Rogue waves in shallow water

Abstract

Most of the processes resulting in the formation of unexpectedly high surface waves in deep water (such as dispersive and geometrical focusing, interactions with currents and internal waves, reflection from caustic areas, etc.) are active also in shallow areas. Only the mechanism of modulational instability is not active in finite depth conditions. Instead, wave amplification along certain coastal profiles and the drastic dependence of the run-up height on the incident wave shape may substantially contribute to the formation of rogue waves in the nearshore. A unique source of long-living rogue waves (that has no analogues in the deep ocean) is the nonlinear interaction of obliquely propagating solitary shallow-water waves and an equivalent mechanism of Mach reflection of waves from the coast. The characteristic features of these processes are (i) extreme amplification of the steepness of the wave fronts, (ii) change in the orientation of the largest wave crests compared with that of the counterparts and (iii) rapid displacement of the location of the extreme wave humps along the crests of the interacting waves. The presence of coasts raises a number of related questions such as the possibility of conversion of rogue waves into sneaker waves with extremely high run-up. Also, the reaction of bottom sediments and the entire coastal zone to the rogue waves may be drastic.