Experiments are carried out in a smooth-wall turbulent boundary layer (TBL) ($\textit{Re}_\tau \geq 3500$) subjected to different pressure gradient (PG) histories. Oil-film interferometry is used to measure the skin friction evolution over the entire history while wide-field particle image velocimetry captures the mean flow field. This data are used to demonstrate the influence of PG history on skin friction as well as other integral quantities such as displacement ($\delta ^*$) and momentum thickness ($\theta$). Based on observations from the data, a new set of ordinary differential equations are proposed to model the streamwise evolution of a TBL subjected to different PG histories. The model is calibrated using a limited number of experimental cases and its utility is demonstrated on other cases. Moreover, the model is applied to data from large-eddy simulations of flows in adverse PG conditions (Bobke et al. 2017, J. Fluid Mech. 820, 667–692). The model is subsequently used to identify the impact of PG history length on the boundary layer. This can also be interpreted as determining the spatial frequency response of the boundary layer to PG disturbances. Results suggest that short spatial variations in PGs primarily affect a small portion of the TBL evolution, whereas longer-lasting ones have a more extensive impact.

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.