深水重力波の相互作用に関する理論的ならびに実験的研究
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概要
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It is well known that most of the energy of sea waves, which causes a lot of damage to ships, off-shore structures and facilities on coasts, is supplied by winds blowing over the ocean. However, if a wind strong enough to generate gravity waves stops, the gravity waves, far from dying out rapidly, will continue to run straight on until they fetch up against something. Once waves have escaped from the wind that made them, they can run for days with very little loss of energy. Therefore, they travel long distance without the influence of winds. Moreover, these wave elements change their properties owing to the mutual interaction during this stage. Accordingly, to understand the nature of sea waves, besides studying the mechanism of wind-wave interaction, it is also imperative to clarify the characteristics of propagation of an individual wave train. In this paper, we deal with the nonlinear dynamics of the deep-water gravity waves and apply it to the experiment to interpret the results concerning the mutual interaction among waves. The contents of each Chapter are as follows. In Chapter 1, we review the basic theory of water waves and formulate the problems from the point of view of a singular perturbation method. In the following two Chapters, experimental and numerical studies concerning the particular condition of the resonant wave interactions are described. In Chapter 2 , long term evolution of tertiary resonant waves are detected experimentally and the direction of propagation of the resonant wave is also obtained for the first time by aid of the cross-spectral analysis. The purpose of the observations is twofold:to examine quantitatively the evolution of the amplitude modulation and to test the validity of weakly non-linear wave theory (Zakharov equation) for the asymptotic behavior of resonant waves by comparing the predicted and the observed properties of the waves. In Chapter 3 , the Zakharov's integro-differential equation is solved numerically and it is shown that the experimental data agree with the solutions in the case of comparatively small wave steepness. Calculations are also performed to determine the dependence of the maximum amplitude of the resonant wave upon the amplitude of primary waves. In Chapter4, comparisons of the experimental results with theories are made both for classical and that by Zakharov. It is concluded that the former is insufficient to explain quantitatively the long term evolution of the tertiary resonant wave and that the latter model of non-linear water waves is applicable for describing the propagation of sea waves because of fairly good agreement of the theory with data. Several theoretical remarks, including the analytical investigation into a particular solution of the discretized Zakharov equation, are offered in Appendices.
- 独立行政法人 海上技術安全研究所の論文
- 1989-09-30