Examination of empirical formulas for wave shoaling and breaking on steep slopes

Estimation of the wave height transformation of shoaling and breaking is essential for the nearshore hydrodynamics and the design of coastal structures. Many empirical formulas have been well recognized to the wave height transformation, but most of them were only applicable for gentle slopes. This paper reports the experimental results of wave shoaling and breaking over the steep slopes to examine the applicability of the previous empirical formulas. Two steep bottom slopes of 1/3 and 1/5, and one gentle slope of 1/10 were conducted in the present experiments. Experimental results show that the shoaling distance of steep slopes become short and the surface waves may be partially reflected from the steep bottom, thus the estimation of wave shoaling using the well-known previous formula did not conform completely to the experimental results. The previous empirical formulas for the wave breaking criteria were also examined, and the modified equations to the steep beaches were proposed in this work. A numerical model was finally adopted to calculate the wave height transformation in the surf zone by introducing the modified breaking index.