Water wave propagation generated by a moving landslide over a porous seabed

This work investigates the dynamics of water wave elevation induced by a landslide traveling horizontally at a steady speed over a porous seabed. The analysis is conducted using three linearized models: the fully dispersive water wave model, the shallow water wave model, and the weakly dispersive water wave model. The one-dimensional horizontal closed-form analytical solutions for the propagation of water waves induced by a solid landslide translating at a steady velocity are attained for the fully dispersive water wave model, followed by the asymptotic solution in the far-field for the linear fully dispersive model. Furthermore, for each of the shallow water wave model and the weakly dispersive water wave model, the formal integral relation of a coupled system for free-surface elevation and velocity potential is derived. Each model provides a distinct approximation of wave dynamics, ranging from fully dispersive effects to shallow water assumptions. Additionally, the resonant solution is examined with the complete leading-wave far-field solution. For each of the three models, the horizontal and vertical velocity profiles are obtained. The impact of the seabed porosity on the propagation of water waves is incorporated through appropriate modifications to the primary equations for the shallow water wave and weakly dispersive water wave. The models provide insights into the influence of porosity on wave propagation characteristics, including amplitude and dispersion effects. The findings reveal that the seabed porosity significantly influences the wave elevation and propagation patterns. Porosity tends to dampen the wave amplitude and alter the dispersion characteristics. These effects are most pronounced in all three models. The obtained results are validated against the scenario of an impermeable seabed for two cases (including an experimental one), offering a comprehensive understanding of the role of the seabed permeability in landslide-induced wave generation.