Step Approximation for Water Wave Scattering by Multiple Thin Barriers over Undulated Bottoms

Abstract

This paper investigates the scattering of oblique water waves by multiple thin barriers over undulation bottoms using the eigenfunction matching method (EMM). In the solution procedures of the EMM, the bottom topographies are sliced into shelves separated by steps. On each step, surface-piercing or/and bottom-standing barriers can be presented or not. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Then applying the conservations of mass and momentum, a system of linear equations is resulted and can be solved by a sparse-matrix solver. If no barriers are presented on the steps, the proposed EMM formulation degenerates to the water wave scattering over undulating bottoms. The effects on the barrier lengths, barrier positions and oblique wave incidences by different undulated bottoms are studied. In addition, the EMM is also applied to solve the Bragg reflections of normal and oblique water waves by periodic barrier over sinusoidal bottoms. The accuracy of the solution is demonstrated by comparing it with the results in the literature.

Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

“…The detailed coefficients of reflection and transmission, K R e iθ R and K T e iθ T , are later determined by applying Equations ( 31) and (32). It must be noted that the proposed EMM formulation degenerates into the formulation to deal with the problem of water wave interactions with impermeable barriers [25] over uneven bottoms during G = 0. In addition, it degenerates into the formulation of water wave scattering by breakwaters [13,20,42] if the L b is null.…”

“…Losada et al [2] and Abul-Azm [5] employed methods of matched eigenfunction expansion to investigate analytical solutions for the diffractions of oblique waves with different configurations of thin vertical barriers. The matched eigenfunction expansion method was used to study the context of wave interactions with vertical slotted barriers [23,24] and impermeable barriers [25].…”

Algebraic Method for Approximate Solution of Scattering of Surface Waves by Thin Vertical Barrier Over a Stepped Bottom Topography

“…For each shelf, the Bragg reflection of oblique waves was analyzed using the eigenfunction matching method based on small amplitude wave theory. Tran et al [9] investigated the scattering of oblique water waves by multiple thin barriers over undulated bottom using matched eigenfunction expansion method after slicing the bottom topography into shelves separated by steps. Borah and Hassan [10] studied the problem of diffraction of water waves by partially submerged floating hollow cylinder placed over a fixed coaxial bottom-mounted obstacle and solved it with the help of matched eigenfunction expansion to obtain analytical expressions of potentials.…”