We consider two-dimensional (2-D) free surface gravity waves in prismatic channels, including bathymetric variations uniquely in the transverse direction. Starting from the Saint-Venant equations (shallow-water equations) we derive a one-dimensional transverse averaged model describing dispersive effects related solely to variations of the channel topography. These effects have been demonstrated in Chassagne et al. 2019 J. Fluid Mech. 870, 595–616 to be predominant in the propagation of bores with Froude numbers below a critical value of approximately 1.15. The model proposed is fully nonlinear, Galilean invariant, and admits a variational formulation under natural assumptions about the channel geometry. It is endowed with an exact energy conservation law, and admits exact travelling-wave solutions. Our model generalises and improves the linear equations proposed by Chassagne et al. 2019 J. Fluid Mech. 870, 595–616, as well as in Quezada de Luna and Ketcheson, 2021 J. Fluid Mech. 917, A45. The system is recast in two useful forms appropriate for its numerical approximations, whose properties are discussed. Numerical results allow the verification of the implementation of these formulations against analytical solutions, and validation of our model against fully 2-D nonlinear shallow-water simulations, as well as the famous experiments by Treske 1994 J. Hyd. Res. 32, 355–370.

We present a theoretical framework and validation for manipulating instability growth in shock-accelerated dual-layer material systems, which feature a light–heavy interface followed by two sequential heavy–light interfaces. An analytical model is first developed to predict perturbation evolution at the two heavy–light interfaces, explicitly incorporating the effects of reverberating waves within the dual-layer structure. The model identifies five distinct control regimes for instability modulation. Shock-tube experiments and numerical simulations are designed to validate these regimes, successfully realising all five predicted states. Notably, the selective growth stagnation of a perturbation at either the upstream or downstream heavy–light interface is realised numerically by tuning the initial separation distances of the three interfaces. This work elucidates the critical role of the wave dynamics in governing interface evolution of a shocked dual layer, offering insights for mitigating hydrodynamic instabilities in practical scenarios such as inertial confinement fusion.

Studying rotating convection under geo- and astrophysically relevant conditions has proven to be extremely difficult. For the rotating Rayleigh–Bénard system, van Kan et al. (J. Fluid Mech., vol. 1010, 2025,A42)have now been able to massively extend the parameter space accessible by direct numerical simulations. Their progress relies on a rescaling of the governing Boussinesq equations, which vastly improves numerical conditioning (Julien et al., arXiv:2410.02702). This opens the door for investigating previously inaccessible dynamical regimes and bridges the gap to the asymptotic branch of rapidly rotating convection.

In this study, we obtain the continuum equations of Arctic sea ice motion starting from the dynamics of a single floe and show that the rheology that emerges from floe–floe interactions is viscous – as conjectured by Reed and Campbell (J. Geophys. Res., vol. 67 (1), 1962, pp. 281–297). The motion of the floe is principally driven by the wind and ocean currents and by inelastic collisions with the neighbouring floes. A mean-field representation of these collisions is developed, neglecting any changes in the floe thickness due to thermal growth and mechanical deformation. This mean-field representation depends on the state of the ice cover, and is expressed in terms of ice concentration and mean thickness. The resulting Langevin equation for the floe velocity, or the corresponding kinetic equation (Kramers–Chandrasekhar equation (KCE)) for its probability density, provides a complete description of the floe’s motion. We then use the floe-scale dynamics to obtain a continuum description of sea ice motion through a Chapman–Enskog analysis of the KCE. The local equilibrium solution to the kinetic equation is found to be the Laplace distribution, in qualitative agreement with observations. Our approach also allows us to establish the dependence of pressure and shear viscosity of the ice cover on ice concentration and mean thickness. Lastly, we show that our results resolve a conflict associated with the choice of the value of shear viscosity in previous idealised numerical studies of Arctic sea ice motion.

Previous studies claimed that the non-monotonic effects of wettability came mainly from the heterogeneity of geometries or flow conditions on multiphase displacements in porous media. For macroscopic homogeneous porous media, without permeability contrast or obvious preferential flow pathways, most pore-scale evidence showed a monotonic trend of the wettability effect. However, this work reports transitions from monotonic to non-monotonic wettability effects when the dimension of the model system rises from two-dimensional (2-D) to three-dimensional (3-D), validated by both the network modelling and the microfluidic experiments. The mechanisms linking the pore-scale events to macroscopic displacement patterns have been analysed through direct simulations. For 2-D porous media, the monotonic effect of wettability comes from the consistent transition pattern for the full range of capillary numbers $Ca$, where the capillary fingering mode transitions to the compact displacement mode as the contact angle $\theta$ decreases. Yet, it is indicated that the 3-D porous geometries, even though homogeneous without permeability contrast or obvious preferential flow pathways, introduce a different $Ca$–$\theta$ phase diagram with new pore-scale events, such as the coupling of capillary fingering with snap-off during strong drainage, and frequent snap-off events during strong imbibition. These events depend strongly on geometric confinements and capillary numbers, leading to the non-monotonicity of wettability effects. Our findings provide new insights into the multiphase displacement dependent on wettability in various natural porous media and offer design principles for engineering artificial porous media to achieve desired immiscible displacement behaviours.

This study utilises large-eddy simulation with the actuator line model to examine the effects of the tip speed ratio (TSR) on the wake-meandering characteristics of a wind turbine in uniform and turbulent inflows. It is shown that as the TSR grows, the onset position of the wake meandering moves closer to the rotor, and the magnitude of wake oscillation is stronger. This aligns with previous work showing that a higher TSR can accelerate the instability and breakdown of tip vortices. Without a nacelle, the Strouhal number of the wake meandering is found to be independent of the TSR under both the uniform and turbulent inflows. However, with a relatively large nacelle, the Strouhal number first increases and then decreases with TSR. Therefore, the current discovery elucidates the crucial role of the nacelle and clarifies the origin of the TSR dependence of the Strouhal number in wake meandering. In addition, the characteristic frequency of the wake meandering under the turbulent inflow is much smaller than that under the uniform inflow, because of the significant influence of the freestream turbulence. Furthermore, the proper orthogonal decomposition (POD) and spectral POD (SPOD) methods are employed to study the spatiotemporal characteristics of the meandering wake and its TSR dependence. It is found that the tip and root vortices are the prominent wake structures under the uniform inflow, whereas more complex multiscale structures from the interaction between the freestream turbulence and tip/root vortices exist under the turbulent inflow. Moreover, an amplitude modulation phenomenon of the POD time coefficients at the optimal TSR is observed in the uniform inflow case. Finally, a reduced-order model is constructed for predicting the wake dynamics by combining the SPOD and the ‘sparse identification of nonlinear dynamics’ algorithm with high accuracy and interpretability.