A Numerical Model Of Water Waves Generated By Landslides Base On The Boussinesq Equation

Water waves generated by submarine landslides is a common disaster.When landslides move in shallow water,such as coasts,rivers,reservoirs,causing the surge spreading along the coast,results in a vast losses of human life and economic.Developing a mathematical model to describe the characteristics of the waves generated by submarine landslides is practical significance for disasters estimation and engineering fortification.A set of model based on the Peregrine's Boussinesq equation and coupled with landslide dynamic is derived to describe the generation and propagation of water waves generated by submarine landslides.According to Beji's method to improve the dispersion of the model.Fourth-order Adams prediction correction method is applied to solve the model.Comparing with the results that water waves generated by the landslide move uniformly in a flat depth water tank between the Boussineq model and analysis solutions,and water waves generated by seabed movement vertical between Boussinesq model and experiment results show that the Boussinesq model is capable to describe the deformation of the free surface generated by landslides.The dispersion of the water waves cannot be ignored in some region.Considering the long movement and the large displacement of submarine landslides,the characteristics of landslides will affect the propagation characteristics of water waves.The effects of landslides,such as velocity,acceleration,height,length,initial submerge depth,and the angle of seabed are studied by the verified model.The results show:(1)considering about landslides move along the seabed with different accelerations,the deformation of free surface is more severe with the increase of accelerations;the height of trough is linear with the acceleration at the initial stage of the movement.(2)Considering about landslides move at the seabed with different speeds,there is less relationship between the deformation of free surface and seabed slope angles;The height of the crest increases first and then decreases with the increase of the velocity of landslides.(3)Considering the actual force of landslides,deformation of the free surface is greater with the increase of the maximum height,the length of the landslide and the seabed slope angle,while decreases with the increase of the initial submerge depth of landslides,the height of the trough is approximately linear with the maximum height of the landslides.Comparing the results of deformation of free surface generated by landslides move along the seabed between Boussinesq model and RANS model,the results show that these two models fit well with each other.Then A process of sea ice impacted by water waves generated by landslides is simulated based on RANS model.