Derivation of fundamental resonant period in width-varying semi-closed basins using modified SWE

Abstract

The natural periods of water basin have a critical role in causing a resonance phenomenon. When the external waves coming into the basin possess similar periods, an increment in the wave amplitude might happen and give rise to serious damage to the surrounding environment. Many of the previous studies focused on finding the resonant period in basins with rectangular width. However, only a few have addressed the problem of basins with varying widths. Using a different analytical approach, we obtained the fundamental resonant period of a rectangular and triangular semi-closed basin. The analytical solution is obtained from modified linear shallow water equations using the separation of variables method. This new approach is simpler yet powerful in deriving the desired period. Furthermore, a modification of the staggered finite volume method is also proposed to find the periods numerically. The proposed scheme can be suitably applied to solve the discussed problem since it is conservative, robust, and free from damping errors. The results show that our analytical solutions align with those obtained from potential flow theory and the developed numerical scheme. Furthermore, we also compared the general characteristics of the resonance phenomenon that occurs in basins with constant and varying width. Since basins with non-constant width have lower fundamental resonant periods, the generated wave elevations are higher than those in constant-width basins.