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.

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.

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.

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 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.

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.

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.

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.

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 paper investigates linear and nonlinear evolution of a radiating mode in a supersonic boundary layer in the presence of an impinging sound wave. Of special interest is the case where the sound wave has wavenumber and frequency twice those of the radiating mode, and so the two share the same phase speed and hence the critical layer. In this case, a radiating mode is sensitive to a small-amplitude sound wave due to effective interactions taking place in their common critical layer. The sound wave influences the development of the radiating mode through the mechanism of subharmonic parametric resonance, which is often referred to as Bragg scattering. Amplitude equations are derived to account for this effect in the two regimes where non-equilibrium and non-parallelism play a leading-order role, respectively. A composite amplitude equation is then constructed to account for both of these effects. These amplitude equations are solved to quantify the impact of the impinging sound wave on linear and nonlinear instability characteristics of the radiating mode. Numerical results show that the incident sound makes the amplification and attenuation of the radiating mode highly oscillatory. With sufficiently high intensity, the impinging sound enhances the radiating mode. For a certain range of moderate intensity, the impinging sound inhibits the growth of the radiating mode and may eliminate the singularity, which would form in the absence of external acoustic fluctuations. The far-field analysis shows that the incident sound alters the Mach wave field of the radiating mode significantly, rendering its pressure contours spiky and irregular.

We investigate suspensions of non-Brownian, millimetric monodisperse spherical particles floating at quasi-two-dimensional fluid interfaces, from dilute to dense concentrations. Building upon the phase diagram in the capillary number ($Ca$) and areal fraction ($\phi$) constructed by Shin & Coletti (2024 J. Fluid Mech. 984, R7), we analyse the dynamics of both aggregation and dispersion. In the capillary-driven clustering regime ($Ca \lt 1$), strong inter-particle bonds yield large, fractal-like clusters that grow by hit-and-stick collisions. In the drag-driven break-up regime ($Ca \gt 1$, $\phi \lt 0.4$), turbulent fluctuations overcome capillarity and result in particles moving similarly to passive tracers and forming clusters by random adjacency. In the lubrication-driven clustering regime ($Ca \gt 1$, $\phi \gt 0.4$), the close inter-particle proximity amplifies lubrication forces and results in large, crystal-like clusters. Above a threshold concentration that depends on $Ca$, self-similar percolating clusters span the entire domain. The particle transport exhibits a classic ballistic-to-diffusive transition, with the long-time diffusivity hindered by the reduced fluctuating energy at high concentrations. Nearby particles separate at initially slow rates due to strong capillary attraction, and then follow a super-diffusive dispersion regime. In dense suspensions, the process is characterised by the time scale associated with inter-particle collisions and by the energy dissipation rate defined by the lubrication force between adjacent particles. Our results provide a framework for predicting particle aggregation in interfacial suspensions such as froth flotation and pollutant dispersion, and may inform the design of advanced materials through controlled colloidal self-assembly.

We analyse moment and probability density function (PDF) statistics of a passive scalar $\Theta$ at a Prandtl number of $Pr=0.71$ in a turbulent jet. For this, we conducted a direct numerical simulation at a Reynolds number of $Re=3500$ and, further, employed Lie symmetries applied to the multi-point moment equations, generalising recent work (Nguyen & Oberlack 2024b under review with Flow Turbul. Combust.) that focused on pure hydrodynamics. It is shown that the symmetry theory also provides highly precise results for free shear flows for all the quantities mentioned and statistical symmetries again play a key role. The scalar statistics are partly similar to the $U_z$ velocity statistics, and in particular, as in the above-mentioned work, a significant generalisation of the classical scalings has been derived so that a variation of the scaling laws solely controlled by the inflow is possible. An exponential behaviour of the scaling prefactors with the moment orders $m$ and $n$ for scalar and velocity is also discovered for any mixed moments. Instantaneous $\Theta$-moments and mixed $U_z$-$\Theta$-moments exhibit a Gaussian distribution with variation of the scaled radius $\eta =r/(z-z_0)$. Therein, the coefficient in the Gauss exponent is nonlinear with varying moment orders $m$ and $n$. The scalar PDF statistics are clearly different from the velocity statistics, i.e. already deviate from the Gaussian distribution on the jet axis, as is observed for the $U_z$ statistics, and become clearly skewed and heavy tailed for increasing $\eta$.

