Bubble flows from underwater orifices are fundamental to gas–liquid operations, although the influence of orifice geometry on bubble dynamics and induced flows remains underexplored. Shadowgraphy and laser-induced fluorescence particle image velocimetry are employed to investigate bubbles released into a quiescent liquid from circular and elliptical orifices with aspect ratios AR = 1–4. Elliptical orifices produce smaller bubbles with higher aspect ratios and greater morphological complexity. These features result from anisotropic contact angles along the orifice edge, which induce non-uniform capillary forces and strong deformation at detachment. This mechanism drives high-amplitude zigzag trajectories, distinct from the spiral paths observed with circular orifices. A force-budget analysis attributes the enhanced lateral drift to rotation-induced forces. In the wake, circular orifices sustain coherent counter-rotating vortices, whereas elliptical orifices promote irregular shedding and multiscale structures. The induced turbulence spectra follow an approximate $-2$ scaling. Furthermore, flows from elliptical orifices exhibit a higher fractal dimension of the turbulent/non-turbulent interface and stronger entrainment, with a marked increase in the engulfment flux. These results quantify the mechanisms by which orifice geometry determines bubble dynamics and the developing flow field.

We investigate the three-dimensional responses of a floating ice sheet on an ideal fluid subjected to moving loads. This study considers the effects of nonlinearity, viscoelasticity and inertia. We develop a fully dispersive model that incorporates quadratic and cubic nonlinearities by using the Taylor expansion of the Dirichlet–Neumann operator within the boundary conditions; we refer to this model as the cubic model. By using the multiple-scale expansion method at the minimum phase speed, we derive the corresponding envelope equation, known as the Benney–Roskes–Davey–Stewartson (BRDS) system. We also examine the bifurcation diagrams of solitary waves within the cubic model and justify it by comparing the bifurcation mechanism to the BRDS theory. Through numerical simulations, we compare the predictions of the cubic model with previous field observations and find strong agreement, confirming its effectiveness. Furthermore, we explore how the ice sheet responds to moving loads at varying velocities. Our findings indicate that both acceleration and deceleration processes increase ice deflection when the target or initial speed of the load exceeds the minimum phase speed. Finally, we verify the reliability of the cubic model in addressing scenarios involving variable load speeds through comparisons with the analytical solution derived from linear theory.

The orientation dynamics of a spheroidal magnetic particle in a viscous fluid subject to a rotating magnetic field is analysed for realistic two-parameter models for the magnetic moment. It is shown that the equations can be mapped onto those for a spherical magnetic particle in a steady magnetic field subject to shear flow. Time evolution equations for the azimuthal and meridional angles of the orientation vector are derived from the condition that the sum of the hydrodynamic and magnetic torques is zero in the viscous limit. One parameter is $\omega ^{\dagger}$, the ratio of the magnetic field frequency and the particle viscous relaxation rate. For the non-hysteretic Langevin model, the second parameter is the ratio of the saturation moment $m_s$ and the susceptibility $\chi$ times the magnetic field $H,\!(m_s/\chi\! H)$. There is parallel corotation of the particle with the field for $\omega ^{\dagger} \lt \omega _b^{\dagger}$, and parallel slip relative to the magnetic field for high $\omega ^{\dagger} \gt \omega _b^{\dagger}$, where $\omega _b^{\dagger}$ is the breakdown frequency. For the hysteretic Stoner–Wohlfarth model, the second parameter is $h$, the ratio of the Zeeman energy and the anisotropy energy due to the misalignment between the moment and the particle axis. There are three states, parallel corotation for low $\omega ^{\dagger}$, precessed corotation for high $\omega ^{\dagger}$ and low $h$, where the orientation precesses relative to the axis of rotation of the magnetic field, and parallel slip at high $\omega ^{\dagger}$ and high $h$.

We propose a novel machine-learning-based turbulence closure framework in which a tensor basis neural network (TBNN) is directly embedded into a Reynolds-averaged Navier–Stokes (RANS) formulation, eliminating reliance on traditional baseline turbulence models. The TBNN is trained to predict the Reynolds stress anisotropic tensor from local invariant inputs and geometry-informed features, including stream function and velocity potential. Its output is processed by a regression model that generates an optimised eddy viscosity field, which is then integrated into the RANS equations as a zero-equation turbulence closure. The framework is evaluated on three turbulent flows over complex geometries: a wavy-bottom channel, a smoothed step and a backward-facing step. Incorporating geometry-informed features significantly enhances model robustness, yielding numerically stable and convergent solutions across all cases. The predicted velocity fields and turbulence distributions closely match large eddy simulation (LES) data, confirming the accuracy of the proposed approach and demonstrating its ability to operate independently of conventional turbulence closures.

