This study investigates the two-dimensional flow of a solitary wave that passes over a submerged rectangular obstacle using a Lagrangian-type numerical method. The main purpose is to investigate vortex generation and evolution caused by the obstacle. The numerical method is based on the combination of vortex methods and boundary integral methods using the Helmholtz decomposition. The simulated flow pattern is compared with the experimental measurements in detail, and the overall agreement is reasonably good. A series of simulations were performed with various wave heights to study the effect of wave height on vortex generation and evolution. The relation between the vorticity field and the drag experienced by the obstacle is also discussed. In the presented cases, the effects of the generated vortices are preserved over a long period, and may cause local scouring of the foundation at the lee side of the obstacle. The deformation of the solitary wave is not much affected by the presence of the vortices, but the drag is significantly affected by the vorticity field. An almost linear relationship between the Reynolds number and the maximum magnitude of the drag (positive and negative) is observed.

In this study, a finite element method was used to establish a two-dimensional numerical model to solve the problem of the Biot equation describing the poroelastic seabed, and to analyze the seepage force on a buried submarine pipeline under the propagation of a solitary wave. The model provides a solution to the displacement of the poroelastic seabed and the variation of the pore-water pressure. By means of numerical simulation, the effects of Young’s modulus and permeability coefficient of the soil on the pore-water pressure and seepage force are discussed. In the simulation of solitary waves passing through fully buried submarine pipelines, numerical results indicate that the smaller the permeability coefficient in dense sandy bed the greater the vertical force acting on the pipeline, and the smaller the permeability coefficient in loose sand bed the smaller the vertical force acting on the pipeline. In general, when the permeability coefficient is large, the smaller the Young’s modulus the more obvious the influence of the vertical force on the pipeline, and when the permeability coefficient is small, the larger the Young’s modulus the more obvious the influence of the vertical force on the pipeline.