Department of Mechanical Engineering, University of San Antonio, TX, 78248, USA
Ann Arbor, Michigan, USA
To improve the understanding of the near-wall region in a rough-wall turbulent boundary layer, we use a three level decomposition as an alternative formulation to the classical Reynolds decomposition. The instantaneous flow variable is now decomposed to a time-space averaged mean flow, a steady mean wake flow around the roughness (i.e. steady but spatially varying motions),and a residual fluctuating flow. In this paper, we present the momentum transport equations for these three components of the decomposition. These transport equations for the three velocity components will facilitate to establish and understand the local interactions of the mean flow, turbulence and wall roughness. We analyze the relative significance of these terms. The fundamental equations are derived within the immersed boundary representation of roughness elements. Total shear stress for rough-wall is obtained from the stress balance equation consisting of stress due to the roughness wake components, the Reynolds stress, the viscous stress and the stress due to the boundary force from the roughness. In order to evaluate the relative contribution of the components in this three-level decomposition, we use direct numerical simulation (DNS) to simulate flow in a channel with rough-walls. Surface roughness has been introduced using immersed boundary methods. The flow simulations are performed at Reτ= 180 and roughness height h+=5, 10, 20 for egg-carton roughness elements.