Oblique wave interaction by two thin vertical barriers over an asymmetric trench

Abstract

A breakwater model is developed to analyse the wave propagation over an asymmetric rectangular trench in presence of two thin vertical partially immersed barriers. With the help of eigenfunction expansion, the problem is reduced to four weakly singular integral equations involving horizontal component of velocity across the gaps below the two barriers and above the two corners of the trench. The integral equations are solved by employing Galerkin technique involving expansion in terms of Chebyshev polynomials for the two unknown velocities across the gaps below the barrier multiplied by an weight function having square root singularity at an end and Gegenbauer polynomials for the other two unknown velocities above the two corners of the trench multiplied by an weight function having one‐third singularity at an end. Numerical results for the reflection and transmission coefficients are presented graphically against wavenumber for different configurations of the barriers and trench. The accuracy of the numerical results is validated by comparing the reflection coefficients and the known results associated with barriers and trench available in the literature.