Long-duration and time-resolved particle image velocimetry measurements were conducted in rough-wall open channel flows (OCFs), with the friction Reynolds number ranging from 642 to 2034. The primary objective is to investigate the impacts of various turbulent motions at different scales on the mean wall-shear stress ($\langle \tau _w \rangle$). To achieve this aim, a physical decomposition of $\langle \tau _w \rangle$ was initially performed utilizing the double-averaged methodology proposed by Nikora et al. (2019 J. Fluid Mech. 872, 626–664). This method enabled the breakdown of $\langle \tau _w \rangle$ into three distinct constituents: viscous, turbulent and dispersive stress segments. The findings underscore the substantial roles that turbulent and dispersive stresses play, accounting for over 75 % and 9 % of $\langle \tau _w \rangle$, respectively. Subsequently, a scale decomposition was further applied to analyse the contributions of coherent motions at different scales to $\langle \tau _w \rangle$. Adopting typical cutoff streamwise wavelengths ($\lambda _x = 3h$ and $10h$), the contribution of large-scale motions (LSMs) and very large-scale motions (VLSMs) to the overall wall-shear stress was quantified. It was revealed that turbulent motions with $\lambda _x \gt 3h$ and $\lambda _x \gt 10h$ contribute more than 40 % and 18 % of $\langle \tau _w \rangle$, respectively. The scale decomposition of the wall-shear stress and the contribution from LSMs and VLSMs exhibit evident dependencies on the Reynolds number. The contribution of LSMs and VLSMs to $\langle \tau _w \rangle$ is lower in rough OCFs compared with those of smooth counterparts. Secondary currents induced by the rough wall are hypothesised to be responsible for the reduced strength of LSMs and VLSMs and decreases in their contribution to $\langle \tau _w \rangle$.

A linear stability model based on a phase-field method is established to study the formation of ripples on the ice surface. The pattern on horizontal ice surfaces, e.g. glaciers and frozen lakes, is found to be originating from a gravity-driven instability by studying ice–water–air flows with a range of water and ice thicknesses. Contrary to gravity, surface tension and viscosity act to suppress the instability. The results demonstrate that a larger value of either water thickness or ice thickness corresponds to a longer dominant wavelength of the pattern, and a favourable wavelength of 90 mm is predicted, in agreement with observations from nature. Furthermore, the profiles of the most unstable perturbations are found to be with two peaks at the ice–water and water–air interfaces whose ratio decreases exponentially with the water thickness and wavenumber.

Active wake control (AWC) has emerged as a promising strategy for enhancing wind turbine wake recovery, but accurately modelling its underlying fluid mechanisms remains challenging. This study presents a computationally efficient wake model that provides end-to-end prediction capability from rotor actuation to wake recovery enhancement by capturing the coupled dynamics of wake meandering and mean flow modification, requiring only two inputs: a reference wake without control and a user-defined AWC strategy. The model combines physics-based resolvent modelling for large-scale coherent structures and an eddy viscosity modelling for small-scale turbulence. A Reynolds stress model is introduced to account for the influence of both coherent and incoherent wake fluctuations, so that the time-averaged wake recovery enhanced by the AWC can be quantitatively predicted. Validation against large-eddy simulations (LES) across various AWC approaches and actuating frequencies demonstrates the model’s predictive capability, accurately capturing AWC-specific and frequency-dependent mean wake recovery with less than 8 % error from LES while reducing computational time from thousands of central-processing-unit hours to minutes. The efficiency and accuracy of the model makes it a promising tool for practical AWC design and optimization of large-scale wind farms.

We explored the dynamics of Taylor–Couette flows within square enclosures, focusing primarily on the turbulence regime and vortex behaviour at varying Reynolds numbers. Laboratory experiments were conducted using particle image velocimetry for Reynolds numbers $Re_{\varDelta }\in [0.23, 4.6]\times 10^3$ based on the minimum gap $\varDelta /d = 1/16$, $1/8$ and $1/4$, where $d$ is the cylinder diameter, or $Re\in [1.8, 9.8]\times 10^3$ based on $d/2$. At lower $Re$, the flow was dominated by well-defined Taylor and Görtler vortices, while higher $Re$ led to a turbulent state with distinct motions. Space–time radial velocity analysis revealed persistent Taylor vortices at lower $Re$, with larger gaps but increased turbulence, and irregular motions at higher $Re$, with smaller gaps. Velocity spectra reveal that the energy distribution is maintained at frequencies lower than the integral-type frequency $f_I$ across varying $\varDelta$ due to the dominance of large vortices. However, there is a monotonic increase in energy at higher frequencies beyond $f_I$. The reduced characteristic frequency $f_I\varDelta /\omega _ir_i \sim 1/10$ indicates that these motions scale linearly with angular velocity, and inversely with the gap. Proper orthogonal decomposition (POD) and spectral POD were used to distinguish between Taylor and Görtler vortices, showing the effects of gap size and the associated energy cascade. Linear stability analysis included as complementary support revealed primary instability of the Taylor vortex, which is similar to the circular enclosure, along with multiple corner modes that are unique to the geometry.