Analytical and Numerical Investigations Applied to Study the Reflections and Transmissions of a Rectangular Breakwater Placed at the Bottom of a Wave Tank

Abstract

The purpose of the work presented in this paper is to study the reflection and transmission coefficients resulting from the interactions of regular waves with a rectangular breakwater sited at the bottom of a tank. The present investigation is devoted to the analysis of the reflection and transmission coefficients within the framework of linearized potential flow theory using two methods, a numerical method based on the improved version of the meshless singular boundary method, and the analytical approach within the plane wave model. The numerical method is first validated by studying the accuracy of the numerical computations with respect to the number of boundary nodes and the location of the vertical boundaries of the computational domain, for different immersion ratios (h/d) and different relative lengths (w/d) of the obstacle. To assess the limitations of the analytical approach, a comparison analysis is carried out between the analytical and numerical results. To improve the calculations and the effectiveness of the analytical model, slight adjustments are made to the analytical procedure, which is termed here the corrected analytical plane wave model. Finally, the effects of the immersion ratio (h/d) and the relative length (w/d) of the obstacle on the reflection and transmission coefficients are computed using the three methods, and discussed for several wave and structural conditions.

Keywords

• breakwater
• analytical approach
• meshless method
• reflection and transmission coefficients
• wave-structure interactions