Analytical approach to the solution of short-crested wave interaction with V-shaped and arc-shaped breakwaters

Abstract

The hydrodynamic performance of short-crested wave diffraction by bottom-mounted V-shaped and arc-shaped breakwaters was examined based on the linear wave theory and the eigenfunction expansion method, respectively. Both types of breakwaters are assumed to be thin, impermeable, vertical, and rigidly embedded in the seabed. With the help of a virtual interface, the fluid domains were subdivided into subdomains and the velocity potential in each subdomain was described by eigenfunctions. The linear algebraic equations that determine the unknown coefficients can be obtained using the boundary and matching conditions. The analytical models fully agree with previous predictions. The major factors including wave propagation direction, opening angle, and water depth that affect wave forces and run-ups were explored. The results showed that the wave patterns of short-crested waves near breakwaters were quite different from those of long-crested waves, and using the long-crested wave model can overestimate the wave-defending effects of the breakwaters in a short-crested sea. An analogous wave attenuation effect was observed for breakwaters with comparable structures, which means that engineering practice has a certain degree of substitutability between them.