A numerical solution is obtained to describe the behaviour of a uniform bore over a sloping beach and the subsequent run-up and back-wash. The results exhibit features which have only previously been described in a qualitative manner. These include the formation’ of a landward-facing bore in the back-wash. A comprehensive set of results are presented for a typical initial subcritical bore height ratio.

Steady Stokes flow driven by gravity down an inclined plane over and around an attached obstacle is considered. The effects of the obstacle are examined for various flow configurations and results produced for flow over hemispherical obstacles. Comparison is made with previously published papers that assume that the obstacle is small and/or the free surface deflection and disturbance velocity are small. Values for the unit normal and curvature of the free surface are found using both finite difference approximations and Hermitian radial basis function interpolations, with the resulting solutions compared. Free surface profiles for thin film flows over hemispherical obstacles that approach the film surface are produced and the effects of near point singularities considered. All free surface profiles indicate an upstream peak, followed by a trough downstream of the obstacle with the peak decaying in a “horseshoe” shaped surface deformation. Flow profiles are governed by the plane inclination, the Bond number, and the obstacle geometry. An extension of this approach provides a new class of solutions where a thin film flows around a cylindrical obstacle. Notably, the static contact line angle between the free surface and the obstacle is introduced as an extra flow parameter and its effect investigated for a given set of flow parameters and fixed boundary conditions. Solutions are obtained where steady flow profiles can be found both over and around a cylindrical obstacle raising the awareness of possible multiple solutions.

In recent years extensive measurements of pollutant concentrations within the environment have been made over Western Europe following reports of unusually high pollution levels within rivers and lakes, especially after the start of the spring melting period. A simple model is presented to describe theoretically the pollutant efflux within the first fractions of melt water released from a snow-pack at the start of the melting season. The dominant features included are the appearance of a wave-front as heading the unsaturated flow of melt water and the pollutant dispersion arising from the interaction of the flow with the porous structure of the snow-pack and molecular diffusion. Computed results are shown describing the evolution of pollutant concentration profiles in the first run-off stage from a snow-pack subjected to an applied uniform surface heating.

A modified Reynolds equation for flow dynamically represented as incompressible is used to model the dynamics of a thin film bearing with slip flow and a rapidly rotating coned rotor. Previous studies including a Navier slip length shear condition on the bearing faces are extended to investigate applications with a coned bearing gap. A modified Reynolds equation for the film flow is coupled, through the pressure exerted by the fluid film, to the dynamic motion of the stator. Introducing a new variable leads to explicit analytical expressions for the pressure field and force on the stator with the equation for the time-dependent face clearance transformed to a nonlinear second-order non-autonomous ordinary differential equation. The face clearance for periodic axial motion of the coned rotor is obtained using a stroboscopic map solver; a focus is investigating bearing behaviour under extreme conditions. The coupled fluid flow and unsteady bearing dynamics are examined for a range of configurations to evaluate potential face contact over a range of bearing surface conditions.