The effects of vegetation density on wave propagation through emergent communities

In this paper, we develop an analytic model for wave propagation through an emergent vegetation community to investigate the effects of vegetation density on the wave dynamics. The model is based on the mass and momentum conservation equations with drag and inertia forces associated with the vegetation stems. After normalizing the basic equations and the corresponding boundary conditions by using representative physical variables of an incident wave, we obtain the dimensionless forms of the equations with governing parameters, including the dimensionless vegetation density, dimensionless wave amplitude of the incident wave, and the Froude number. By solving the equations with a linear approximation of the drag force, wave characteristics through the vegetation community, such as a decay rate of wave height, wavelength, celerity, group velocity, and wave energy, are derived explicitly with respect to the dimensionless governing parameters. The result of sensitivity analysis shows that the drag force is more important for wave attenuation in the vegetation community compared with the inertia force. It is also obvious that the decay rate of the wave height and energy, wave number, and celerity are much influenced by the vegetation population density as well as the wave amplitude of the incident wave.