Soliton interaction as a possible model for extreme waves in shallow water P. Peterson1, T. Soomere2, J. Engelbrecht1, and E. van Groesen3 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.
Citation: Peterson, P., Soomere, T., Engelbrecht, J., and van Groesen, E.: Soliton interaction as a possible model for extreme waves in shallow water, Nonlin. Processes Geophys., 10, 503-510, doi:10.5194/npg-10-503-2003, 2003.