The Influence of Surface Tension on Oblique Wave Scattering by a Rectangular Trench

The diffraction of obliquely incident wave by a symmetric rectangular submarine trench with the effect of surface tension at the free surface is investigated using two dimensional linearized potential theory. The reflection and transmission coefficients are computed numerically using appropriate multiterm Galerkin approximations involving ultraspherical Gegenbauer polynomials. These coefficients are represented graphically against the wave number in a number of figures. The theoretical observations are validated computationally. The derived result will coincide analytically and graphically with the results already present in the literature neglecting the effect of surface tension, which confirms the correctness of the result presented here. We observed the zero reflection phenomenon in the graphical representation. It is also noted that the values of reflection coefficient decreases as the surface tension increases. We conclude that realistic changes in surface tension on the free surface have a significant effect on the present study.

Keywords:

Galerkin approximation , Water wave scattering , Surface tension , Submarine trench , Reflection and transmission coefficients