Law-of-the-wall in a boundary-layer over regularly distributed roughness elements

Abstract

ABSTRACTAs opposed to the log-region, the roughness sublayer present above rough surfaces is still poorly understood due to the complex interaction between wakes developing behind roughness elements. To investigate the spatially averaged flow velocity in this region, a data-set has been collected from several direct numerical simulations and wind-tunnel experiments available in the literature. A generalised law-of-the-wall has been derived, applicable to a roughness sublayer present over regularly distributed roughness elements. The key roughness parameter of this new law is the effective height ϵ, which characterises the interaction between the roughness and the outer flow in a temporally and spatially averaged sense. A morphometric study reveals that ϵ is closely related to a new roughness density parameter, λ2, that accounts for the roughness element shape and the inter-element spacing. This allows ϵ to be a universal parameter on roughness characterisation. The derived values of the classical roughness length z0 of the log-law compare well with previous experimental data and geometrical model predictions. Finally, the main properties of the roughness sublayer such as its height are discussed using the geometrical and the roughness parameters proposed in the study.