Linear wave reflection by trench with various shapes

Abstract

Two types of analytical solutions for waves propagating over an; symmetric trench are derived. One is a long-wave solution and the other is a mild-slope solution, wh ch is applicable to deeper water. The water depth inside the trench varies in proportion to a power)f the distance from the center of the trench (which is the deepest water depth point and the origin o 'x-coordinate in this study). The mildslope equation is transformed into a second-order ordinar. differential equation with variable coefficients based on the longwave assumption [Hunt's, 197!,. Direct solution of wave dispersion equation. journal of Waterway, Port, Coast. and Ocean Engin !ering 105, 457-4591 as approximate solution for wave dispersion. The analytical solutions are the i obtained by using the power series technique. The analytical solutions are compared with the nurr 2rical solution of the hyperbolic mildslope equations. After obtaining the analytical solutions und !r various conditions, the results are analyzed.