Wave propagating over poro-elastic bed

In this study, the problem of waves propagating over poro-elastic seabed is studied. The fluid motion is described by the linear wave theory. The poro-elastic seabed is modeled by the Biot theory, and the governing equations of the sixth-order differential equations for the displacements, and the fourth-order differential equation for the pressure are used. The seabed is currently considered infinite. Interfacial boundary conditions at the seabed surface are dynamic pressure and kinematic velocity continuity. In the solution procedure, the fluid motion and the seabed response are assumed to be periodic. General solution forms for the wave motion and the poro-elastic seabed can be derived. The coefficients in the solutions can be determined from the boundary conditions, and a dispersion equation for water waves is also obtained. The present analytic model can be simplified to the ones developed by Hsu and Jeng (1994), and by Tsai (1995). The present analytic solutions compare favorably well with experimental results by Yamamoto et al (1978) for both fine and coarse sands. Using the present analytic solution, effects of the porosity and stiffness of the elastic seabed on the wavelength are studied. Energy dissipation of propagating waves over poro-elastic seabed, and pressure variation along the water depth, can be estimated.