Microswimmers display an intriguing ability to navigate through fluids with spatially varying viscosity, a behaviour known as viscotaxis, which plays a crucial role in guiding their motion. In this study, we reveal that the orientation dynamics of chiral squirmers in fluids with uniform viscosity gradients can be elegantly captured using the Landau–Lifshitz–Gilbert equations, originally developed for spin systems. Remarkably, we discover that chiral swimmers demonstrate negative viscotaxis, tracing spiral trajectories as they move. Specifically, a chiral squirmer with a misaligned source dipole and rotlet dipole exhibits a steady-state spiral motion – a stark contrast to the linear behaviour observed when the dipoles are aligned. This work provides fresh insights into the intricate interplay between microswimmer dynamics and fluid properties.

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 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 $\eta$.

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.

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.

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.

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.

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.

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.