Free-surface flow past a submerged cylinder

This study employs a Lagrangian frame numerical method to investigate two-dimensional free-surface flow induced by a submerged moving cylinder. This method combines the advantages of vortex methods and boundary integral methods, and is capable of capturing the complex motion of free surface and vortices. A series of computations are performed to investigate the effects of Froude number, the depth of submergence and still water depth on the flow motion. Free surface deformation, wake vortex and hydrodynamic forces are studied.

     

Lifting of a large object from a rigid porous seabed

This study investigates the flow field induced by the tilting lift of a large object from a rigid porous seabed and the induced force acting on the object using an analytical approach. In the corners between the object and the seabed, we assume the flow is a corner flow with a low Reynolds number, and the porous media flow in the seabed obeys Brinkman equations. The complete boundary conditions for viscous flow, including the continuity of velocities and stresses, are utilized at the seabed-water interface. The Helmholtz decomposition theorem, which decomposes the flow field into irrotational and rotational parts, and a perturbation expansion are employed to solve the boundary-value problem. Leading-order analytical solutions for the flow in the water and in the porous seabed are presented, indicating that the flow inside the corners is not a parallel flow, and the porous media flow inside the seabed is a Stokes boundary layer flow that does not obey Darcy’s law.

     

Laminar Water Wave and Current Passing Over Porous Bed

The problem of the dynamic interaction of water waves, current, and a hard poroelastic bed is dealt with in this study. Finite-depth homogeneous water with harmonic linear water waves passing over a semi-infinite poroelastic bed is investigated. In order to reveal the importance of viscous effect for different bed forms, viscosity of water is considered herein. In a boundary layer correction approach, the governing equations of the poroelastic material are decoupled without losing physical generality. The contribution of pressure effect and shear effect to the hard poroelastic bed, which is a valuable indication to the mechanism of ripple formation, is clarified in the present study. This approach will be helpful in saving time and storage capacity when it is applied to numerical computation.     

Effects of Weakly Nonlinear Water Waves on Soft Poroelastic Bed with Finite Thickness

Since porous material is usually of a finite thickness in nature, the effects of periodically nonlinear water waves propagating over a soft poroelastic bed with finite thickness are hence noticed and studied in this work. The water waves are simulated by potential theory while the porous bed is governed by Biot’s theory of poroelasticity herein. The conventional Stokes expansion of water waves based on a one-parameter perturbation expansion fails to solve the soft poroelastic bed problem; therefore, the boundary layer correction approach combined with a two-parameter perturbation expansion is proposed, which enables us to solve the problem of soft poroelastic bed with finite thickness. The results are compared to the similar problem with an infinite-thickness porous bed. The boundary effects of the impervious rock are significant on wave-induced pore water pressure and effective stresses, but are of very little significance on wave profiles at the free surface and the porous bed surface. However, the rigid boundary is insignificant to the pore water pressure and effective stresses when the thickness of porous bed is larger than about one wavelength.