Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer

Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (τ) acting on the surfaces, the surface shear stress on the ground between the elements (τ_S) and the drag force on the elements for each roughness array. The measurements indicated that τ_S quickly reduced near the leading edge of the roughness compared with τ, and a τ_S minimum occurs at a normalized distance (x/h, where h is element height) of (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average τ_S : τ values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.