We demonstrate experimentally the existence of a family of gravity-induced finite-amplitude water waves that propagate practically without change of form in shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional, and periodic. The basic template of a wave is hexagonal, but it need not be symmetric about the direction of propagation, as required in our previous studies (e.g. Hammack et al. 1989). Like the symmetric waves in earlier studies, the asymmetric waves studied here are easy to generate, they seem to be stable to perturbations, and their amplitudes need not be small. The Kadomtsev-Petviashvili (KP) equationis known to describe approximately the evolution of waves in shallow water, and an eight-parameter family of exact solutions of this equation oughtto describe almost all spatially periodic waves of permanent form. We present an algorithm to obtain the eight parameters from wave-gauge measurements. The resulting KP solutions are observed to describe the measured waves with reasonable accuracy, even outside the putative range of validity ofthe KP model.
Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves
Zweidimensionale periodische Wellen in flachem Wasser - Teil 2: asymmetrische Wellen
Journal of Fluid Mechanics ; 285 ; 95-122
1995
28 Seiten, 14 Bilder, 2 Tabellen, 17 Quellen
(2 Anhänge)
Article (Journal)
English
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