Reflection of Waves over Various Shear Currents and Trenches

Abstract

The reflection coefficients of monochromatic water waves over various shear currents and trenches were estimated analytically. The diffraction of waves by abrupt depth changes and shear currents was formulated by the eigenfunction expansion method. The regions where shear currents and the bottom topography varied were represented by a finite number of tiny steps. The propagating and evanescent modes were considered to investigate the role of evanescent modes. The proper numbers of steps and evanescent modes needed for a trench and constant water depth topography were proposed by a series of convergence tests. Four typical types of shear currents, rectangular, triangular, sinusoidal and exponential shapes, which have the maximum velocity at the center of the shear currents, were used in this study, and investigating domains were limited from shallow water to intermediate water regions. Reflection coefficients with and without shear currents at the same topography were visualized to show the significance of shear currents. The characteristics of reflection coefficients for various shear currents conditions were examined. The symmetric and asymmetric trenches with shear currents were also examined and the optimal slope of symmetric trench was found and the role of the order of the transition slopes was checked. The accuracy of the predicted reflection coefficients was checked by estimating the wave energy.