Mathematical Study on Wave Propagation through Emergent Vegetation

Abstract

In this paper, the problem of the interaction between a periodic linear wave and offshore aquatic vegetation is investigated. The aquatic vegetation field is considered as a flexible permeable system. A vegetation medium theory is proposed based on Lan-Lee's poro-elastomer theory, in which linearizing vegetation friction resistance is used to describe fluid motion in the vegetation medium. The study involves boundary conditions for free surface water in emergent vegetation media that have been of less concern in previous studies. The analytical solutions of the vegetation medium and wave fields are derived by the partitioning method combined with matching boundary conditions for neighboring regions. An estimation formula for a modification factor is proposed to evaluate the linear vegetation friction coefficient, which can reasonably compare the analytical solution with relevant past cases in terms of wave transmission. Wave reflection, transmission, and attenuation induced by the effects of the characteristics of the vegetation are studied. The results indicate that an increase in the drag coefficient, stem diameter, stem density, spatial coverage, and plant stiffness leads to the emergency vegetation inducing higher wave energy dissipation and reducing the wave transmission. Vegetation stiffness is a significant factor affecting the drag coefficient.