A modified Raupach's model applicable for shear-stress partitioning on surfaces covered with dense and flat-shaped gravel roughness elements

A commonly used measure to prevent soil wind erosion is to cover the surface with gravel. Gravel can inhibit soil erosion by covering the surface directly, changing the airflow field near the surface and sharing the shear stress of wind. Similar to other roughness elements, the protective effect of gravel on soil is usually expressed in terms of the ratio of the shear stress on the exposed soil surface to the total shear stress on the rough surface due to wind, i.e. through a shear-stress partitioning model. However, the existing shear-stress partitioning models, represented by Raupach's model (RM93), are only applicable when the lateral coverage of the roughness elements, λ < 0.10, and the applicability of the models to flat-shaped roughness elements is unclear. The purpose of this study is to verify the applicability of RM93 for dense and flat-shaped gravel roughness elements by using shear-stress data from wind-tunnel measurements pertaining to roughness elements with different densities (0.013 ≤ λ ≤ 0.318) and flat shapes (height-to-width ratios in the range 0.20 ≤ H/W ≤ 0.63), and to modify RM93 to enhance its predictive ability. The results indicate that RM93 cannot accurately predict the shear-stress partitioning for surfaces covered by densely distributed and flat-shaped gravel roughness elements. This phenomenon occurs because, when roughness elements are distributed densely or are flat-shaped, the proportion of the shear stress on the top surface of the roughness elements (τ_c) to the total shear stress (τ) is large; in this case, τ_c plays a dominant role and serves as an essential component in the shear-stress partitioning model. Consequently, RM93 is modified by incorporating τ_c into the calculation of τ. Under conditions of λ < 0.32 and H/W > 0.2, the modified RM93 can yield satisfactory predictions regarding the shear-stress partitioning.