Wave Diffraction by Array of Thin‐Screen Breakwaters

Abstract

The diffraction of water waves by an offshore breakwater consisting of an infinite row of equally spaced vertical screens is investigated theoretically. A Green’s function approach is utilized and the use of geometric periodicity reduces the problem to that of a singular integral equation for the potential difference across a single screen element. The integral equation is then solved numerically by expressing this potential difference as a series of Chebyshev polynomials with unknown coefficients. The reflected and transmitted wave systems each consist of a finite number of propagating wave components. The accuracy of the numerical scheme is verified based on energy considerations. A reflection coefficient is defined in terms of the amplitude of the asymptotic wave traveling in a direction opposite to that of the incident wave system. Reflection coefficients are presented for a variety of angles of wave incidence and screen width-to-spacing ratios. These results indicate that for certain parameter combinations significant wave reflection can be obtained utilizing this type of breakwater configuration.