Bragg scattering of long flexural gravity waves by an array of submerged trenches and the analysis of blocking dynamics

Abstract

Bragg scattering of long flexural gravity waves due to an array of submerged trenches is studied under the shallow water approximation and small amplitude structural response in the presence of lateral compressive force. The group velocity vanishes at two different points in the frequency space for specific values of the compressive force, which are referred to as primary and secondary blocking points. Between these two blocking points, three propagating modes exist for each frequency, of which two are associated with the positive group velocity and one with the negative group velocity. Of the three propagating wave modes, the contribution to the energy relation by the lowest wavenumber is predominant near the secondary blocking frequency. In contrast, the higher wavenumber is dominant in the proximity of the primary blocking frequency. The study reveals the occurrence of Bragg scattering of flexural gravity waves in the presence of compressive force for more than two submerged trenches, which is analogous to that of surface gravity waves. However, within the blocking limits of the compressive force, the superposition of multiple propagating wave modes and the change in the incident wave mode contribute to certain irregularities and an increase in wave amplitude in the Bragg reflection pattern. The response amplitude of the structure and the pulse rate increase with an increase in the number of trenches.