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

Abstract

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.

Simplifying Raupach's model of shear‐stress partitioning by clarifying the relationship between β and σ and quantifying the shear‐stress probability density based on numerical simulation

“…We extended the previously developed model for cylindrical obstacles by changing the aspect ratio and σ based on the gravel model of Li et al (2021). We defined the height of the cylinder as h (cm) and the diameter as d (cm), and the aspect ratio ( h / d ) ranges from 0.5 to 4.0. d was kept constant at 1 cm (Figure 1a) and 2 cm (Figure 1b), and h was set to 0.5, 1, 2, 3 or 4 cm.…”

“…We used a logarithmic velocity profile to describe the inlet boundary conditions: where u z is the velocity at height z , u * is the friction velocity (with values of 0.33, 0.39, 0.47, 0.54 and 0.60 m/s during our experiments), z 0 is the aerodynamic roughness length, with a value of 0.0033 cm (Li, 2021) and κ is the von‐Karman constant (0.4). The pressure at the outlet is 0, indicating that the airflow reached a steady state.…”

“…When wind erosion occurs on a surface without roughness elements, the surface shear stress is homogeneously distributed. However, the presence of roughness elements on the surface directly affects the direction of the ambient airflow, thereby changing the vertical and horizontal structures of the near‐surface airflow, which leads to a nonhomogeneous distribution of the near‐surface flow field and the surface shear stress (Li, 2021; Mayaud et al, 2016; Raupach et al, 1993). The surface shear stress increases on both sides of the roughness elements due to acceleration of the airflow (Fu et al, 2019), with erosion occurring when the shear stress exerted by the airflow becomes larger than the threshold surface shear stress for particle entrainment; erosion therefore increases at the sides and decreases both in front and behind the roughness elements (Liu, 2021; Zhang, 2019).…”

“…The distribution of shear stress on a rough surface has been studied using wind tunnel experiments, field measurements and numerical simulations. The studies of the influence of roughness elements on surface shear stress have been most common in wind tunnels (Brown et al, 2008; Crawley & Nickling, 2003; Li et al, 2021) and have mostly focused on the partitioning of shear stress and on the drag coefficient under the influence of different roughness elements. Li et al (2021) studied the effect of gravels with different diameters but the same height on the surface shear‐stress distribution in wind tunnel experiments and modified Raupach et al's (1993) partitioning of shear stress by adding the term τ c to describe the shear stress on the top of the roughness elements to make the model more applicable at larger λ .…”

“…The studies of the influence of roughness elements on surface shear stress have been most common in wind tunnels (Brown et al, 2008; Crawley & Nickling, 2003; Li et al, 2021) and have mostly focused on the partitioning of shear stress and on the drag coefficient under the influence of different roughness elements. Li et al (2021) studied the effect of gravels with different diameters but the same height on the surface shear‐stress distribution in wind tunnel experiments and modified Raupach et al's (1993) partitioning of shear stress by adding the term τ c to describe the shear stress on the top of the roughness elements to make the model more applicable at larger λ . Gillies et al (2000) investigated the effect of plant structure on the drag coefficient and found that the drag coefficient for plants was greater than the coefficient for rigid roughness elements.…”