Waves and currents over a fixed rippled bed .1. Bottom roughness experienced by waves in the presence and absence of currents

Several theoretical models have been advanced for turbulent boundary layers associated with wave and current flows over a rough bed. Although these models differ, particularly in the sophistication with which turbulence is modeled, they all share one common feature: the bottom roughness is characterized by a single roughness length scale k(n). However, no experimental data have been presented which accurately characterize the bottom roughnesses for wave and current boundary layers such that this basic assumption can be considered verified. This paper and a companion paper [Mathisen and Madsen, this issue] present results of an experimental study to verify this basic assumption. In this paper, wave roughnesses (i.e., bottom roughnesses experienced by pure waves and waves in the presence of a current) are compared with the roughness experienced by a pure current. The roughnesses for pure currents and pure waves are shown to be the same if determination of the pure wave roughness from measurements of wave energy dissipation includes the phase difference between the near-bottom horizontal orbital velocity and bottom shear stress. When these analysis procedures are extended to combined wave-current flows, the roughness experienced by waves in the presence of a current is shown to be that obtained for pure waves.