Bragg resonance in a two-layer fluid with the inclusion of current and tension at both surface and interface

Abstract

In this study, the scattering of water waves by an undulating bottom in a two-layer fluid with current, surface tension, and interfacial tension is investigated. The perturbation technique followed by the Fourier transform technique are applied to solve the coupled boundary value problem. A Bragg resonance arises between the surface waves and the bottom ripples, which is associated with the reflection of incident wave energy. Hence, the Bragg coefficients namely, Bragg reflection and transmission coefficients, and associated velocity potentials are analysed which are obtained in integral forms. In order to clearly understand the efficacy of the present study, a certain type of undulating bottom, known as sinusoidal bottom undulation, has been examined. It has been shown that when the combined effects of surface tension, interfacial tension, and current are taken into account, the wave reflection is minimal. Moreover, a shift in the Bragg resonant frequency is seen with a change in current speed. In addition, interfacial tension influences both surface and interfacial waves, whereas surface tension primarily impacts surface waves. The results obtained here are expected to be qualitatively helpful in tackling problems of flexural gravity waves in two-layer fluid in the presence of current.