Semianalytical One-Dimensional Solution for Linear Wave Reflection over Varying Topography

Abstract

A new technique of predicting a one-dimensional wave transformation due to bottom variation was developed by using analytical and numerical approaches. The coefficients of the governing equation, the mild slope equation, were approximated as polynomial forms using the least squares method. The power series technique was applied to solve the second-order ordinary differential equation originally converted from the mild slope equation. Because the approximation was carried out after setting the coefficient of the highest-order term of the equation to unity, there was no singular point. This solution became, consequently, applicable to arbitrarily varying topography. Comparison of results from this study with the numerical solutions calculated by the finite element method showed good agreement for various cases.