We report the first streamwise-localised travelling-wave solution in square-duct flow that acts as an edge state in the full phase space, without any imposed spatial symmetries. Performing edge tracking and Newton iteration, we identify a steady travelling wave that possesses a codimension-one stable manifold, which (at least locally) forms the boundary between the basins of laminar and turbulent attractors. Parametric continuation identifies this solution as the lower branch of a saddle-node bifurcation pair. Perturbation analysis places both solutions on the laminar–turbulent boundary and uncovers a heteroclinic connection that links the two branches and is likewise confined to the basin boundary. This symmetry-free, localised edge state expands the catalogue of invariant solutions in wall-bounded shear flows and provides a geometric framework for understanding the transition dynamics in extended systems.

We derive the asymptotic solution for the onset of steady, linear, Boussinesq convection in a rapidly rotating system with stress-free, fixed-flux boundary conditions. While the fixed-temperature (FT) case is attainable analytically with relative ease, the fixed-flux (FF) configuration presents greater complexity. However, in the rapidly rotating limit, the leading-order interior solution remains unaffected by the choice of thermal boundary conditions. We exploit this property by employing an asymptotic approach to characterise the differences between the FT and FF systems. Specifically, this involves constructing a composite boundary layer structure comprising an Ekman layer of thickness $ {\textit{Ta}}^{-1/4}$, where $ \textit{Ta}$ is the Taylor number ($ \textit{Ta} \gg 1$ for rapid rotation), and a thermal boundary layer of thickness $ {\textit{Ta}}^{-1/6}$, to accommodate the FF boundary condition. To capture both scales systematically, we introduce the small parameter ${\varepsilon } = {\textit{Ta}}^{-1/12}$, representing the ratio between the two boundary layer thicknesses, and use it to guide the asymptotic expansion. The asymptotic corrections capturing the differences between the two systems are combined with the FT system to construct the corresponding solution for the FF system. We find an asymptotic correction of ${\mathcal{O}} ( {\textit{Ta}}^{-1/2} )$ to the critical Rayleigh number, corresponding wavenumber, vertical velocity and temperature, along with a correction of ${\mathcal{O}} ( {\textit{Ta}}^{-1/6} )$ to the vertical vorticity.

Stochastic models of near-wall turbulence commonly rely on the Markovian assumption, despite evidence that coherent structures induce long-lived temporal correlations. Here, we test the validity of this assumption using micron-sized particle resuspension from the viscous sublayer. Analysis of direct numerical simulation (DNS) data reveals that while high- and low-drag events occur with Poissonian statistics, their internal dynamics is strongly persistent, with a Hurst exponent $H \approx 0.84$, indicating intrinsic non-Markovian behaviour. We therefore develop a non-Markovian resuspension model based on a fractional Ornstein–Uhlenbeck process, with physical parameters extracted directly from the DNS flow. Comparative simulations show that the empirical success of classical Markovian models arises not from an accurate description of the near-wall dynamics, but from their free parameter $C_{0}$ acting as a phenomenological surrogate for unresolved flow memory. We further identify a critical regime transition controlled by the event decay rate $\lambda$: strong intermittency ($\lambda \lt 0.2$) invalidates the Markovian approximation, whereas weak intermittency ($\lambda \gt 0.2$) renders it physically justifiable. These results define quantitative limits on stochastic modelling in near-wall turbulence.

Supersonic diamond airfoils operating in ground effect exhibit choking phenomena, where slight variations in free-stream Mach number can induce significant alterations in the ground effect flow structure and consequently affect the aerodynamic loading on the airfoil. However, existing models for predicting the choking limit Mach number demonstrate systematic discrepancies. This study establishes a novel predictive model by analysing the steady inviscid supersonic flow field around a two-dimensional diamond airfoil in ground effect. Benchmarking against numerical simulations demonstrates that the prediction errors for the choking limit Mach number across various diamond airfoil geometries are all below 3.5 %. These results affirm the high accuracy of the proposed predictive model. Under critical choking conditions, the ground effect flow field manifests multiple shock structures, including regular reflection, curved reflection and strong Mach reflection. Crucially, all of these configurations share the characteristic feature of the reflected shock impinging on the lower vertex of the airfoil. Consequently, the problem of predicting the choking limit is reformulated as determining the free-stream Mach number at which the reflected shock strikes the lower vertex of the airfoil. To circumvent complications from the reflected shock curvature inherent to critical choking, the model solves mass and momentum conservation equations for a strategically defined control volume. This approach eliminates curvature-induced errors, enabling precise prediction of the choking limit Mach number for supersonic diamond airfoils in ground effect.

