Internal waves are an important feature of stratified fluids, both in oceanic and lake basins and in other settings. Many works have been published on the generic feature of internal wave trapping onto planar wave attractors and super-attractors in two and three dimensions and the exceptional class of standing global internal wave modes. However, most of these works did not deal with waves that escape trapping. By using continuous symmetries, we analytically prove the existence of internal wave whispering gallery modes (WGMs), internal waves that propagate continuously without getting trapped by attractors. The WGM’s neutral stability with respect to different perturbations enables whispering gallery beams, a continuum of rays propagating together coherently. The systems’ continuous symmetries also enable projection onto two-dimensional planes that yield effective two-dimensional billiards preserving the original dynamics. By examining rays deviating from these WGMs in parabolic channels, we discover a new type of wave attractor that is located along the channel’s critical depth – the depth at which the bottom slope is identical to the ray slope, instead of cross-channel, as in previous works. This new critical-slope wave attractor leads to a new understanding of WGMs as sitting at the border between the two basins of attraction. Finally, both critical-slope wave attractors and whispering gallery beams are used to propose explanations for along-channel energy fluxes in submarine canyons and tidal energy intensification near critical slopes.

We present computations of individual mode-to-mode energy transfers from direct numerical simulations of homogeneous isotropic turbulence. Unlike previous approaches based on shell-filtered velocity fields, this method distinguishes between the energy exchanged by each pair of modes within a triad. We introduce a potential function based on the energy content of the modes involved, and show that it predicts the distribution of intense energy transfers in the vicinity of the sampling mode considered. By performing simulations with forcing applied at intermediate wavenumbers, we demonstrate that the region of most intense transfers is determined by the spectral location of the energy-containing scales rather than by the local or non-local character of the triad. Direct energy exchanges with the energy-containing range are suppressed by geometric constraints from the divergence-free condition, but persist as residuals when the sampling mode is close to the energy-containing scales. The comparison with an estimator derived from eddy-damped quasi-normal Markovian theory shows good agreement and recovers the forward, scale-local nature of energy transfer consistent with the cascade picture.

We aim to understand how landslides affect the shape and rotational motion of small rubble planetary bodies. We limit ourselves to axisymmetric global landslides and take the primordial shape of the body to be axisymmetric as well. The landslides are modelled as shallow granular surface flows using depth averaging, while incorporating the effects of the body’s rotation, topographical changes from previous landslides, its non-uniform gravity field and possible surface mass shedding. The body’s rotational dynamics is coupled to its shape change due to the transport of regolith – surface grains – and also accounts for the influence of radiation torque. We utilise our framework to investigate regolith motion on idealised rubble bodies and actual asteroids. We then study the evolution of the shape and spin state of an initially spherical rubble asteroid undergoing multiple global landsliding events over millions of years – a time scale comparable to typical asteroidal lifetimes. We find that shape changes due to landsliding resist spin-up due to radiation torque and, in some instances, may even cause the body to spin down. Furthermore, rotational fission is delayed, and may even be suppressed, by regolith redistribution toward the body’s equator. Finally, top-shaped configurations may emerge rapidly, which may explain the prevalence of top-shaped asteroids in near-Earth orbits.

This study focuses on the modelling and dynamics of gravity-driven, axisymmetric thin liquid film flow along a conical surface. Spatial linear stability analysis is performed on the basis of a Benney-type equation derived for the present configuration. In particular, streamwise curvature of the free surface is found to exert a crucial influence on the stability threshold. For simulations of surface waves, a second-order low-dimensional model is developed under the long-wave assumption, achieving accuracy comparable to direct numerical simulations at far lower cost. With this model, the characteristics of both linear and nonlinear waves are examined. A key difference from the flow over a flat plate is the dependence of the wave dynamics on the radial distance from the cone apex. At relatively high flow rates, a transition from solitary to sinusoidal waves is observed, with the transition position correlating closely with the linear stability threshold. Within the parameter range investigated, quantitative results of the conical film flow are almost identical to those in the flat-plate case when local parameters are substituted, indicating that inertial effects of the conical geometry are negligible. The models and findings presented in this paper may aid the design and optimisation of industrial processes such as film coating and liquid-film-based heat and mass transfer on conical surfaces.

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves. Nevertheless, research on depth-induced NED has been predominantly confined to unidirectional irregular waves, while the role of directionality remains largely unexplored. The scarce studies on multidirectional waves mainly rely on numerical simulations and have yielded conflicting results. In this work, we report on an experimental investigation of wave directionality on the depth-induced non-equilibrium wave statistics. High-order statistical moments, skewness and kurtosis, are used as proxies for the non-equilibrium wave response. Our results indicate that the directional spreading has a minor effect on decreasing the maximum values of these statistical moments. In contrast, the incidence direction plays a significant role in the non-equilibrium wave response, which is attributed to the effective bottom slope.