Linear Wave Reflection by Trench with Various Shapes

Abstract

Two types of analytical solutions for waves propagating over an asymmetric trench are derived. One is a shallow water wave model and the other is an extended model applicable to deeper water. The water depth inside the trench varies in proportion to a power of distance from the center of the trench (where the center means the deepest water depth point and the origin of -coordinate in this study). The mild-slope equation is transformed into a second order ordinary differential equation with variable coefficients based on the longwave assumption or Hunts (1979) approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed.