Citation: Placidi, M. & Ganapathisubramani, B. (2015). Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers. Journal of Fluid Mechanics, 782, pp. 541-566. doi: 10.1017Mechanics, 782, pp. 541-566. doi: 10. /jfm.2015 This is the accepted version of the paper.This version of the publication may differ from the final published version. Experiments were conducted in the fully-rough regime on surfaces with large relative roughness height (h/δ ≈ 0.1, where h is the roughness height and δ is the boundary layer thickness). The surfaces were generated by distributed LEGO TM bricks of uniform height, arranged in different configurations. Measurements were made with both floating-element drag-balance and high-resolution particle image velocimetry on six configurations with different frontal solidity, λ F , at fixed plan solidity, λ P , and vice versa, for a total of twelve rough-wall cases. Results indicate that the drag reaches a peak value λ F ≈ 0.21 or a constant λ P = 0.27, whilst it monotonically decreases for increasing values of λ P for a fixed λ F = 0.15. This is in contrast with previous studies in the literature based on cube roughness that show a peak in drag for both λ F and λ P variations. The influence of surface morphology on the depth of the roughness sublayer (RSL) is also investigated. Its depth is found to be inversely proportional to the roughness length, y 0 . A decrease in y 0 is usually accompanied by a thickening of the the RSL and vice-versa. Proper orthogonal decomposition analysis was also employed. The shapes of the most energetic modes calculated using the data across the entire boundary layer are found to be selfsimilar across the twelve rough-walls cases, however, when the analysis is restricted to the roughness sublayer, differences that depend on the wall morphology are apparent. Moreover, the energy content of the POD modes within the RSL suggest that the effect of increased frontal solidity is to redistribute the energy towards the larger-scales (i.e. larger portion of energy is within the first few modes) whilst the opposite is found for variation of plan solidity. Permanent

Wind-tunnel experiments were carried out on fully-rough boundary layers with large roughness (δ/ h ≈ 10, where h is the height of the roughness elements and δ is the boundary-layer thickness). Twelve different surface conditions were created by using LEGO™ bricks of uniform height. Six cases are tested for a fixed plan solidity (λ P ) with variations in frontal density (λ F ), while the other six cases have varying λ P for fixed λ F . Particle image velocimetry and floating-element drag-balance measurements were performed. The current results complement those contained in Placidi and Ganapathisubramani (J Fluid Mech 782:541-566, 2015), extending the previous analysis to the turbulence statistics and spatial structure. Results indicate that mean velocity profiles in defect form agree with Townsend's similarity hypothesis with varying λ F , however, the agreement is worse for cases with varying λ P . The streamwise and wall-normal turbulent stresses, as well as the Reynolds shear stresses, show a lack of similarity across most examined cases. This suggests that the critical height of the roughness for which outer-layer similarity holds depends not only on the height of the roughness, but also on the local wall morphology. A new criterion based on shelter solidity, defined as the sheltered plan area per unit wall-parallel area, which is similar to the 'effective shelter area' in Raupach and Shaw (Boundary-Layer Meteorol 22:79-90, 1982), is found to capture the departure of the turbulence statistics from outer-layer similarity. Despite this lack of similarity reported in the turbulence statistics, proper orthogonal decomposition analysis, as well as two-point spatial correlations, show that some form of universal flow structure is present, as all cases exhibit virtually identical proper orthogonal decomposition mode shapes and correlation fields. Finally, reduced models based on proper orthogonal decomposition reveal that the small scales of the turbulence play a significant role in assessing outer-layer similarity.

