Roughness effects on wall-bounded turbulent flows

Abstract

This paper outlines the authors' experimental research in rough-wall-bounded turbulent flows that has spanned the past 15 years. The results show that, in general, roughness effects are confined to the inner layer. In accordance with Townsend's Reynolds number similarity hypothesis, the outer layer is insensitive to surface condition except in the role it plays in setting the length and velocity scales for the outer flow. An exception to this can be two-dimensional roughness which has been observed in some cases to suffer roughness effects far from the wall. However, recent results indicate that similarity also holds for two-dimensional roughness provided the Reynolds number is large, and there is sufficient scale separation between the roughness length scale and the boundary layer thickness. The concept of similarity between smooth- and rough-wall flows is of great practical importance as most computational and analytical modeling tools rely on it either explicitly or implicitly in predicting flows over rough walls. Because of the observed similarity, the roughness function (ΔU⁺), or shift in the log layer, is a useful way of characterizing the roughness effect on the mean flow and the frictional drag. In the fully rough regime, it is shown that the hydraulic roughness length scale is related to the root-mean-square height (k_rms) and skewness (s_k) of the surface elevation probability density function. On the other hand, the onset of roughness effects is seen to be associated with the largest surface features which are typified by the peak-to-trough height (k_t). Roughness function behavior in the transitionally rough regime varies significantly between roughness types. Since no “universal” roughness function exists, no single roughness length scale can characterize all roughness types in all the flow regimes. Despite this, research using roughness with a systematic variation in texture is ongoing in an effort to uncover surface parameters that lead to the variation in the frictional drag behavior witnessed in the transitionally rough regime.