A Numerical Model of Wave Propagation on Mild Slopes

Propagation of waves from Deep Ocean to a shoreline has been numerically modeled. Model equations govern combined effects of shoaling, refraction, diffraction and breaking. Linear, harmonic, and irrotational waves are considered, and the effects of currents and reflection on the wave propagation are assumed to be negligible. To describe the wave motion, mild slope equation has been decomposed into three equations that are solved in terms of wave height, wave approach angle and wave phase function. It is assumed that energy propagates along the wave crests, however, the wave phase function changes to handle any horizontal variation in the wave height. Model does not have the limitation that one coordinate should follow the dominant wave direction. Different wave approach angles can be investigated on the same computational grid. Finite difference approximations have been applied in the solution of governing equations. Model predictions are compared with the results of semicircular shoal tests performed by WHALIN (1971) and with the measurements of elliptic shoal experiment conducted by BERKOFF et al. (1982). Utility of the model to real coastal areas is shown by application to Obakoy on the Mediterranean Sea of Turkey.