Phase‐Averaged Drag Force of Nonlinear Waves Over Submerged and Through Emergent Vegetation

Abstract

Aquatic vegetation protects the shoreline by dissipating the wave energy and reducing the mean water level. For the latter, the phase‐averaged depth‐integrated drag force induced by vegetation ( trueFd‾) plays an essential role. For linear waves, the trueFd‾ exerted by submerged vegetation ( trueFdsub‾) and by the submerged part of emergent vegetation ( trueFdtrough‾) equal 0. As the wave nonlinearity increases, the profile of the horizontal velocity (u) becomes skewed and non–cosine shaped, and thus, both trueFdsub‾ and trueFdtrough‾ are nonzero (phase average of u|u|≠0) and their significance increases. This study examines the effects of wave nonlinearity and vegetation submergence on trueFd‾ based on stream function wave theory. In deep water, it is found that the wave nonlinearity slightly affects trueFdtrough‾ due to the negligible weight of trueFdtrough‾ in the overall trueFd‾. Both the wave nonlinearity and vegetation submergence have negligible effects on trueFdsub‾ as well. In shallow water, trueFdtrough‾ takes up a large percentage in the overall trueFd‾ for emergent vegetation, and a linear relationship between trueFdsub‾ and vegetation submergence exists for waves with relatively small wave heights. The applicable range of the linear wave theory based trueFd‾ is determined using trueFd‾ from stream function wave theory as a reference solution. Moreover, a parametric model is developed for evaluating trueFd‾ for random waves. The mean water level changes, or wave setup, on a vegetated sloping beach are validated and quantified using experimental data obtained from literature.