High-resolution particle image velocimetry data obtained in rough-wall boundary layer experiments are re-analysed to examine the influence of surface roughness heterogeneities on wind resource. Two different types of heterogeneities are examined: (i) surfaces with repeating roughness units of the order of the boundary layer thickness (Placidi & Ganapathisubramani. 2015 J. Fluid Mech. 782 , 541–566. ( doi:10.1017/jfm.2015.552 )) and (ii) surfaces with streamwise-aligned elevated strips that mimic adjacent hills and valleys (Vanderwel & Ganapathisubramani. 2015 J. Fluid Mech. 774 , 1–12. ( doi:10.1017/jfm.2015.228 )). For the first case, the data show that the power extraction potential is highly dependent on the surface morphology with a variation of up to 20% in the available wind resource across the different surfaces examined. A strong correlation is shown to exist between the frontal and plan solidities of the rough surfaces and the equivalent wind speed, and hence the wind resource potential. These differences are also found in profiles of and (where U is the streamwise velocity), which act as proxies for thrust and power output. For the second case, the secondary flows that cause low- and high-momentum pathways when the spacing between adjacent hills is beyond a critical value result in significant variations in wind resource availability. Contour maps of and show a large difference in thrust and power potential (over 50%) between hills and valleys (at a fixed vertical height). These variations do not seem to be present when adjacent hills are close to each other (i.e. when the spacing is much less than the boundary layer thickness). The variance in thrust and power also appears to be significant in the presence of secondary flows. Finally, there are substantial differences in the dispersive and turbulent stresses across the terrain, which could lead to variable fatigue life depending on the placement of the turbines within such heterogeneous terrain. Overall, these results indicate the importance of accounting for heterogeneous terrain when siting individual turbines and wind farms. This article is part of the themed issue ‘Wind energy in complex terrains’.

In this work, we study the development of the internal boundary layer (IBL) induced by a surface roughness discontinuity, where the downstream surface has a roughness length greater than that upstream. The work is carried out in the EnFlo meteorological wind tunnel, at the University of Surrey, in both thermally neutral and stable cases with varying degrees of stability. For the neutrally-stratified boundary layer, the IBL development in the log-law region shows good agreement with the diffusion model proposed by Panofsky and Dutton (Atmospheric turbulence, Wiley, New York, 1984) provided that a modified origin condition is introduced and its growth rate is dictated by a constant diffusion term. However, the model over-predicts the growth of the IBL in the outer layer, where the IBL depth grows slowly with fetch following a power function with exponent n being 0.61 (whereas the original model prescribes $$n\approx 0.8$$ n ≈ 0.8 ). For the stably-stratified boundary layers, n is found to further reduce as the bulk Richardson number, $$\textrm{Ri}_\textrm{b}$$ Ri b , increases. The analysis of the top region of the IBL shows that the slow growth rate is due to a combination of the decay of the diffusion term and a significantly negative mean wall-normal velocity, which transports fluid elements towards the wall. Considering these two effects, a modified diffusion model is proposed which well captures the growth of the IBL for both neutrally and stably-stratified boundary layers. Graphical abstract

In this work, we study the development of the internal boundary layer (IBL) induced by a surface roughness discontinuity, where the downstream surface has a roughness length greater than that upstream. The work is carried out in the EnFlo meteorological wind tunnel, at the University of Surrey, in both thermally neutral and stable cases with varying degrees of stability. For the neutrally-stratified boundary layer, the IBL development shows good agreement with the diffusion model proposed by Panofsky and Dutton (1984) providing that a modified origin condition in the log-law region is introduced and its growth rate is dictated by a constant diffusion term. However, the model over-predicts the growth of the IBL in the outer layer, where the IBL depth grows slowly with fetch following a power function with exponent n being 0.61 (whereas the original model prescribes n≈0.8). For the stably-stratified boundary layers, n is found to further reduce as the outer layer Richardson number, Rib, increases. The analysis of the top region of the IBL shows that the slow growth rate is due to a combination of the decay of the diffusion term and a significantly negative mean wall-normal velocity, which transports fluid elements towards the wall. Considering these two effects, a modified diffusion model is proposed which well captures the growth of the IBL for both neutrally and stably-stratified boundary layers.