Two-dimensional periodic waves in shallow water

Experimental data are presented that demonstrate the existence of a family of gravitational water waves that propagate practically without change of form on the surface of shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional and fully periodic, i.e. they...

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Bibliographic Details
Published in:Journal of fluid mechanics 1989-12, Vol.209, p.567-589
Main Authors: Hammack, Joe, Scheffner, Norman, Segur, Harvey
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic waves
Marine
Physics
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Summary:Experimental data are presented that demonstrate the existence of a family of gravitational water waves that propagate practically without change of form on the surface of shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional and fully periodic, i.e. they are periodic in two spatial directions and in time. The amplitudes of these waves need not be small; their form persists even up to breaking. The waves are easy to generate experimentally, and they are observed to propagate in a stable manner, even when perturbed significantly. The measured waves are described with reasonable accuracy by a family of exact solutions of the Kadomtsev-Petviashvili equation (KP solutions of genus 2) over the entire parameter range of the experiments, including waves well outside the putative range of validity of the KP equation. These genus-2 solutions of the KP equation may be viewed as two-dimensional generalizations of cnoidal waves.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112089003228