We present the results of an experimental investigation into the motion of large buoyant rigid spheres rising through highly concentrated collections of hydrated hydrogel particles. The concentration of the soft highly poroelastic particles is such that the mechanical properties of the material are that of a soft solid that can also flow very slowly. Despite the established time-dependent, non-Newtonian character of hydrogel packings, we find that when the upper surface of the material is free, an immersed buoyant sphere travels through the material at a constant speed. Qualitatively distinct behaviour is found when a rigid lid is placed on the surface of the material. In these cases, sublinear time-dependent motion of the sphere is found. The effects of the motion are generally observed to be highly localised around the sphere in all cases. However, when the translational speed of the sphere is constant, it is accompanied by significant flow at the surface of the sample whereas surface movement is suppressed when a lid is present. When the stress exerted on the material is changed by varying the mass of the sphere, its terminal velocity is found to depend exponentially on buoyancy. We use these observations to support a hypothesis that links the exponential stress dependence of the drag coefficient induced by the material to the effects of the boundary conditions on the kinematics of the intruder.

Aircraft icing poses a critical threat to aviation safety in cold climates, with the dynamic glaze ice accretion process governed by the transient behaviour of wind-driven runback water film and rivulet (WDRWF/R) flows on wing surfaces. Despite its significance, accurately modelling this complex multiphase flow phenomenon remains a fundamental challenge for conventional numerical and theoretical approaches. This study introduces a physics-guided Fourier neural operator (PGFNO) that achieves unprecedented accuracy in predicting the spatiotemporal evolution of WDRWF/R flows relevant to aircraft icing. To establish a high-fidelity training dataset, we conducted an extensive experimental campaign utilising a novel digital image projection (DIP) technique, which enables temporally and spatially resolved measurements of water film thickness distributions over a flat plate under diverse operating conditions. The PGFNO architecture incorporates a composite loss function that enforces physical constraints, ensuring both accurate field reconstruction and mass conservation. The trained model demonstrates robust predictive capability across a wide range of flow conditions, including extrapolation to unseen wind speeds, water flow rates and initial conditions, while accurately capturing both the film thickness field and its spectral characteristics. A comprehensive ablation study systematically evaluates the contributions of key architectural components to model performance, including the physics-guided loss function, embedding-layer configuration and Fourier mode/block selection. Long-term predictions via recurrent forecasting achieve errors approaching the experimental uncertainty of DIP measurements, while robustness tests with spatially distributed random noise confirm exceptional model stability. These results establish PGFNO as a powerful predictive framework for complex multiphase flows, with direct implications for aircraft icing prediction and mitigation strategies.

We report an experimental study of the free decay of magnetohydrodynamic homogeneous isotropic turbulence at low magnetic Reynolds number and interaction parameter $(N\sim 1)$. An initially isotropic turbulent state is generated in a cubic vessel by eight converging jets under a uniform magnetic field, and the velocity field is measured using particle image velocimetry. After the jets are switched off, the kinetic energy decays in two successive stages, following a $t^{-1/2}$ scaling at early times and a $t^{-3/2}$ scaling at later times. Energy budget analysis shows that these regimes correspond to distinct decay mechanisms: Joule dissipation dominates the early decay, whereas viscous dissipation controls the late-time dynamics. Owing to the anisotropic nature of Joule dissipation, turbulent motions with gradients perpendicular to the magnetic field are preferentially damped, leading to a transient increase in kinetic energy anisotropy, with a maximum ratio of 1.54 at $N = 1.28$. This process also causes the two-dimensional energy spectrum to deviate from isotropy and leads to a steepening of the energy spectrum associated with the velocity component perpendicular to the magnetic field. Mode-to-mode energy transfer analysis indicates the coexistence of forward and inverse transfers at perpendicular scales, while only forward transfer persists along the magnetic field. As a consequence, vortical structures progressively elongate in the field direction, with the integral length scale growing as $t^{1/2}$.

Motivated by the need to extrapolate the results from ground-based experiments to the conditions of high-speed flight, we present the Lie equivalence-symmetry analysis of the hypersonic stagnation-point boundary layers (BLs). We demonstrate the application of the equivalence symmetry on the set of coupled ordinary differential equations (ODEs) which are physically relevant in hypersonics. By allowing the property laws to transform along with the independent and dependent variables, the invariants derived within the similarity-reduced stagnation-point ODE formulation identify families of nonlinear maps that can be used to extrapolate the laboratory-scale predictions to flight. In practice, implementing these maps requires the laboratory-scale ODE solution together with the laboratory- and flight-side thermochemical-property data, which are generally available from existing databases. The maps are derived for the similarity-reduced non-dimensional temperature across the BL and show reasonable agreement with independently computed flight solutions for the cases considered, with maximum pointwise relative errors up to approximately $3.3\,\%$ in the near-wall region and $4.1\,\%$ across the full BL. The broad impact of the study is that it suggests a new equivalence-symmetry-based route for addressing scale-bridging problems in fluid mechanics.

