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In this paper, water waves interaction with two thin vertical barriers over shelf bottom topography is analysed using linearised wave theory. The associated mixed boundary value problem is solved with the aid of method involving eigenfunction expansions of the velocity potential and orthogonality relation of the eigenfunctions. Further, the resulting system of algebraic equations is solved using the least square method to find the physical quantities, that is, reflection and transmission coefficients, free surface elevation and non-dimensional horizontal force experienced by the barriers. The energy balance relation is derived from Green's identity which ensures the correctness of the present results. The obtained results are also compared with the results available in the literature for validation purpose. With the help of different plots, the effect of depth ratios, length of the barriers, angle of incidence and gap between the barriers is investigated for various values of physical parameters. The study reveals that the phenomena of zero reflection, that is, full transmission can be avoided by using non-identical barriers or asymmetric shelf bottom topography. Also, it is highlighted that the presence of two barriers instead of a single barrier over shelf topography will help to reduce the transmitted wave energy near the seashore. A generalisation of number of surface piercing barriers over the shelf bottom topography is also demonstrated.

Scattering of water waves by two thin vertical barriers over shelf bottom topography