Waves and currents over a fixed rippled bed. Part 3: Bottom and apparent roughness for spectral waves and currents

This paper is the third in a series of three that presents the results of experiments designed to verify the use of a single bottom roughness length scale for waves and currents over a rough bed. While the first two papers concentrated on the bottom roughness experienced by monochromatic wave and current boundary layer flows, this paper presents the results of additional experiments that investigate the use of an equivalent wave representation to extend these results to spectral wave and current boundary layer flows. Spectral waves, simulated by five components, and currents were generated in a 20-m-long wave flume with a fixed rippled bottom. Attenuation due to bottom friction is determined from total attenuation measurements for individual wave components by removing the effects of sidewall dissipation and wave-wave interactions. These attenuation estimates are used to establish representative friction factors, which are used in conjunction with an existing eddy viscosity model to determine bottom roughness. The bottom roughnesses experienced by spectral waves (in the presence and absence of a current) match the bottom roughnesses for monochromatic waves. When these experimentally determined bottom roughnesses are used in conjunction with the eddy viscosity model, predictions of attenuation for individual wave components closely match measurements. When the wave boundary layer thickness is defined to be the height at which the predicted velocity deficit in the wave boundary layer is within 5% of the free stream velocity, excellent agreement is obtained between predicted and measured velocity profiles for currents in the presence of codirectional waves. Therefore these experiments show that a single bottom roughness, when used in conjunction with an equivalent wave representation, adequately characterizes both monochromatic and spectral wave-current boundary layer flows over a fixed rippled bed.