Bottom shear stress, wave height and wave set-up under wave transformation

Abstract

This study is concerned with the influence of wave transformation and bed shear stress on wave height and wave set-up. The ultimate goal is the prediction of wave height and mean water level in the nearshore zone. In order to develop such a predictive model, relevant empirical relationships were determined based on data measured during a two-dimensional hydraulic model study with a scale of 1:12 representing the Ala Moana reef on the south shore of Oahu. For predicting the wave height from deep water to inside the breaker zone, a new empirical relationship is obtained for the parameters, H/nrms, and Pa=Ha/Lacoth^2(D/La). The relationship is based on data from this experiment and from Hansen and Svendsen (1979). The hydraulic model used in this study had a compound slope of roughly 0, 1:80, 1:32 and 1:20, while Hansen and Svendsen used a plane slope of 1:34. The bed shear stress was determined by direct measurements of wave forces on the bed and of fluid velocities near the bed under breaking waves and other highly nonlinear waves. The resulting friction factors are compared with the existing friction factor curve by Jonsson (1964), which was established under sinusoid81 wave conditions. Under the assumption that the dominant factors for the dissipation of energy are bottom friction and the wave breaking phenomenon, the energy dissipation is determined based on linear wave theory for the friction loss and on bore similarity for the breaking loss. Correction factors to these theoretical dissipations are empirically obtained. The effect of the mean shear stress on wave set-up is examined by comparing measured mean water levels with results calculated using the computational procedure developed in this study. It is concluded that the new curve for wave height prediction is applicable in the entire nearshore region, even in the breaking zone, at least for slopes ranging from 0 to 1:34. The Jonsson's friction factor curve for rough turbulence, developed from linear waves, accurately predicts friction factors for highly nonlinear waves, provided that an appropriate particle amplitude at the bed is used. The mean shear stress, which is usually considered to be negligible, is important in the calculation of wave set-up.