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

Abstract

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 ≈ −42 (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 Boundary-Layer Meteorol (2007) 122:367-396 shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment. List of SymbolsA f frontal area of roughness elements (m 2 ) A u unit area over which surface shear stress associated with a roughness element is distributed (m 2 ) b element breadth (m) Cd surface drag coefficient Cd e roughness element drag coefficient Cd r rough surface drag coefficient Cd s smooth surface drag coefficient cv coefficient of variation d displacement height (m) F force on a roughness element (N) g acceleration due to gravity (m s −2 ) h element height (m) IBL internal boundary layer ISL inertial sublayer m empirical constant between 0 and 1 n number of roughness elements occupying the ground area of the roughness array NDD normalized downwind distance (x/h) NED normalized element drag R average friction velocity ratio R l local friction velocity ratio at different positions in a roughness array Re Reynolds number R t threshold wind friction velocity ratio SD standard deviation of a mean value u wind speed (m s −1 ) u * wind friction velocity (m s −1 ) u * tR threshold wind friction velocity with roughness elements (m s −1 ) u * tS threshold wind friction velocity of bare surface (m s −1 ) x downwind distance (m) z reference height above surface (m) z w roughness sublayer height (m) z o a...

Numerical modelling of aeolian erosion over rough surfaces

“…All values from the numerical simulations grouped in Figure 4 are in close agreement with measurements from Lyles and Allison (1975), Gillette and Stockton (1989), Musick and Gillette (1990), McKenna Neuman and Nickling (1995), Figure 4. Comparison of the friction velocity ratio R t from various sources (Marshall, 1971;Lyles and Allison, 1975;Gillette and Stockton, 1989;Musick and Gillette, 1990;McKenna Neuman and Nickling, 1995;Crawley and Nickling, 2003;Gillies et al, 2007) with those from the numerical simulations presented in this paper. Error bars ±20% represent the accuracy of the Gillette and Stockton (1989) Crawley and Nickling (2002) and Gillies et al (2007), but consistently exceed Marshall's (1971) values, particularly at large values of λ.…”

Vegetation in Drylands: Effects on Wind Flow and Aeolian Sediment Transport

“…During the 1990s, more attention was given to the development of drag partitioning techniques that could establish the wind momentum flux at the soil surface in the presence of roughness elements. The schemes of Raupach [57,121] and Marticorena and Bergametti [118] were widely adopted on the basis of their good agreement with wind tunnel experiments using solid objects on non-complex surfaces (e.g., [51,71,[140][141][142][143]). However, the drag partition schemes have also been found to be limited in application in several respects.…”

“…Other disadvantages of the λ parameter include scaling issues, whereby tall (>0.10 m) elements appear to influence sand transport in a way that cannot be accounted for based solely on knowledge of roughness density [141,142]. This deficiency is minimised in large homogeneous areas of randomly or regularly spaced vegetation of the same height, but becomes problematic in natural environments displaying structural anisotropy [27,58].…”

Sediment Mobilisation by the Wind

“…A drag balance, buried with the measuring element flush to the surface or attached to a roughness element, directly measures the force applied by the wind and records it on a sensitive load cell. Both technologies have been successfully tested in wind tunnels and dryland field locations to measure wind forces on bare sediment and vegetated surfaces in a variety of flow conditions and surface roughness configurations (Gillies et al, 2000;King, Nickling and Gillies, 2005;Gillies, Nickling and King, 2007;Walker and Nickling, 2003).…”

“…This intercept clearly describes z 0 as defined as the depth of air at the surface with an effective zero velocity. When plotted in the manner of Figure 18.2, z 0 can be determined from the slope and intercept components of the regression equation by Such an approach is common practice and works well for flat and noncomplex surfaces Gillies, Nickling and King, 2007;Gillies et al, 2000;King, Nickling and Gillies, 2005;Sherman et al, 1998;Wiggs et al, 1994;Weaver, 2008). However, defining a clear intercept on complex or patterned (e.g.…”