Drag coefficient prediction model for simulating breaking waves propagating on partly submerged vegetated sloping beaches using a RANS model

Abstract

Accurate prediction of vegetation drag coefficients (C_D) is crucial for simulating breaking wave propagation on partly submerged vegetated sloping beaches. This study conducted a comprehensive investigation involving physical experiments and numerical modeling to address the limitations of existing empirical formulas for C_D. The experiments varied incident wave heights (H_i = 0.02–0.10 m), wave periods (T = 1.0–1.8 s), vegetation densities (N_v = 41–590 units/m²), vegetation zone lengths (L_v = 0.8–1.6 m), and beach slope gradients (m = 1/10–1/30), generating a database of 750 calibrated C_D values. Numerical simulations using a Reynolds-Averaged Navier-Stokes (RANS) model coupled with the stabilized k−ω SST turbulence model and the volume-of-fluid (VOF) method revealed that C_D correlates strongly with the Iribarren number (ξ₀), while being highly sensitive to vegetation density and zone length. Two prediction models were developed: a multivariate nonlinear regression (MNLR) model and an M5P-tree machine learning model. Both models utilized ξ₀, vegetation volume fraction (φ), and relative vegetation zone length (λ_L) as input parameters. The MNLR model provided a compact formula with moderate accuracy (R = 0.87, RMSE = 0.77), while the M5P-tree model partitioned the parameter space using φ and ξ₀, generating three tailored sub-models with superior performance (R = 0.91, RMSE = 0.64). Further validation with independent datasets confirmed that the M5P-tree model outperformed the MNLR model in simulating wave height evolution over vegetated sloping beaches. These findings demonstrate the potential of the M5P-tree model as a robust tool for enhancing simulations of breaking wave propagation on vegetated sloping beaches and optimizing vegetated coastal defenses.