Bragg resonance due to an undulated elastic bottom in the presence of current

Abstract

This paper explores Bragg scattering in a homogeneous fluid, focusing on the interaction between oblique waves and an undulated elastic bottom in the presence of a uniform current. It uses linear wave theory to analyze the effects of a uniform current and flexible floor on wave interaction, where the fluid propagates in two modes: free-surface and flexural mode. The study uses analytical derivation and numerical exploration of Bragg resonance conditions for various physical parameters, including perturbation and Fourier transform methods. The study computes Bragg transmission and reflection for various physical parameters and verifies the energy relations, assuring the accuracy of the results. The findings reveal that when waves propagate due to the free-surface mode, reflection coefficients decrease with increasing current speed. When waves propagate through the flexural mode, the reflection coefficients decrease as the flexural rigidity increases, while the transmission coefficients increase as the current speed increases.