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

• Published in: Journal of engineering mathematics Vol. 79; no. 1; pp. 1 - 12
• Main Author: Cooker, Mark J.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-04-2013
• Subjects: Applications of Mathematics; Barriers; Breakwalls; Breakwaters; Channels; Computational fluid dynamics; Computational Mathematics and Numerical Analysis; Fluid flow; Fluids; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Theoretical and Applied Mechanics; Jet; Porous structure; Wave impact pressures
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-012-9558-9

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,
β
, of the barrier. If
β
is in the range 0 ≤
β
< 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
β
is in the range 0.5774 ≤
β
≤ 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
β
gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall.