Surface waves interaction with the system of M fixed rectangular obstacles in the fluid of finite depth

Abstract

Analytical solution of a problem of surface waves interaction with M fixed rectangular obstacles in a fluid of finite depth is constructed. The fluid is supposed to be ideal, incompressible, homogeneous, and its motion has a velocity potential. Small oscillations of the fluid caused by interaction of incoming waves and obstacles are considered. A linear two-dimensional mixed problem for the Laplace equation is solved by the partition method in subareas and by the linear operator expansion in terms of eigenfunctions. Orthogonalization procedure is applied to simplify the system of infinite linear algebraic equations. The system solutions produce the terms of the generalised Fourier series for the velocity potential of the fluid motion. All necessary kinematic and dynamic wave characteristics of movement and force interaction between waves and obstacles are calculated. Possibility of the received solution application to obstacles with more complicated shapes is demonstrated.