In the present work, the scattering of water waves by undulating bottom in a two-layer fluid system is investigated by the inclusion of current, surface tension and interfacial tension to better understand the phenomenon of wave blocking. The perturbation technique followed by the Fourier transform method is applied to solve the coupled boundary value problem. The associated velocity potentials, Bragg reflection coefficients, and Bragg transmission coefficients are obtained in integral forms. A particular case of the undulating bottom, namely sinusoidal bottom undulation, has been taken into consideration for showing the effects of current speed and surface tension. A shift in the Bragg resonant frequency is observed with a change in the current speed. Further, the combined effects of Bragg resonance and wave blocking are investigated. For some values of opposing current, the group velocity vanishes at two distinct points in the frequency space; the maxima is known as the primary blocking point and the minima is called as the secondary blocking point. For each frequency, there exist three propagating modes between these two blocking points. Certain abnormalities and a sharp increase in the Bragg reflection and transmission coefficients are caused by the superposition of various propagating wave modes and triad interaction within the blocking points as well as a change in the incident wave mode.
Mathematics Subject Classification: 76B15, 42A38, 35Q35.