Scattering of Nonlinear Periodic (Cnoidal) Waves by a Partially Immersed Box-Type Breakwater

Abstract

This paper presents a combined analytical and numerical (CAN) model to simulate the scattering of cnoidal waves by a fixed and partially immersed box-type breakwater. A set of Boussinesq equations are solved in the outer region using the finite-difference method to model the propagation of cnoidal waves and their subsequent reflection and transmission after encountering the breakwater. The two-dimensional (2D) velocity potential in the inner region beneath the body is derived analytically by solving the equations formulated from the orthogonality of eigenfunctions and the interfacial matching conditions. Experimental measurements on the wave profiles were carried out in a wave tank to verify the model solutions. Reflected and transmitted wave elevations obtained from the present CAN model match closely with the measured data. Additionally, the calculated horizontal and vertical forces on the body using the developed CAN model are in reasonable agreement with those from a potential 2D flow-based fully nonlinear wave model (FNWM). The method and proposed CAN model, if applied to a simple parametric investigation, can provide the expected trends in terms of applied forces, wave reflection, and transmission.