Numerical Modeling of Surface Waves over Submerged Flexible Vegetation

Abstract

This paper presents a coupled wave–vegetation model for simulating the interaction between water waves and submerged flexible plants. The balance of forces for the vegetation motion includes buoyancy, damping, stiffness of the vegetation, and gravity as restoring forces, and drag and inertia as driving forces. The governing equation for vegetation motion is solved by the high-order finite element method (FEM) together with an implicit time differencing scheme. The results of the vegetation model exhibit a fourth-order convergence rate. The vegetation-induced drag and inertia are introduced into the wave model as a source term in the momentum equation. This coupled model is rigorously verified by comparing numerical results with theoretical solutions for single swaying vegetation cases and with experimental data for large-scale swaying vegetation cases. Excellent agreement is achieved. A scaling analysis is performed on the governing equation for vegetation motion to understand the importance of each force involved in the vegetation vibration. For cases in which damping becomes significant compared with other restoring forces, a theoretical relationship between movements of vegetation stem and water particle is derived, and a dimensionless parameter, incorporating characteristics of waves and material as well as geometric properties of vegetation, is obtained. The vegetation deformation model developed in this paper can be coupled with other wave models to simulate wave and vegetation interactions.