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 used computational fluid dynamics to simplify Raupach's model by clarifying the relationship between the parameter & beta; (the ratio of element to surface drag coefficients) and the roughness-element shape parameter & sigma; using a k-& omega; shear-stress transport (SST) turbulence model with rigid cylindrical roughness elements. Results showed that & beta; ranged between 102 and 242 and the parameter m (a relationship between the average and the peak surface shear stresses) ranged between 0.15 and 0.32 for partitioning of surface shear stress. & beta; decreased with increasing & sigma;, and the relationship followed a power law. We confirmed this relationship by comparing wind tunnel and field measurements for different types of roughness element (blocks, hemispheres, trapezoids and plants based on the results from previous studies). However, the model has some limitations due to the characteristics such as streamline and porosity of plants. The peak mean stress ratio (a) ranged between 2.09 and 3.61. We also confirmed that the probability-density function for the surface shear stress proposed by Zou et al. (2022) described the distribution of the surface shear stress among roughness elements well, which is essential to accurately estimate surface erosion by wind.

Automated summary

We simplified Raupach's model using computational fluid dynamics to clarify the relationship between the parameter β (ratio of element to surface drag coefficients) and the roughness-element shape parameter σ. Our results showed a power law relationship, with β decreasing as σ increased. We confirmed this relationship through wind tunnel and field measurements, although the model has limitations regarding plant characteristics such as streamline and porosity. We also validated the proposed probability-density function for surface shear stress, which is crucial for accurate estimation of surface erosion by wind.