Parameterizing the Tip Effects of Submerged Vegetation in a VARANS Solver

This paper presents an experimental and numerical investigation of submerged vegetation flow, with a particular focus on vegetation-related terms, especially in the vicinity of the free end. Experimental results indicate that substantial shear stress is observed near the top of vegetation, where the drag coefficient increases significantly due to the disturbance caused by the free end. Furthermore, wake generation is notably suppressed, particularly at heights where wake-generated turbulence dominates, leading to a reduction in turbulent kinetic energy (TKE). A numerical model based on the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations was developed, incorporating a vertically varying drag coefficient. The two-scale k−ε turbulence model is further modified with the inclusion of a new damping function to capture the suppression of wake generation. The model accurately simulates both unidirectional and oscillatory flows, as well as the associated turbulence structures, with good agreement with experimental measurements. The influence of the tips on wave-induced currents, mass transport and TKE distribution is also investigated. It was found that the tip effects play a significant role in strengthening wave-induced currents at the top of loosely arranged, short, and sparse vegetation, with shear kinetic energy (SKE) serving as a critical component of TKE, contributing to the nonuniform distribution. Both Eulerian currents and Stokes drift contribute to streaming in the direction of wave propagation near the vegetation top, which intensifies with increasing solid volume fraction, while tip effects further enhance the onshore mass transport. Within the vegetation, mass transport is more sensitive to wave period and wave height, shifting from onshore to offshore as wavelength increases under constant water depth.