A study on the drag coefficient of emergent flexible vegetation under regular waves

The drag coefficient is a vital quantitative indicator within the field of wave attenuation by vegetation, thus receiving considerable critical attention. A systematic understanding of the drag coefficient under single flexible vegetation dynamic and emergent conditions is still insufficient. The present study aimed to quantitatively investigate the drag coefficient of emergent flexible vegetation based on a flume experiment and an emergent flexible vegetation dynamic model. Simulation results demonstrated the acceptability of constant skin friction coefficient and added mass coefficient in simulating the vegetation dynamics and determining the drag coefficient. Based on the calibration method, the obtained drag coefficients are more influenced by the Reynolds number, the Cauchy number, and the drag-to-stiffness ratio under the present investigation conditions. Vegetation flexibility can have evident influences on the drag coefficient of emergent flexible vegetation under waves. Then, a new empirical formula including the drag-to-stiffness ratio and relative vegetation length was proposed to estimate the drag coefficient. The effectiveness of the formula was demonstrated after evaluating the performance in both calculating the drag coefficient and simulating the emergent flexible vegetation dynamics. This study also provided evidence for the uncertainty in the formula establishment, and identified the uncertainty that different determination methods of characteristic wave velocity and utilizations of wave theory can lead to in the formula establishment. The findings can contribute to the understanding of the drag coefficient of emergent flexible vegetation, and highlight the potential usefulness of other parameters associated with vegetation flexibility in drag coefficient prediction.