| Summary: | 碩士 === 國立中山大學 === 海洋環境及工程學系 === 87 === By linearizing the problem of the surface-waves propagating on a gentle sloping beach in two dimension, this paper has developed by a suitable perturbation expansion in the bottom slope to any order and the analytical solution has been derived to third order . Furthermore, the Eulerian form is transformed to the Lagrangian form by making use of a transform function to describe the solution.
The Lagrangian form can be computerized by the numerical quadrate procedure with a personal computer program of continence. This program can easily calculate the result for the diverse surface-waves propagating on the any gentle sloping beach. When the momentary serial data of the undulate waves was calculated, it could combine into the dynamic three-dimension graph of full-time evolution by the skills of the multimedia.
Finally, performs a practical experiment to inspect the theoretical and numerical result and researches the agreements between the reality and the solution.
Comparing the experimental data with the solutions for the different wave steepness of the deep water on the three kinds sloping beach (1/5,1/10,1/20), the wave height proportion value is between 0.892 to 1.177,the wavelength proportion value between 0.953 to 1.163 and the wave steepness proportion value between 0.901 to 1.087. Over 95% the experiment data and solutions, the errors between them are less than 10%. Hereinbefore, These evidences can prove out the theoretical solution and numerical result, which can suffice the reality.
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