Mathematical investigations of wave-structure interaction problems

Abstract

This thesis presents a comprehensive mathematical framework for analyzing wave scattering by single and multiple structures under the assumption of small-amplitude water wave theory. The primary goal of the thesis is to deepen the understanding of wave structure interactions near the shore, particularly the behavior of strong waves and the role of different structural configurations in mitigating wave energy. The study considers various breakwater geometries, including cylindrical, rectangular, and inverse T-shaped structures. In this thesis, the fluid is assumed to be inviscid, incompressible, and irrotational flow, with negligible surface tension on the free surface. This assumption allows the use of a velocity potential governed by the Laplace equation. To find this velocity potential, the method of separation of variables is used to derive explicit expressions, where the unknown coefficients are determined by applying boundary conditions—namely, dynamic, kinematic, and seabed conditions.