Semianalytical Model of Depth-Integrated Vegetal Drag Force Based on Stokes Second-Order Wave Theory

The phase-averaged depth-integrated vegetal drag force (F-v) directly impacts the mean water level (MWL) change in vegetation. Evaluated from linear wave theory, F-v integrated along the submerged part of vegetation becomes zero due to the symmetric profile of horizontal velocity. In this study, a semianalytical model for estimating F-v on vegetation stems exposed to Stokes waves is developed based on Stokes second-order wave theory (STK). By assuming a narrow-banded wave spectral density and Rayleigh-distributed wave heights, the proposed model can be applied to random waves. STK-based formulas of the maximum depth-integrated vegetal drag force, bending moment, and bending stress are provided to assess the breakage of vegetation stems. Moreover, by taking the solutions from the stream function wave theory as references, the applicable ranges of the STK-based semianalytical model of F-v and drag-induced bending moment are determined.