Dynamic Response of Poroelastic Bed to Water Waves

Abstract

The problem of a small‐amplitude water wave propagating in a channel of constant depth with a horizontal poroelastic bed of infinite thickness is investigated. Using the theory of poroelasticity derived in Huang and Chwang (1990), three decoupled Helmholtz equations are applied to study the present problem. The general solution is obtained, and five physical parameters, m, ε, Λ, Π, Ψ, for the porous media flow are defined. The first of these physical parameters represents the relative stiffness of solid and fluid, the second represents penetrability, while the other three reveal Mach numbers of two longitudinal waves and one transverse wave of the porous medium when penetrability is low, i.e., when ‖ε‖≪1. It is believed that these parameters will be especially useful for experimental modeling. We not only clarify the required constraints of Yamamoto et al. (1978) and Liu (1973) that are not explained in their articles, but also demonstrate successfully the generality of the present work.