This study examines the cross-flow vortex-induced vibration (VIV) of a circular cylinder in combined current–oscillatory inflows, revealing a distinct multi-frequency response characterised by beat-like modulation. Systematic water-channel experiments were conducted across a range of reduced velocities, inflow oscillation intensities and frequency ratios to investigate the synchronisation mechanisms among inflow velocity variations, cylinder motion and hydrodynamic loading. Results show that the presence of oscillatory inflow can lead to significant deviations of vibration amplitudes from quasi-steady predictions within the upper-branch regime. At a given reduced velocity, the cylinder motion is dominated by a primary frequency component similar to that observed in steady flow, but accompanied by two secondary components. The contributions of these supplementary frequencies increase with inflow oscillation intensity but diminish as the oscillation frequency rises. Analysis of time-varying hydrodynamic forces reveals that, in the upper-branch regime, the vortex-force phase angle deviates substantially from quasi-steady estimation based on instantaneous reduced velocity, which is associated with non-quasi-steady vortex-shedding patterns. Particle image velocimetry measurements reveal that when the minimum vortex-force phase angle lies between 0$^\circ$ and 180$^\circ$ over the inflow oscillation cycle, a mixed vortex-shedding mode emerges. This mode is characterised by a vortex sequence resembling the ‘2P’ (two-pair) shedding pattern but with negligible secondary vortices, occurring predominantly during intervals of low inflow velocity. A theoretical framework incorporating nonlinear damping and excitation coefficients assuming quasi-steady response well predicts VIV amplitudes and elucidates the influence of inflow oscillation intensity and frequency on the emergence of supplementary vibration frequencies.

This study experimentally investigates bubble size evolution and void fraction redistribution in an unexplored, coalescence-dominated regime of a decaying turbulent bubbly flow. The flow is generated downstream of a regenerative pump in a duct, with bulk Reynolds number (Re) $\sim \mathcal{O}(10^5)$, Taylor-scale Reynolds number (Re$_\lambda$) $\sim \mathcal{O}(10^3)$ and void fraction ($\phi$) $\sim \mathcal{O}(1\,\%)$, where the inlet turbulence is extremely intense (turbulence intensity $\gt 30\,\%$) but decays rapidly along the duct. Shadowgraph imaging and particle shadow velocimetry are used for measurements. The experimentally obtained turbulent dissipation in the duct flow decays as $\varepsilon \sim \mathcal{L}^{-2}$, where $\mathcal{L}$ is the axial position, in close agreement with the homogeneous isotropic turbulence prediction of $\varepsilon \sim \mathcal{L}^{-2.2}$. High-speed imaging and statistical analysis reveal that bubble coalescence dominates over breakup across most of the domain, leading to monotonic growth in the Sauter mean diameter ($d_{32}$) and progressive broadening of the bubble size distribution. The normalised extreme-to-mean diameter ratio ($\mathcal{D}$) increases axially and asymptotically from ${\sim} 1.9$ (breakup regime) and saturates at ${\sim} 2.2$ (coalescence regime), indicating the emergence of a quasi-self-similar bubble size distribution. The probability density function of the bubble diameter exhibits a dual power-law tail with exponents $-10/3$ and $-3/2$ near the duct inlet. However, after a few hydraulic diameters, a single $-3/2$ power-law scaling emerges, indicating a regime of pure coalescence in which all bubbles are smaller than the Hinze scale. The cumulative distribution plotted against $d/d_{32}$ shows that the slope decreases and the distribution width increases with both axial position and void fraction $(\phi )$. Although classical Hinze scaling gives $d_{\textit{H}} \propto \mathcal{L}^{0.9}$, our theory for $d_{32}$ and $d_{99.8}$ (99.8th percentile bubble diameter) in a pure-coalescence regime predicts the slower law $\propto \mathcal{L}^{0.5}$, which our experimental results confirm – indicating negligible breakup and sub-Hinze growth. Concurrently, in contrast to current models, transient $\phi$ profiles evolve from nearly uniform to sharply core-peaked Gaussian distributions in the developing regime, with increasing centreline values and decreasing near-wall values, due to lift-force reversal. These results provide the first spatially resolved characterisation of coalescence-dominated bubbly flows at high Re, advancing the design of industrial systems as in nuclear cooling and multiphase forming processes (e.g. paper manufacturing, chemical reactors).

