Analytical and numerical studies for seiches in a closed basin with various geometric shapes of longitudinal section

Seiches are long-period standing waves with a unique period called a natural resonant period, during which the phenomenon of resonance occurs. The occurrence of resonance in coastal areas can cause destruction to surrounding natural and man-made structures. By determining the resonant period of a given basin, we can pinpoint the conditions that allow waves to achieve resonance. In this study, a mathematical model is developed from the shallow water equations to examine seiches and resonances in various types of closed basin. The developed model is solved analytically using the separation of variables method to determine the seiches' fundamental resonant periods. Comparisons between the analytical solutions and experimental measurements for resonant periods are also provided. It is shown that the analytical resonant period confirms the experimental data for closed basin of various geometric profiles. Using a finite volume method on a staggered grid, the model is solved numerically to simulate the wave profile when resonance phenomenon occurs. Through those numerical simulations, we also obtain the fundamental resonant period for each basin which agrees with the derived analytical period