Extensive experiments were performed in the highly turbulent shear layer and in the reverse-flow region downstream of a normal plate followed by a long splitter plate in its plane of symmetry. Whereas the earlier measurements of Ruderich & Fernholz (1986) and Castro & Haque (1987) concentrated on the plane of symmetry (x, y-plane, z = 0), the present investigation reveals the full extent of the three-dimensional behaviour of the flow by presenting data in the whole flow field. Spanwise measurements of five components of the Reynolds stress tensor, of integral timescales, and of mean and fluctuating values of the skin friction were carried out by the pulsed-wire technique. Integral lengthscales and spectra outside the reverse-flow region were measured using hot wires. In order to keep three-dimensional effects as small as possible, the aspect ratio was large (model width was 2.55 times the length of the reverse-flow region) and the blockage ratio and free-stream turbulence intensity were low. Despite these efforts the flow investigated here must be considered three-dimensional and classified as both pressure and shear driven. There appears to be a connection between the shape of the reverse-flow region and the level of the fluctuating velocities. Measurements of power spectral densities revealed no flapping motion of the separated turbulent shear layer.

We treat the problem of the stability of an infinite horizontal array of cylinders, spaced periodically, by a direct numerical simulation of the Navier–Stokes equations for steady flow at Reynolds numbers less than or equal to 100. We find that the only stable configuration for the array is one with equal spacing between cylinders and all cylinders lying on a line perpendicular to the flow. The array is found to be stable under displacements of the cylinders perpendicular and parallel to the array. We say a perturbation is stable when it gives rise to a force which acts to restore the original stable configuration. Our results are consistent with experiments in which spheres were confined by the sidewalls of a fluidized bed to move in two dimensions. As a secondary issue we consider the variation with parameters of the length and width of wakes behind cylinders.

In this paper we consider the interaction of two unequal solitary waves travelling in opposite directions. The interaction equations are derived from the perturbation expansion of the Euler equations, which lead to the Boussinesq equation at lowest order. These equations are recast to obtain two weakly coupled KdV equations which are solved by the method of inverse scattering. We show that the amplitude of each solitary wave after interaction is reduced. This change in the amplitudes is shown to be fifth order in ε, the order of magnitude of the amplitude of the waves. This is in agreement with the change of amplitude produced by the interaction of two equal waves which arises in the reflection of a wave by a vertical wall.

Matched asymptotic expansions are used to analyse the flow past a two-dimensional planing surface in shallow water. A simple momentum conservation relation is obtained connecting leading-edge height, trailing-edge height, and ambient water depth, from which the (initially unknown) wetted length can be determined. This relationship is confirmed by an explicit solution for the flow in the splash zone near the leading edge. The theory is used to discuss the dynamics of a freely skimming board carrying a given weight whose point of application is a given distance ahead of the trailing edge.