The Kadomtsev-Petviashvili (KP) equation is tested as a model for these biperiodic waves. This equation is the direct three-dimensional generalization of the famous KortewegdeVries (KdV) equation for weakly nonlinear waves in two dimensions. It is known that the KP equation admits an infinite dimensional family of periodic solutions which are defined in terms of Riemann theta functions of genus N. Genus 2 solutions have two real periods and are similar in structure to the hexagonally shaped waves observed in the experiments. A methodology is developed which relates the free parameters of the genus 2 solution to the temporal and spatial data of the experimentally generated waves. Comparisons of exact genus 2 solutions with measured data show excellent agreement over the entire range of experiments. Even though near-breaking waves and highly three-dimensional wave forms are encountered, the total rms error between experiment and KP theory never exceeds 20 percent, although known sources of error are introduced. Hence, the KP equation appears to be a very robust model of nonlinear three-dimensional waves propagating in shallow water, reminiscent of the KdV equation in two dimensions.


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    Titel :

    Stable Three-Dimensional Biperiodic Waves in Shallow Water


    Beteiligte:

    Erschienen in:

    Erscheinungsdatum :

    1988


    Format / Umfang :

    12831658


    Medientyp :

    Report


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



    Klassifikation :


    PERIODIC, BIPERIODIC AND CHAOTIC DYNAMICAL BEHAVIOUR OF RAILWAY VEHICLES

    Kaas-Petersen, Christian / True, Hans | Taylor & Francis Verlag | 1986


    Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves

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    Ship waves in shallow water

    Jiang,T. / Univ.Hamburg,DE / Univ.Duisburg,DE | Kraftfahrwesen | 2001


    Abnormal shallow water wind waves

    Hendy, N.R. / Corlett, E.C.B. | Tema Archiv | 1984


    Energy Losses of Waves in Shallow Water

    Grosskopf, William G. / Vincent, Charles Linwood | HENRY – Bundesanstalt für Wasserbau (BAW) | 1982

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