The collision of a solitary wave, travelling over a horizontal bed, with a vertical wall is investigated using a boundary-integral method to compute the potential fluid flow described by the Euler equations. We concentrate on reporting new results for that part of the motion when the wave is near the wall. The wall residence time, i.e. the time the wave crest remains attached to the wall, is introduced. It is shown that the wall residence time provides an unambiguous characterization of the phase shift incurred during reflection for waves of both small and large amplitude. Numerically computed attachment and detachment times and amplitudes are compared with asymptotic formulae developed using the perturbation results of Su & Mirie (1980). Other features of the flow, including the maximum run-up and the instantaneous wall force, are also presented. The numerically determined residence times are in good agreement with measurements taken from a cine film of solitary wave reflection experiments conducted by Maxworthy (1976).

Liquid impact problems for hemispherical fluid domain are considered. By using the concept of pressure impulse we show that the solution of the flow induced by the impact is reduced to the derivation of Laplace's equation in spherical coordinates with Dirichlet and Neumann boundary conditions. The structure of the flow at the impact moment is deduced from the spherical harmonics representation of the solution. In particular we show that the slip velocity has a logarithmic singularity at the contact line. The theoretical predictions are in very good agreement both qualitatively and quantitatively with the first time step of a numerical simulation with a Navier-Stokes solver named Gerris. Figure 1: Sketch of an impact problem involving a liquid domain of arbitrary shape and a solid boundary. The red dots represent the position of the contact line.

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Numerical solutions for fully nonlinear two-dimensional irrotational free-surface flows form the basis of this study. They are complemented and supported by a limited number of experimental measurements. A solitary wave propagates along a channel which has a bed containing a cylindrical bump of semicircular cross-section, placed parallel to the incident wave crest. The interaction between wave and cylinder takes a variety of forms, depending on the wave height and cylinder radius, measured relative to the depth. Almost all the resulting wave motions differ from the behaviour which was anticipated when the study began. I n particular, in those cases where the wave breaks, the breaking occurs beyond the top of the cylinder. The same wave may break in two different directions: forwards as usual, and backwards towards the back of the cylinder. In addition small reflected waves come from the region of uniform depth beyond the cylinder. Experimental results are reported which confirm some of the predictions made. The results found for solitary waves are contrasted with the behaviour of a group of periodic waves.