Waves and currents over a fixed rippled bed: 2. Bottom and apparent roughness experienced by currents in the presence of waves

Abstract

This paper is the second of two papers which present the results of an experimental study to verify the use of a single bottom roughness length scale to characterize wave and current boundary layer flows over a rough bed. While the first paper [Mathisen and Madsen, this issue] included analysis of wave attenuation measurements to estimate the bottom roughness experienced by waves in the presence and absence of a current, this paper includes the analysis of time‐averaged velocity profiles to estimate the bottom and apparent roughness experienced by a current in the presence of waves. In this paper, velocity profiles predicted by the Grant and Madsen [1986] model are compared with measured velocity profiles. Apparent hydraulic roughness predictions of the Grant and Madsen [1986] model are shown to underpredict the apparent hydraulic roughnesses experienced by the current. This difference is shown to be a result of an underprediction of the wave boundary layer thickness and of a steady streaming or mass transport which is induced by the wave motion within the wave boundary layer of the combined wave‐current flow. By modifying the wave boundary layer thickness and estimating the wave‐induced mass transport from pure wave experiments, the bottom roughness for pure current, pure wave, and combined wave‐current boundary layer flows is shown to be characterized by a single roughness scale.