Wave packet focusing in shallow water

In coastal engineering, as shoaling waves break in shallow water, most wave-breaking research has been focused on depth-induced wave breaking. However, violent wave breaking under storm conditions may be caused by superposition of many shoaling wave components. In order for simulating extreme waves in open ocean, theories to focus wave-packets, assuming that wave speed of each wave component is unchanged during propagation (i.e. deep water or shallower water without bathymetry changes), have been derived, while shoaling effects of the focusing process in shallower waters have not been considered in the previous studies. The extension to shoaling coastal wave-packets may aid in simulating extreme coastal wave breaking under violent storm conditions via laboratory experiments. Here, we derive the general wave-packet focusing conditions for arbitrary water depth. The proposed conditions were used to simulate shoaling wave-packet focusing on flat and sloped bottoms in shallow water experiments for validation purposes. The effects of depth-induced wave breaking in the focusing wave groups are discussed in this paper. The current focusing technique can fully control the focus location and time in wave experiments with an arbitrary bottom structure, which may be useful for further extreme wave research in coastal engineering.