Bragg scattering of long gravity waves by an array of floating elastic plates in the presence of a series of rectangular trenches is studied under the assumption of linearized water wave theory and small amplitude structural response. Bragg reflection occurs in the case of an array of multiple floating flexible plates and trenches in isolation or combination, and the number of sub-harmonic peaks between two consecutive peaks is two less than the number of plates/trenches. In the case of long-wave scattering by an array of trenches in the absence of floating plates, wave reflection becomes zero minimum for a certain fixed wavenumber at the end of the first cycle (as referred to 0 < k1h1 < 0.32), irrespective of the even/odd number of trenches. Furthermore, the Bragg resonant reflection pattern of the second cycle is a mirror image of the reflection occurring in the first cycle. Conversely, the symmetric pattern of Bragg reflection exhibited in the case of an array of trenches does not occur for an array of plates in isolation or for plates and trenches in combination. Between consecutive harmonic peaks, the minima/maxima in the wave reflection occur in the case of the even/odd number of trenches/plates in isolation. In contrast, it occurs within the first cycle in the case of trenches and plates in combination. Between consecutive harmonic peaks, maxima/minima of wave reflection coincide for a certain wavenumber, irrespective of the even/odd number of trenches/plates in isolation. In addition, these maxima attained for a certain wavenumber for the even number of trenches/plates are 180° out of phase to that of minima for an odd number of trenches/plates. However, similar phenomena occur within the first cycle of Bragg resonance in the case of trenches and plates in combination. Moreover, the amplitude of oscillation in the wave reflection increases with an increase in plate rigidity. Time-dependent motion due to Bragg scattering by trenches and plates is demonstrated in different cases.

Flexural-gravity wave propagation under the action of a compressive force and in the presence of flow vorticity is studied under the framework of linear water wave theory. The occurrences of wave blocking which is analogous to the free surface gravity wave propagation against an opposing current as well as light wave propagation in curved space-time near a black hole are shown to exist. Moreover, negative energy waves that are responsible for making the total energy of the fluid flow less than that without the waves are also analyzed. The effects of compressive force, Froude number, and vorticity on the existence of negative energy waves as well as the occurrence of flexural-gravity wave blocking are graphically illustrated. The variation in group velocity for different flow parameters such as the vorticity, the Froude number, and the compressive force is analyzed. Time-dependent simulations of the propagation of wave packets are calculated.

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The interaction between oblique water waves and floating bridge in the presence of a vertical partial flexible permeable barrier is studied under the assumption of the linear water wave theory in finite water depth. The associated mathematical problem is handled for a solution using the least-square approximation method. The reflection and transmission coefficients, free surface elevation, wave force acting on the bridge and barrier are computed to study the effects of various wave and structural parameters for three different edge conditions. The study reveals that wave reflection decreases with an increase in porosity, and a reverse pattern is found in the case of wave transmission. As the normalized spacing between the barrier and the floating bridge increases, the reflection coefficient follows a periodically oscillatory pattern. Furthermore, it is noticed that regardless of the barrier configurations, the wave reflection increases for an increase in the angle of incidence. It is also found that the surface-piercing barrier is more efficient than the bottom-standing barrier as a wave barrier. Moreover, the results indicate that by placing a porous flexible barrier at an appropriate position, the wave force on the bridge can be reduced significantly.

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