A theory for the impact of a wave breaking onto a permeable barrier with jet generation

We model a water wave impact onto a porous breakwater. The breakwater surface is modelled as a thin barrier composed of solid matter pierced by channels through which water can flow freely. The water in the wave is modelled as a finite-length volume of inviscid, incompressible fluid in quasi-one-dimensional flow during its impact and flow through a typical hole in the barrier. The fluid volume moves at normal incidence to the barrier. After the initial impact the wave water starts to slow down as it passes through holes in the barrier. Each hole is the source of a free jet along whose length the fluid velocity and width vary in such a way as to conserve volume and momentum at zero pressure. We find there are two types of flow, depending on the porosity, ß , of the barrier. If ß : 0 = ß < 0.5774 then the barrier is a strong impediment to the flow, in that the fluid velocity tends to zero as time tends to infinity. But if ß : 0.5774 = ß = 1 then the barrier only temporarily holds up the flow, and the decelerating wave water passes through in a finite time. We report results for the velocity and impact pressure due to the incident wave water, and for the evolving shape of the jet, with examples from both types of impact. We account for the impulse on the barrier and the conserved kinetic energy of the flow. Consideration of small ß gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall

A comparison of pre-impact gas cushioning and Wagner theory for liquid-solid impacts

ACKNOWLEDGEMENTS Snizhana Ross was supported by the Development Trust of the University of Aberdeen.Peer reviewedPostprintPublisher PD

Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity. The linear theory of the velocity potential is employed by assuming inviscid, incompressible fluid and irrotational flow. As the problem is set in 3-D space, the employment of the Wagner condition is essential. The set of equations we pose, is presented as a mixed boundary value problem for Laplace's equation in 3-D. Apart from the mixed-type of boundary conditions, the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface. We make some simple assumptions at the start but otherwise we proceed analytically. We find closed-form relations for the hydrodynamic variables, namely the time dependent potential, the pressure impulse, the shape of the wave front (from the contact point to beyond the cylinder) and the slamming force