Dense suspensions of rod-shaped granular particles are widespread in nature and manufacturing, where their fluid mechanical properties are often paramount. We have developed a particle-based simulation that models such suspensions under simple shear flow, providing predictions of the viscosity and microstructure for a given solids volume fraction and particle aspect ratio. The model tracks the trajectories of spherocylindrical rods under the action of short-range frictional contact and hydrodynamic forces, inspired by similar tools that have generated new insight into suspensions of granular spheres. It incorporates new schemes for the computation of lubrication forces between spherocylinders and the dynamic determination of the time step. For aspect ratios up to 20, the model predicts a viscosity spike at shear startup, giving way to steady-state viscosities that increase systematically with volume fraction and aspect ratio. Likewise, particle alignment increases with volume fraction up to an aspect-ratio-dependent critical point. Our model corroborates the limited experimental rheology data available for suspensions of granular rods, and offers a tool for fundamental exploration of the fluid mechanics, microstructure and rheology of this widespread material.

This study identifies a low-frequency, shock-dominated global mode orchestrating thermal choking in confined supersonic flow. The mode exhibits spatial coherence and a bidirectional acoustic–convective feedback loop. Its existence is confirmed – and its inviscid core isolated – through a controlled computational two-dimensional experiment, then validated in fully three-dimensional simulations. Crucially, comparison with one-dimensional Rayleigh flow reveals that choking occurs at a significantly lower heat addition than theoretically predicted, underscoring the dominance of multi-dimensional, mechanically driven choking mechanisms over purely thermal limits. These findings establish a new paradigm for choking transitions and highlight the necessity of multi-dimensional analysis for accurate prediction of supersonic-flow stability.

A new framework for modelling vibrational non-equilibrium in high-speed combustion is presented and evaluated. Our model builds upon a wide range of historical modelling paradigms to account for vibrational non-equilibrium exchange mechanisms, including translational–vibrational (T–V), vibrational–vibrational (V–V) and chemical–vibrational (C–V) processes, as well as vibrationally informed chemical reactions. Complementary forms of the T–V and V–V exchange processes are presented and compared, revealing how T–V exchange controls relaxation by driving each species towards vibrational equilibrium, whereas V–V exchange controls redistribution by driving each species towards a common, relative level of vibrational non-equilibrium. A modified form of the V–V exchange probability is proposed to ensure that vibrational energy does not leak into other modes. Additionally, a generalised vibrational efficiency function for complex reactions is derived. This form is subsequently used to derive the C–V exchange rate, which controls creation and destruction of vibrational energy from chemical reactions, resulting in a generalised, coupled vibration–chemistry–vibration model. Each of these processes (T–V, V–V and C–V exchange), as well as the vibrational efficiency function, is defined for general systems. We then examine each process in the context of high-speed combustion applications, in which temperatures are below 5000 K, and implement model simplifications where applicable. This model is used to predict the role of vibrational non-equilibrium in hydrogen chain-branching reactions and is shown to perform similarly to more complex, historical models. The model represents a physically grounded, tractable approach for including vibrational non-equilibrium effects in high-speed combustion applications.

We formulate a weakly nonlinear exit condition for open ends of acoustic waveguides; to our knowledge, this is the first time a general acoustic open end has been analysed outside the linear regime. The formulation neglects mean flow, vortex separation and viscous effects. The resulting admittance boundary condition, and its weakly nonlinear counterpart, extend recent weakly nonlinear modelling of curved ducts Jensen & Brambley (2026 J. Fluid Mech., vol. 1030, A19) to include open ends. We approximate free space by considering the open-ended duct to be enclosed within a much larger hard-walled concentric duct; within the larger duct, the smaller duct exit is modelled as an acoustic discontinuity. Importantly, the superposition principle is unneeded, allowing the model to be applied in the nonlinear regime. The exit condition can be calculated without needing to solve the full problem in either the outer or inner ducts, making it numerically efficient. The exit condition is validated in the linear regime by comparison with Wiener–Hopf solutions of the duct end correction, and a novel nonlinear end correction is proposed; we find that both non-plane waves and nonlinearity cause the end correction to vary significantly from Rayleigh’s classical $0.6$ radii result. A number of numerical illustrations are then discussed, demonstrating nonlinear effects, sound radiating from curved ducts, sound radiating from an exponential horn (representative of brass instrument bells) and the harmonic effects of the open end on in-duct resonances. The model has potential applications to sound in woodwind and brass instruments. Matlab source code is provided in the supplementary material.