Scattering and trapping of the higher order free long waves over a submerged step are investigated. As incident waves, two wave components with slightly different frequencies and obliquely incident angles to the step are considered. The forced waves and the free long waves are obtained up to the second order of the perturbation method. Applicability of these solutions are investigated. It is found that depending on the wave and the step conditions, the free long waves of the progressive mode can not exist in the deeper region but can exist in the shallower region.
When the short waves propagate over an uneven bottom, nonlinear effects generate higher order harmonics of free waves, which are radiated from the region of abrupt change of the depth. Massel(1983) analyzed these nonlinear effects on a submerged step using a perturbation method and showed the mechanism of generation of the higher order free waves on the second order expansion. Agnon and Mei(1988) studied a similar problem where groups of short waves are incident on a shelf and showed that free long waves are generated and trapped on the shelf. Massel's analysis is restricted on two-dimensional problem with one component of incident waves. Agnon and Mei extended to threedimensional problem with groups of short waves as the incident waves. But they ignored the contributions from evanescent modes of the linear waves to the forcing function for the long waves in their multiple- scale method. The basic mechanism of generation of the higher order free waves is that the forced waves have discontinuity across the abrupt change of the depth and the higher order free waves are generated to compensate this discontinuity.
