Investigations of the law‐of‐the‐wall over sparse roughness elements

This paper examines the application of the law‐of‐the‐wall or gradient method for calculating the shear velocity, roughness length, and displacement height over three increasing roughness densities replicated with three different sized cubes within a recirculating wind tunnel. We compare these aerodynamic parameter estimates with estimates of the same parameters derived from other established methods: Reynolds stress analysis and the outer‐layer velocity‐defect law. By using more than one roughness height for the same roughness density (λ), dependencies of these parameters on roughness element height were also evaluated. Using the vertical wind speed logarithmic profile layer (determined graphically), resulted in shear velocity estimates that are greater by more than a factor of two than those determined using hot‐film anemometry. The law‐of‐the‐wall method provided a good estimate of the roughness length when applied to only that portion of the wind speed profile identified by Reynolds stress measurements to be within the constant stress layer; however, the shear velocity was overestimated by an average of 43% compared with that measured directly by hot‐film anemometry. The best prediction of both of the roughness length and shear velocity, compared to estimates using Reynolds stress analysis, was obtained using the outer‐layer velocity‐defect law. We advocate that the velocity‐defect law method be used in wind tunnel testing for calculating the shear velocity and roughness length from velocity profiles over sparsely spaced roughness elements, or when flow is highly heterogeneous, instead of the law‐of‐the‐wall.