Dynamic Response of Poroelastic Bed to Nonlinear Water Waves

The nonlinear oscillatory water wave propagating over a constant depth channel with a horizontal poroelastic bed of infinite thickness is investigated. The channel flow is treated as potential flow, while the channel bed is considered a poroelastic material. Applying proper boundary conditions, this study uses the Stokes expansion of deep water wave to the second order to handle the problem. The result is compared to the linear wave solution of Huang and Song in order to show the nonlinearity effect, and is also compared to experimental data to verify the correctness of this study. It is found that because the wavelength of the second longitudinal wave inside the porous bed is much shorter than that of the water wave when the bed material is soft, the conventional Stokes expansion of deep water wave based on k₀a is only valid for hard bed material but invalid for soft bed material even though the Ursell parameter is small. An extra constraint for permeable soft bed material other than the Ursell parameter is thus proposed in this study in order to make the Stokes expansion of deep water wave be valid. It is also found that Biot's theory of poroelasticity is proper in simulating hard material bed. The nonlinear effect of water wave with a permeable hard material bed occurs easily even when both $\left|{\mathit{k}}_0\mathit{a}\right|$ and the Ursell parameter are very small. And the major influence of the nonlinearity is only on the water wave itself, not on the porous medium.