Theoretical and numerical investigation of wave attenuation on vegetated seabeds

Environmental issues have become increasingly important, with vegetation impacting ecosystems and the transport of nutrients and sediments. The present research aims to analyse, from a theoretical and numerical point of view, the attenuation of monochromatic waves by an array of rigid submerged cylindrical stems on a horizontal bottom. First, both the numerical and theoretical models were properly calibrated using data from the literature. Subsequently, the theoretical model's effectiveness was validated through numerical simulations performed with a 3D weakly compressible smoothed particle hydrodynamics (WCSPH) model coupled with a sub-particle scale (SPS) approach for turbulent stresses, analysing different wave behaviours and various configurations of cylindrical arrays. The results confirmed the theoretical model's reliability in predicting wave height reduction and energy dissipation caused by submerged cylindrical obstacles on a horizontal bottom, demonstrating its practical applicability. Furthermore, utilizing the capabilities of 3D LES, SPH simulations have been used to inspect and detail the wave-induced vorticity behaviour around the stems. The results showed an antisymmetric vorticity around the stems driven by wave action. Additionally, the effects of the Keulegan–Carpenter (KCr) number, the submergence ratio (α) and the Ursell number (Ur) on the drag coefficient (CD) were examined. Finally, wave-attenuation analysis was conducted to emphasize the importance of accounting for wave damping produced by stem spacing (d), submergence ratio and hydrodynamic parameters, (e.g., still water depth h, incident wave height H and wave period T). The results highlight that (i) for the same stem spacing, the wave height damping is more severe as the submergence ratios increases; (ii) for the same submergence ratio, the wave height damping is more severe as the stem spacing decreases; (iii) for the same submergence ratio, the wave height damping is more severe as the relative wave height (H/h) and wave steepness (H/L) increase.