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.

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.

We investigate the dynamics of a cavitation bubble near rigid surfaces decorated with a single gas-entrapping hole to understand the competition between the attraction of the rigid and the repulsion of the free boundary. The dynamics of laser-induced bubbles near this gas-entrapping hole is studied as a function of the stand-off distance and diameter of the hole. Two kinds of toroidal collapses are observed that are the result of the collision of a wide microjet with the bubble wall. The bubble centroid displacement and the strength of the microjet are compared with the anisotropy parameter $\zeta$, which is derived from a Kelvin impulse analysis. We find that the non-dimensional displacement $\delta$ scales with $\zeta$.

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.