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Title: Stable three-dimensional biperiodic waves in shallow water
Authors: Scheffner, Norman W.
Keywords: Kadomstsev-Petviashvill equation
Water waves
Publisher: Coastal Engineering Research Center (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Miscellaneous paper (U.S. Army Engineer Waterways Experiment Station) ; CERC-88-4.
Description: Miscellaneous paper
Abstract: 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.
Rights: Approved for public release; distribution is unlimited.
Appears in Collections:Miscellaneous Paper

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