139 / 2024-02-19 16:15:16

Semi-Empirical Wave Shoaling Model

wave shoaling,energy flux conservation,linear wave,cnoidal wave,simple wave model

Wave height transformation is usually computed using the energy flux conservation law based on linear (1st-order Stokes) wave theory. It is well-known that linear wave theory underestimates shoaling wave height at locations with a large Ursell number near the breaking point. To overcome the underestimation of the linear wave model, several combined (Stokes and cnoidal) wave models were proposed to compute wave shoaling. Stokes and cnoidal wave theories are used in the regions of small and large Ursell numbers. The main disadvantage of cnoidal wave models is the complexity in calculation. The governing equations are in the form of implicit equations, and they have to be solved by an iterative method. In the present study, a semi-empirical method is proposed to simplify the calculation. To account for wave nonlinearity, the linear wave model is modified by enhancing a correction factor in the energy flux equation. To avoid the iteration, the correction factor is proposed as a function of the deepwater Ursell number. A total of 757 cases from 6 sources of published experimental results are used to calibrate and examine the models. The experiments were performed in small-scale wave flumes under fixed plane beach conditions with a wide range of wave conditions. The accuracy of the modified model is compared with that of three existing wave models, i.e., the linear wave model and combined (1st-order Stokes and cnoidal) models of Svendsen and Brink-Kjaer (1972) and Isobe (1985). It was found that the present model and combined models yield significantly better accuracy than the linear wave model. Compared to the combined models, the present model is much simpler yet offers slightly better accuracy.