| Summary: | 碩士 === 國立中山大學 === 海洋環境及工程學系研究所 === 88 === The main purpose of this paper is to analyze the surface progressive gravity waves propagating on a gentle sloping beach in two dimension. Instead of using the method of Eulerian system by the previous investigators, we introduce the governing equations completely in the Lagrangian system directly. All the characteristics of the wave system is expressed by a suitable perturbation expansion in the bottom slope under linearizing the problem in wave amplitude, then all the governing equations are systematically expanded to order. The solution of the wave system is to be solved to second order , even to high order could also be obtained. Based on the obtained results, the velocity potential, pressure and motion of the fluid particle in the wave system in time and space is therefore presented, and we can see that the bottom slope is a main factor to screw the wave field to deform to break. Finally, the experimental result is cited to compare and verify.
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