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 ((Formula presented.)) plays an essential role. For linear waves, the (Formula presented.) exerted by submerged vegetation ((Formula presented.)) and by the submerged part of emergent vegetation ((Formula presented.)) equal 0. As the wave nonlinearity increases, the profile of the horizontal velocity (u) becomes skewed and non–cosine shaped, and thus, both (Formula presented.) and (Formula presented.) are nonzero (phase average of u|u|≠0) and their significance increases. This study examines the effects of wave nonlinearity and vegetation submergence on (Formula presented.) based on stream function wave theory. In deep water, it is found that the wave nonlinearity slightly affects (Formula presented.) due to the negligible weight of (Formula presented.) in the overall (Formula presented.). Both the wave nonlinearity and vegetation submergence have negligible effects on (Formula presented.) as well. In shallow water, (Formula presented.) takes up a large percentage in the overall (Formula presented.) for emergent vegetation, and a linear relationship between (Formula presented.) and vegetation submergence exists for waves with relatively small wave heights. The applicable range of the linear wave theory based (Formula presented.) is determined using (Formula presented.) from stream function wave theory as a reference solution. Moreover, a parametric model is developed for evaluating (Formula presented.) 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.