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Analytical Solution For Predicting None Breaking Wave Run-Up Over Multi Slope Coastal Zone

The run-up of long water waves traveling at high speed across the oceans is one of the most important factors in the design of a coastal structure. As a result, a number of empirical formulas, analytical results, and numerical techniques have been developed to predict the wave runup elevation. The utility of these formulas and schemes depends on their ability to predict the wave runup and their convenience of use. However, in the empirical formulas, the coefficients can not provide insight into the nature of the physical processes involved. But analytical asymptotic formulas, indeed could provide considerable insight into the process because, the parameter dependence is explicit in the coefficients. The first objective of this study is to generalize the wave runup formulas for both periodic and solitary waves on composite (multi-slope) beaches using the linear shallow water wave equations. This task will be accomplished by expanding the existing solution of simple slope beaches for periodic and solitary waves. The second objective is to solve the linear shallow water equations numerically using finite difference method to check the validity of the derived formulas. A number of figures are presented showing a comparison between the analytical and numerical results.