Relationship between the Aerodynamic Roughness Length and the Roughness Density in Cases of Low Roughness Density*

This paper presents measurements of roughness length performed in a wind tunnel for low roughness density. The experiments were performed with both compact and porous obstacles (clusters), in order to simulate the behavior of sparsely vegetated surfaces. The experimental results have been used to investigate the relationship between the ratio z₀/h and the roughness density, and the influence of an obstacle's porosity on this relationship. The experiments performed for four configurations of compact obstacles provide measurements of roughness length z₀ for roughness densities between 10^–3 and 10^–2 which are in good agreement with the only data set available until now for this range of low roughness densities. The results obtained with artificial porous obstacles suggests that the aerodynamic behavior of such roughness elements can be represented by the relationship established for compact obstacles, provided a porosity index has been used to determine the efficient roughness density (the fraction of the silhouette area actually sheltered by solid elements) rather than counting the porous object as solid. However, the experiments have been performed with relatively low porosity indices (maximum =25%) for which the porosity has a negligible influence. In this range of porosity index, representing the aerodynamic behavior of porous obstacles using the relationship established for compact obstacles, should not lead to a significant error. However, the influence of the porosity may be important for porosity indices larger than 30%.