Wave interaction with a pair of thick barriers over a pair of trenches

ABSTRACT

This study develops analytical solutions to oblique water wave interaction with a pair of thick barriers over a pair of trenches. The potential functions are reduced to linear integral equations employing the eigenfunction expansions along with the Havelock inversion formula followed by a matching process. The solutions are found after solving the integral equations utilise the multi-term Galerkin method involving the Gegenbauer polynomials of order 1/6 with suitable weights as basis functions. The comparison of the numerical solution with the results available in the literature shows a good agreement that implies the present result's correctness. The energy balance relation is derived and used to check the accuracy of numerical results. The effects of various parameters are analysed through different graphs for a pair of thick barriers over a pair of trenches. It is observed that the physical parameters of the structure have a significant effect on the present study.

KEYWORDS:

• Water wave interaction
• reflection and transmission coefficients
• thick barriers
• asymmetric trenches
• Gegenbauer polynomial of order 1/6
• galerkin approximation

Disclosure statement

No potential conflict of interest was reported by the authors.