Journal of Ocean Engineering and Science

Volume 6, Issue 2

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

Anjan Sasmal, Soumen De^∗

Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India

Received 30 April 2020; received in revised form 15 September 2020; accepted 19 November 2020

Available online 28 November 2020

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.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Keywords: Water wave scattering; Surface tension; Asymmetric trench; Gegenbauer polynomial of order 1/6; Galerkin approximation; Reflection and transmission coefficients.