Structure of rough-wall turbulent boundary layers

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Abstract
Recent experiments have shown that, in rough‐wall turbulent boundary layers, drag varies systematically with the spanwise aspect ratio λz (span/height) of roughness elements. In this paper, the effect of λz on turbulence structure has been examined. Based on λz, the roughness in a transversely grooved surface (λz≫1) is the opposite extreme of model plant canopies (λz≪1) studied in wind tunnels, whereas sandgrain is an intermediate type [λz=O(1)]. Second‐, third‐, and fourth‐order turbulence moments have been measured in turbulent boundary layers over transversely grooved and smooth surfaces and compared with available turbulence structure measurements over other types of surfaces. The near‐wall turbulence structure is found to vary with λz. The instantaneous motions involved in the flux of shear stress near the wall in smooth and transversely grooved surfaces are opposite in sign to those in three‐dimensional roughness. The former is explained in terms of hairpin vortices alone while the latter group is modeled to have an additional vortex, viz., the so‐called necklace vortex which straddles a three‐dimensional roughness element near its base.