Propagation of oblique water waves by an asymmetric trench in the presence of surface tension

Abstract

An analysis is presented for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free surface. Reflection and transmission coefficients are evaluated applying appropriate multi-term Galerkin approximation technique in which the basis functions are chosen in terms of Gegenbauer polynomial of order 1/6 with suitable weights. The energy identity relation is derived by employing Green’s integral theorem in the fluid region of the problem. Reflection and transmission coefficients are represented graphically against wave numbers in many figures by varying several parameters. The correctness of the present method is confirmed by comparing the results available in the literature. The effect of surface tension on water wave scattering is studied by analyzing the reflection and transmission coefficients for a set of parameters. It can be observed that surface tension plays a qualitatively relevant role in the present study.