Soliton interaction as a possible model for extreme waves in shallow water
1Institute of Cybernetics, Tallinn Technical University, Akadeemia tee 21, 12618 Tallinn, Estonia
2Marine Systems Institute, Tallinn Technical University, Akadeemia tee 21, 12618 Tallinn, Estonia
3Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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.