Dispersive effects of water waves generated by submerged landslide

Abstract

In this study, we developed three solutions with different degrees of dispersion for an idealized model where the landslide moves along a flat bottom; this was to elucidate the effects of landslide acceleration on the dispersive property of the generated water waves. Both free surface elevations and velocity profiles are obtained with their integral forms for the three solutions. Based on the derivations of the solutions, it is found theoretically that landslide acceleration can cause the generated water waves to be dispersive. Numerical integrations are carried out by using the extended trapezoidal rule and the solutions are validated by comparison with the available experimental results. Case studies are carried out by the three models, and the results show that the amplitude of water waves increases with the increase in landslide acceleration. Evident dispersive effects caused by the landslide acceleration can be found, especially with the increase in water depth. This confirms the theoretical findings in this study. In addition, the wide range of applications of these three solutions are indicated.