Evolution of Wave Groups in Shallow Water and Wave Group Properties of Random Waves

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Abstract
This paper firstly examines the evolution of wave groups of finite length having a single carrier frequency in finite constant water depth, by both hydraulic experiments and numerical simulations. In the numerical simulations, the nonlinear Schrödinger equation is employed. Based on the results of the experiments and the numerical simulations, and in the light of the knowledge on properties of weakly nonlinear waves, we discuss the spatial change of wave grouping of random waves in a wave flume and the wave group property of long-travelled swells observed at Caldera Port, Costa Rica, in Central America. Main results are as follows: (1) It was confirmed that if the nondimensional water depth kh (k: the wavenumber of the carrier wave, h: the water depth) is larger than 1.36, an arbitrary wave group evolves into several solitons, whereas if kh2.0 (k1/3: the wavenumber of the significant wave), in which a systematic change of wave energy spectrum can be seen. Where k1/3h<1.0, wave groups in random waves become flattened with the propagating distance. (3) The wave group property of swells can be explained from a viewpoint of evolution process of wave groups, such as the formation of envelope solitons in deep water and the flattening of the solitons during propagation in shallow water region.

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