Based on the generalised Saint-Venant equations for granular flow on an inclined chute, we show how to generate solitary waves from localised perturbations at the inlet. Such perturbations usually give rise to a group of roll waves, but by choosing the system parameters appropriately, the formation of all but the first wave can be suppressed, thus turning this first one into a solitary wave. This calls for a highly diffusive flow, which is realised for inclination angles close to the minimal angle required to keep the granular material flowing.

The recirculating flow at the rear of a flat-base three-dimensional body with ground proximity is investigated for different body attitudes defined by the pitch angle varying in the range $-1.5^\circ \lt \alpha \lt +2.6^\circ$ and the yaw angle in the range $0^\circ \lt \beta \lt +12^\circ$. Experiments measuring the three components of the mean velocity field in two perpendicular planes intersecting the recirculation area as well as the base pressure distribution are conducted for 50 different attitudes. They provide a clear correlation between the orientation of the spatially averaged reversed flow and the gradient at the centre of the base pressure distribution. Both vectors are found to be in the same so-called w-plane, that is perpendicular to the base of which the azimuthal position changes with the body attitude due to either the flow orientation at the base separation or sometimes to a ground separation for large nose-up pitch. Numerical simulations of the same geometry realised for 10 attitudes show satisfactory agreement with the force coefficients measured in the experiment. Base flow variations induced by attitude changes are also well captured, particularly that of the w-plane. The full three-dimensional simulation data are used to show that the inner structure of the separation bubble is always a tilted recirculation torus, where the tilt orientation is given by the base pressure gradient. At the bubble closure, a pair of longitudinal vortices symmetrically located on both sides of the w-plane are permanently observed with circulations consistent with the circulation of the dividing streamline separation in the w-plane.

Ice shelves that spread into the ocean can develop rifts that can trigger iceberg calving and enhance ocean-induced melting. Fluid mechanically, this system is analogous to an extensionally dominated radial spreading of a non-Newtonian fluid into a relatively inviscid and denser ambient fluid. Laboratory experiments have shown that rift patterns can emerge when the spreading fluid is shear thinning. Linear stability analysis supports these findings, predicting that while the instability mechanism is active in Newtonian fluids, it is suppressed by stabilising secondary-flow cellular vortices. Here, we explore the fully nonlinear evolution of a radially spreading Newtonian fluid, assessing whether large-amplitude perturbations could drive an instability. We use a quasi-three-dimensional numerical simulation that solves the full nonlinear shallow-shelf approximation, tracing the evolving fluid front, and validate it with known axisymmetric solutions and predictions from linear-stability theory. We find that large-amplitude perturbations induce nonlinear effects that give rise to non-axisymmetric patterns, including cusp-like patterns along the fluid front and complex secondary-flow eddies, which have neither been predicted theoretically nor observed experimentally. However, despite these nonlinear effects, large-amplitude perturbations alone are insufficient to induce rift-like patterns in Newtonian fluids. Strain-rate peaks at the troughs of the fluid front suggest that shear-thinning fluids may become more mobile in these regions, potentially leading to rift formation. This coincides with the likely weakening of stabilising forces as the fluid becomes more shear-thinning. These findings elucidate the critical role of nonlinear viscosity on the formation of rift-like patterns, which is the focus of Part 2 of this study.