assumptions such as periodicity and/or the asymptotic nature of the boundary layer (BL) no longer apply and the shape of the bodies of these vehicles can give rise to moderate levels of pressure drag. Here, we explore the effect of riblets on both sides of a finite-size foil consisting of a streamlined leading edge and a flat body in the Reynolds number range of $12\,200$–$24\,200$. We use high-resolution two-dimensional, two-component particle image velocimetry, with a double illumination and a consecutive-overlapping imaging technique to capture the velocity field in both the BL and the far field. We find the local velocity profiles and shear stress distribution, as well as the frictional and pressure components of the drag force and show the possibility of achieving reduction in both the frictional and pressure components of the drag force and record a maximum cumulative drag reduction of up to $6.5\, \%$. We present the intertwined relationship between the distribution of the spanwise-averaged shear stress distribution, the characteristics of the velocity profiles and the pressure distribution around the body, and how the local distribution of these parameters work together or against each other in enhancing or diminishing the drag-reducing ability of the riblets for the entirety of the body of interest.

The fate of deformable buoyancy-driven bubbles rising near a vertical wall under highly inertial conditions is investigated numerically. In the absence of path instability, simulations reveal that, when the Galilei number, $Ga$, which represents the buoyancy-to-viscous force ratio, exceeds a critical value, bubbles escape from the near-wall region after one to two bounces, while at smaller $Ga$ they perform periodic bounces without escaping. The escape mechanism is rooted in the vigorous rotational flow that forms around a bubble during its bounce at high enough $Ga$, resulting in a Magnus-like repulsive force capable of driving it away from the wall. Path instability takes place with bubbles whose Bond number, the buoyancy-to-capillary force ratio, exceeds a critical $Ga$-dependent value. Such bubbles may or may not escape from the wall region, depending on the competition between the classical repulsive wake–wall interaction mechanism and a specific wall-ward trapping mechanism. The latter results from the reduction of the bubble oblateness caused by the abrupt drop of the rise speed when the bubble–wall gap becomes very thin. Owing to this transient shape variation, bubbles exhibiting zigzagging motions with a large enough amplitude experience larger transverse drag and virtual mass forces when departing from the wall than when returning to it. With moderately oblate bubbles, i.e. in an intermediate Bond number range, this effect is large enough to counteract the repulsive interaction force, forcing such bubbles to perform a periodic zigzagging-like motion at a constant distance from the wall.

This paper presents a method to stabilise oscillations occurring in a mixed convective flow in a nearly hemispherical cavity, using actuation based on the receptivity map of the unstable mode. This configuration models the continuous casting of metallic alloys, where hot liquid metal is poured at the top of a hot sump with cold walls pulled in a solid phase at the bottom. The model focuses on the underlying fundamental thermohydrodynamic processes without dealing with the complexity inherent to the real configuration. This flow exhibits three branches of instability. The solution of the adjoint eigenvalue problem for the convective flow equations reveals that the regions of highest receptivity for unstable modes of each branch concentrate near the inflow upper surface. Simulations of the linearised governing equations show that a thermomechanical actuation modelled on the adjoint eigenmode asymptotically suppresses the unstable mode. If the actuation’s amplitude is kept constant in time, which is easier to implement in an industrial environment, the suppression is still effective but only over a finite time, after which it becomes destabilising. Based on this phenomenology, we apply the same actuation during the stabilising phase only in the nonlinear evolution of the unstable mode. It turns out stabilisation persists, even when the unstable mode is left to evolve freely after the actuation period. These results not only demonstrate the effectiveness of receptivity-informed actuation in stabilising convective oscillations but also suggest a simple strategy for their long-term control.

The dynamics of wall-mounted flexible structures, such as aquatic vegetation, is essential for analysing collective behaviours, flow distributions and vortex formation across different scales. To accurately model these structures under various flow conditions, we develop a novel numerical method that couples the immersed boundary method (IBM) with the vector form intrinsic finite element (VFIFE) method, referred to as the IBM–VFIFE method. We simulate both flexible and rigid stems, each with a constant aspect ratio of 10, mounted on an impermeable bottom in uniform flow with the Reynolds number ranging from 200 to 1000. In the rigid case, we identify three distinct flow regimes based on the vortex dynamics and lift spectral characteristics. Due to the influences of downwash flow at the free end and upwash flow near the junction, vortex shedding varies significantly along the vertical direction. For the flexible case, we examine a wide range of stem stiffness values to explore potential dynamic responses. The results reveal that stiffness plays a key role in stem behaviour, leading to three distinct classifications based on amplitude magnitude and displacement spectra respectively. Notably, the vortex dynamics of a flexible stem differs significantly from that of a rigid stem due to shape deformation and stem oscillation. A flexible stem with relatively high stiffness experiences greater hydrodynamic loads compared with its rigid counterpart. This study highlights the unique stem behaviours and vortex dynamics associated with flexible stems. We find that stem oscillation, combined with a near-wake base vortex, contributes to an upwash flow near the stem bottom, which significantly weakens (or, in some cases, eliminates) the downwash flow. Additionally, low-frequency oscillations in the streamwise and vertical directions are observed, while the transverse oscillation exhibits a dominant frequency one order of magnitude higher. Overall, this study provides valuable insights into the response and vortex dynamics of a single stem in uniform flow.

We present a numerical scheme that solves for the self-similar viscous fingers that emerge from the Saffman–Taylor instability in a divergent wedge. This is based on the formulation by Ben Amar (1991, Phys. Rev. A, vol. 44, pp. 3673–3685). It is demonstrated that there exists a countably infinite set of selected solutions, each with an associated relative finger angle, and furthermore, solutions can be characterised by the number of ripples located at the tip of their finger profiles. Our numerical scheme allows us to observe these ripples and measure them, demonstrating that the amplitudes are exponentially small in terms of the surface tension; the selection mechanism is driven by these exponentially small contributions. A recently published paper derived the selection mechanism for this problem using exponential asymptotic analytical techniques, and obtained bifurcation diagrams that we compare with our numerical results.

