Mean momentum balance analysis of rough-wall turbulent boundary layers

Abstract

Mean momentum balances (MMB) are carried out for zero pressure gradient rough-wall turbulent boundary layer flows. The balance characterizes the mean dynamical mechanisms and reveals dominant terms in the governing equation, which constitutes a necessary step in the derivation of scaling behaviors. The Reynolds stress profiles in rough-wall boundary layers are, however, quite scattered and the uncertainty in the data poses challenges for educing the MMB. The present study employs a method that invokes theoretical constraints to more reliably reveal Reynolds stress gradient behaviors in the presence of data scatter. Properties of the rough-wall mean momentum balances are compared to those of the smooth-wall case. Important qualitative features of the layer structure that exists for the smooth-wall are shown to also exist for rough-wall boundary layers. Specifically, the present analysis reveals the existence of a stress gradient balance layer, and thus the importance of the viscous force term well above the roughness crests. The smooth-wall Reynolds stress peak position scales in proportion with the geometric mean of inner–outer characteristic lengths. Roughness, however, imposes new dynamical length scales and evidence is provided to indicate that the scale separations between the inner length, roughness length, peak Reynolds stress length and outer length are important. The failure of the rough-wall Reynolds stress profiles to merge under smooth-wall meso-scalings clearly reveals the additional richness of the problem. Although more data are required to gain a complete characterization, the present results provide evidence that the combined roughness-Reynolds number problem exhibits significantly greater complexity than captured by the prevalent scheme for characterizing and classifying roughness regimes.