Shallow Water Equations on modeling resonant waves evolution in a rough varying-width basin

Wave resonance is known to be extremely damaging to the coastal areas surrounding it, particularly if the wave has tsunami-like features, as it can amplify the height and energy of the wave propagating to the shorelines. The installation of a rough material on the bottom is one of the solutions to protect the coast from resonance. In this study, we examine the resonant wave evolution and its frequency in a triangular or rectangular semi-closed basin using a varying-width Shallow Water Model. The basins are assumed to feature a rough bottom topography as well as an uneven width. The resonant frequencies are obtained analytically and numerically using separation of variables and the finite volume method on a staggered grid, respectively. The computational approach is also used to assess the evolution and properties of resonant waves. The numerical scheme is validated by comparing simulation results to analytical solutions, which show relatively good agreement. Further, it is discovered that a greater friction coefficient induces a higher resonant frequency in both types of basins but results in a lower maximum resonant wave amplitude. It is also found that the resonant frequencies of both types of varying-width basins are greater than those of the prior study's constant-width basins. However, the effect of the variations in the maximum width of the basin on its resonant frequency is found to be insignificant. Moreover, sensitivity analyses of the basin's length and maximum basin depth are presented, with the maximum water depth being directly proportional to the maximum wave amplitudes and resonant frequencies of both basins. In contrast, the resonant frequency decreases and the maximum wave amplitude fluctuates as the length of the basin grows.