This paper is concerned with mathematical models representing the unidirectional propagation of weakly nonlinear dispersive waves. Interest will be directed toward two particular models that are originally studied in the context of surface-wave phenomena in open-channel flows. The purpose of the present paper is to make a quantitative comparison between the solutions to the initial-value problem for each of these models. The basic conclusion of the study is that, on a long time scale T naturally related to the underlying physical situation, the equations predict the same outcome to within their implied order of accuracy. In this case the choice of one of these models over the other to describe a physical problem is apparently immaterial, with factors of incidental convenience probably providing the main criteria in a given situation. (Author).

This paper describes some experimental observations of free-surface flows arising when fluid poured over the end of a flat plate into a reservoir well below the plate. This class of flows was found to be highly unstable with over seven hundred qualitatively different flows being observed in the experiment. At very small values of the flux the liquid fell from the plate into the reservoir in the form of droplets which developed periodically at a number of sites on the underside of the plate. As the flux was increased these 'sites' were able to sustain continuous, unbroken streams and combinations of drip sites and continuous streams were possible. At still larger values of the flux there was a tendency for the liquid to fall in 'sheets' and several combinations of 'sheet flows' and continuous streams were observed, some of which flows exhibited a rather chaotic temporal behavior. At even larger flux values the flow resembled that of the classic waterfall, but here there were also some unexpected instabilities where the attachment line of the free surface of the liquid with the plate developed corrugations. Keywords: Hydrodynamic stability; Chaotic behaviour; Free-surface flows.

A description is given of some experiments made to examine the possible trapping of surface waves by a submerged cylindrical sill in an otherwise uniform ocean. Theories by Longuet-Higgins (1967) and Renardy (1981) indicate that, at certain dangerous frequencies, nearly resonant conditions may obtain, leading to unusually large wavefields over the sill. These resonances have been sought experimentally by examining two functionals of the wavefield over the sill to see if they should become unusually large near certain of the dangerous frequencies. The results show no manifestation whatsoever of the resonances. Possible reasons for the discrepancies are considered. It has, however, been observed that, at certain locations over the sill, the waves were amplified by a factor of four or five times their magnitude in the 'ocean', irrespective of the frequency in a certain interval. This could be an important consideration for the siting of rigs on prominent topographic features of the ocean bed.