A Study Of Analytical Solutions To The Interactions Between Water Waves And Submerged Barriers

Oceans bring people both great fortunes and disasters. So when human beings make efforts to develop marine environments to benefit themselves, they must be prepared for the precaution of their negative effects. In designing of marine and offshore constructions, the research on interactions between water waves and barriers is the most important and contributes to the safety and economy of engineering structures.In offshore engineering, most problems refer to the interactions between waves and barriers. Among them, the studies of wave scattering and force characteristics of breakwaters are fundamental subjects.At the present, there are three methods with the calculation of transmission and reflection coefficients. The first is the analytical method. Since the breakwater geometry and boundary conditions have a great effect on the complexity of problem solution, only those geometries that are regular have explicit solutions. The second is the numerical computation method, which, with the help of computers, the Laplace equation is numerically simulated under certain boundary conditions. This method is suitable for arbitrary cross-section shape of breakwaters. The third is the synthesis method, which is the combination of the above two. As for the analytical solution, eigenfunction development and integral equation methods are used. This paper tries the two methods for analyzing and solving the wave scattering problems by vertical thin and rectangle barriers. As for the cases of submerged vertical thin barriers under infinite and finite depths, this paper investigated the scattering problems via Havelock Development and Integration Equation method, obtained both transmission and reflection coefficients and made comparisons with experiments and numerical computations; as for the case of submerged rectangular thick breakwaters, it used eigenfunction development method to deal with the scattering problems, and got the representations of transmission and reflection coefficients and wave-force coefficients. Then, approximations under plane wave and long wave conditions are made. Especially, detailed investigations and comparisons with experiments and numerical computations are made under plane-wave approximations, and in turn, similar results to the full solutions are obtained by very simple computations.