Soliton interaction as a possible model for extreme waves in shallow water

Abstract

Abstract. Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area of the waves. Shown is that extreme surface elevations up to four times exceeding the amplitude of the incoming waves typically cover a very small area but in the near-resonance case they may have considerable extension. An application of the proposed mechanism to fast ferries wash is discussed.

Variational modelling of extreme waves through oblique interaction of solitary waves: application to Mach reflection

“…When the incident wave interacts with a ship moving downwind, the effective ship length increases, leaving more time for the stem wave to develop to its maximum amplitude. Peterson et al (2003) also studied the formation of extreme waves in shallow water and explained under which conditions they are likely to occur and threaten ships. Kalogirou and Bokhove (2016) developed numerical models of waves impacting buoys and ships.…”

Variability in spatial patterns of long nonlinear waves from fast ferries in Tallinn Bay

“…The joint influence of the slope and the wall causes an interplay of the depth-induced changes of the entire wake system, bottom refraction and shoaling, and reflection from the wall. The typical result from such an interplay is a local increase of the wave heights and slopes of the water surface in areas where the incoming ship wakes interfere with the reflected waves (Miles, 1977;Peterson et al, 2003). This increase may override the refraction-induced decrease of the local wave height due to energy spreading along the bottom isolines.…”

Rogue waters

“…Only a small part of the simulated surface is shown. Reproduced with permission from [Peterson et al, 2003]. …”