Scattering of Water Waves by a Circular Trench

Abstract

Under the assumption of linear theory, the two-dimensional problem of scattering of surface waves by a circular trench is investigated here. A judicious application of Green’s integral theorem together with the boundary element method reduced the corresponding boundary value problem to a system of linear algebraic equations. Solving the system of linear equations, the physical quantities like reflection and transmission coefficients are evaluated and depicted graphically against the wavenumber for various values of the parameters. It observed that in the absence of the trench, the transmission coefficient is nearly about one and the reflection coefficients are near about zero. However, in the presence of the trench, the reflection and the transmission coefficients exhibit oscillatory behaviour. For certain values of the wavenumber, it is observed that there is no reflection of waves. Also, the semi-circular trench with larger radius enhances the reflection and reduce the transmission of wave energy.