In this work, we revisit the Generalised Navier Boundary Condition (GNBC) introduced by Qian et al. in the sharp interface volume-of-fluid context. We replace the singular uncompensated Young stress by a smooth function with a characteristic width $\varepsilon \gt 0$ that is understood as a physical parameter of the model. Therefore, we call the model the ‘contact region GNBC’ (CR-GNBC). We show that the model is consistent with the fundamental kinematics of the contact angle transport described by Fricke, Köhne and Bothe. We implement the model in the geometrical volume-of-fluid solver Basilisk using a ‘free angle’ approach. This means that the dynamic contact angle is not prescribed, but reconstructed from the interface geometry and subsequently applied as an input parameter to compute the uncompensated Young stress. We couple this approach to the two-phase Navier–Stokes solver and study the withdrawing tape problem with a receding contact line. It is shown that the model allows for grid-independent solutions and leads to a full regularisation of the singularity at the moving contact line, which is in accordance with the thin film equation subject to this boundary condition. In particular, it is shown that the curvature at the moving contact line is finite and mesh converging. As predicted by the fundamental kinematics, the parallel shear stress component vanishes at the moving contact line for quasi-stationary states (i.e. for $\dot \theta _d=0$), and the dynamic contact angle is determined by a balance between the uncompensated Young stress and an effective contact line friction. Furthermore, a nonlinear generalisation of the model is proposed, which aims at reproducing the molecular kinetic theory of Blake and Haynes for quasi-stationary states.

Shock–boundary-layer interactions on hypersonic cone-step flows exhibit a range of intrinsic unsteady behaviours, from shear-layer oscillations to large-scale pulsations. This work investigates the unsteadiness in a cone-step geometry at Mach 6 under quiet-flow conditions at different free-stream Reynolds numbers using time-resolved schlieren imaging and spectral proper orthogonal decomposition. Experimental results are compared with high-fidelity axisymmetric and three-dimensional simulations. Results demonstrate regime transition in the parameter space, across the unsteadiness boundary, all the way from shear-layer breakdown to shock system oscillations and ultimately to large-amplitude pulsations. The dominant mode in the experiments and the simulations corresponds to a Strouhal number St $\approx 0.17$ for small oscillations reducing to St $ \approx 0.13$ for large pulsations. A detailed description of the unsteady shock dynamics and an analysis of the nonlinear limit cycle is presented.

Bed shear stress is a key parameter governing sediment transport and fluxes at the sediment–water interface. In vegetated channels, predicting bed shear stress, especially for rough beds, remains a challenge. This study developed a unified theoretical model for bed shear stress that smoothly spans conditions from bare bed to vegetated bed for both smooth and rough beds. Building on phenomenological turbulence theory, the model relates bed shear stress to the characteristic velocities of the larger energy-containing eddies and the smaller, near-bed eddies, with the new assumption that the bottom boundary layer (BBL) thickness controls the larger, energy-containing eddy length scale. The BBL was defined as the region within which the bed shear stress contributed significantly, compared to vegetation drag, and a force balance predicted that the BBL thickness scales with the ratio of bed shear stress to vegetation drag. In the limit of zero vegetation density, the BBL thickness equals the water depth, and the bed shear stress model reduces to the classical bare bed formulation. With increasing vegetation density (drag), the thickness of the boundary layer decreases, and the bed friction coefficient increases, which is consistent with previous observations. For rough beds, the bed friction coefficient increases with bed roughness, but is not dependent on the mean velocity. In contrast, for smooth beds, the bed friction coefficient decreases with increasing mean velocity. The coupled models for bed shear stress and BBL thickness were compared against 114 physical and numerical experiments from multiple previous studies.

Kinetic theory offers a promising alternative to conventional turbulence modelling by providing a mesoscopic perspective that naturally captures non-equilibrium physics such as non-Newtonian effects. In this work, we present an extension and theoretical analysis of the kinetic model for incompressible turbulent flows developed by Chen et al. (Atmosphere, 2023, vol. 14(7), p. 1109), constructed for unbounded flows. The first extension is to reselect a relaxation time such that the turbulent transport coefficients are obtained consistently and better align with well-established turbulence theory. The Chapman–Enskog (CE) analysis of the kinetic model reproduces the linear eddy-viscosity and gradient diffusion models for Reynolds stress and turbulent kinetic energy flux at the first order, and yields nonlinear eddy-viscosity and closure models at the second order. In particular, a previously unreported CE solution for turbulent kinetic energy flux is obtained. The second extension is to enable the model for wall-bounded turbulent flows with preserved near-wall asymptotic behaviours. This involves developing a low-Reynolds-number model incorporating wall damping effects and viscous diffusion, with boundary conditions enabling both viscous sublayer resolution and wall function application. Comprehensive validation against experimental and direct numerical simulation data for turbulent Couette flow demonstrates excellent agreement in predicting mean velocity profiles, skin friction coefficients and Reynolds shear-stress distributions, although the near-wall-normal stress anisotropy is underestimated. The results show that averaged turbulent flow behaves similarly to rarefied-gas flow at finite Knudsen number, capturing non-Newtonian effects beyond linear eddy-viscosity models. This kinetic model provides a physics-based foundation for turbulence modelling with reduced empirical dependence.