Examination of outer-layer similarity in wall turbulence over obstructing surfaces
JOURNAL OF FLUID MECHANICS(2023)
摘要
Turbulent flows over canopies of rigid filaments with different densities are studied using direct numerical simulations at moderate Reynolds numbers Re-tau approximate to 550-1000. The canopies have heights h(+ )approximate to 110-220, and are used as an instance of obstructing substrate for the assessment of outer-layer similarity. We show that conventional methods used to determine the zero-plane displacement Delta y can be at odds with proper outer-layer similarity and may not be applicable for flows at moderate Re-tau. Instead, we determine Delta y and the length and velocity scales that recover outer-layer similarity by minimising the difference between the smooth-wall and canopy diagnostic function everywhere above the roughness sublayer, not just in the logarithmic layer. In addition, we explore the possibility of the zero-plane displacement and the friction velocity being set independently, but find that outer-layer similarity is recovered more consistently when they are coupled. We observe that although the K & aacute;rm & aacute;n constant, kappa may not have smooth-wall-like values, the flow statistics are smooth-wall-like in the logarithmic layer and above if the surface effect is limited within the near-wall region. This suggests a modified outer-layer similarity, where kappa is not 0.39, but turbulence is otherwise smooth-wall-like. When the canopy is dense, the flow above the tips is essentially smooth-wall-like, with smooth-wall-like kappa approximate to 0.39 and origin essentially at the tip plane. For canopies with intermediate density, the overlying flow perceives a deeper zero-plane displacement into the canopy, which is consistent with observations reported by previous studies, but exhibits a lower K & aacute;rm & aacute;n constant, kappa approximate to 0.34-0.36. For sparse canopies, kappa tends back to its smooth-wall value, and the zero-plane displacement height is at the canopy bed. For all canopies studied, the decrease in kappa never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.
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关键词
turbulent boundary layers
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