Oblique Wave Interaction With Flexible Plate in Ocean of Uneven Bottom

Abstract

The present work analyzes the interaction of oblique waves by a porous flexible breakwater in the presence of a step-type bottom. The physical models for both scattering and trapping cases are considered and developed within the framework of small amplitude water-wave theory. Darcy’s law is used to model the wave interaction with the porous medium. It is assumed that the varying bottom extends over a finite interval, connected by a finite length of uniform bottom near an impermeable wall, and a semi-infinite length of bottom in the open water region. The boundary value problem is solved using the eigenfunction expansion method in the uniform bottom regions, while a modified mild-slope equation (MMSE) is used for the region with the varying bottom. Additionally, a mass-conserving jump condition is employed to handle the solution at slope discontinuities in the bottom. A system of equations is derived by matching the solutions at interfaces. The reflection coefficient and force on the breakwater and impermeable wall are plotted and analyzed for various parameters, such as the length of the varying bottom, depth ratio, angle of incidence, and flexural rigidity. It is observed that moderate values of flexural rigidity and depth ratio significantly contribute to an optimum reflection coefficient and reduce the wave force on the wall and breakwater. Remarkably, the outcomes of this study are assumed to be applicable in the construction of this type of breakwater in coastal regions.

Keywords

Porous flexible breakwater / Varying bottom / Mild-slope equation / Reflection coefficient / Wave force

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