The classical water-wave theory often neglects water compressibility effects, assuming acoustic and gravity waves propagate independently due to their disparate spatial and temporal scales. However, nonlinear interactions can couple these wave modes, enabling energy transfer between them. This study adopts a dynamical systems approach to investigate acoustic–gravity wave triads in compressible water flow, employing phase-plane analysis to reveal complex bifurcation structures and identify steady-state resonant configurations. Through this framework, we identify specific parameter conditions that enable complete energy exchange between surface and acoustic modes, with the triad phase (also known as the dynamical phase) playing a crucial role in modulating energy transfer. Further, incorporating spatial dependencies into the triad system reveals additional dynamical effects that depend on the wave velocity and resonance conditions: we observe that travelling-wave solutions emerge, and their stability is governed by the Hamiltonian structure of the system. The phase-plane analysis shows that, for certain velocity regimes, the resonance dynamics remains similar to the spatially independent case, while in other regimes, bifurcations modify the structure of resonant interactions, influencing the efficiency of energy exchange. Additionally, modulated periodic solutions appear, exhibiting changes in wave amplitudes over time and space, with implications for wave-packet stability and energy localisation. These findings enhance the theoretical understanding of acoustic–gravity wave interactions, offering potential applications in geophysical phenomena such as oceanic microseisms.

Many hypersonic flows of interest feature high free-stream stagnation enthalpies, which lead to high flow-field temperatures and thermochemical non-equilibrium (TCNE) effects, such as finite-rate chemistry and vibrational excitation. However, very few studies have considered receptivity for high-enthalpy flows. In this paper, we investigate the receptivity of a high-enthalpy Mach 5 straight-cone boundary layer to slow and fast acoustic free-stream waves using direct numerical simulation alongside linear stability theory and the linear parabolised stability equations. In addition, we investigate the TCNE effect on receptivity by comparing results between the TCNE gas model and a thermochemically frozen gas model. The dominant instability mechanism for this flow configuration is found to be Mack’s second mode, with the unstable mode being the fast mode. Second-mode receptivity coefficients are obtained for a number of frequencies. For free-stream slow acoustic waves, these receptivity coefficients are found to generally increase with frequency. For a small subset of the considered frequency range, the receptivity coefficients corresponding to free-stream fast acoustic waves are found to be several times larger than for free-stream slow acoustic waves. The TCNE effects are found to lead to higher peak $N$-factors while also reducing second-mode receptivity coefficients, indicating that TCNE effects have competing impacts on receptivity versus stability for the considered frequencies.

The phenomenon of bulge evolution under the action of gravity on shallow water is prevalent both in natural occurrences and engineering industries. However, despite its ubiquity, its physical process remains largely unexplored. The evolution of bulge contains two fundamental physical processes: collapse and propagation. The collapse process can be further divided into two sub-processes: squeezing process and diffusion process. Based on the weakly nonlinear shallow water assumption with the classical perturbation method, the governing equations controlling the surface elevations in the diffusion process and the propagation process have been theoretically derived, where a bulge-induced surface pressure is modeled for the propagation process. Moreover, their scaling laws for the decay of wave height are also established, which have been validated by direct numerical simulation results. The derived scaling laws for wave height attenuation of bulge evolution provide profound insights, which hold the potential to applications in the engineering industry.

The motion of several plates in an inviscid and incompressible fluid is studied numerically using a vortex sheet model. Two to four plates are initially placed in line, separated by a specified distance, and actuated in the vertical direction with a prescribed oscillatory heaving motion. The vertical motion induces the plates’ horizontal acceleration due to their self-induced thrust and fluid drag forces. In certain parameter regimes, the plates adopt equilibrium ‘schooling modes’, wherein they translate at a steady horizontal velocity while maintaining a constant separation distance between them. The separation distances are found to be quantised on the flapping wavelength. As either the number of plates increases or the flapping amplitude decreases, the schooling modes destabilise via oscillations that propagate downstream from the leader and cause collisions between the plates, an instability that is similar to that observed in recent experiments on flapping wings in a water tank (Newbolt et al., 2024, Nat. Commun., vol. 15, 3462). A simple control mechanism is implemented, wherein each plate accelerates or decelerates according to its velocity relative to the plate directly ahead by modulating its own flapping amplitude. This mechanism is shown to successfully stabilise the schooling modes, with remarkable impact on the regularity of the vortex pattern in the wake. Several phenomena observed in the simulations are obtained by a reduced model based on linear thin-aerofoil theory.

The settling of highly elastic non-Brownian closed fibres (called loops) under gravity in a viscous fluid is investigated numerically. The loops are represented using a bead–spring model with harmonic bending potential and finitely extensible nonlinear elastic stretching potential. Numerical solutions to the Stokes equations are obtained with the use of HYDROMULTIPOLE numerical codes, which are based on the multipole method corrected for lubrication to calculate hydrodynamic interactions between spherical particles with high precision. Depending on the elasto-gravitation number $B$, a ratio of gravitation to bending forces, the loop approaches different attracting dynamical modes, as described by Gruziel-Słomka et al. (2019 Soft Matt. 15, 7262–7274) with the use of the Rotne–Prager mobility of the elastic loop made of beads. Here, using a more precise method, we find and characterise a new mode, analyse typical time scales, velocities and orientations of all the modes, compare them and investigate their coexistence. We analyse numerically the transitions (bifurcations) to a different mode at certain critical values of the elasto-gravitation number.