Bragg scattering of long waves by an array of trenches

In the present study, the occurrence of Bragg resonance has been demonstrated due to scattering of long gravity waves by an array of submerged trenches in the presence of the sloping sea bed. The closed-form long wave analytical solutions are derived using the solutions of Bessel equations and validated with numerical results obtained via the boundary element method (BEM). Known results in case of submerged breakwaters in water of uniform depth are reproduced as special cases, while both analytic and numerical results are compared for accuracy. Role of various physical parameters such as trench configurations, depth, width, sloping angle and distance between the adjacent trenches are investigated by analyzing the reflection coefficient. Optimal collocation curves for different trench configurations reveal that maximal peak Bragg reflection varies approximately linearly with a change in water depth in case of a pair of trenches and follows certain non-linear pattern in the case of multiple trenches. The study reveals that Bragg reflection is larger due to a change in seabed slope between the trenches than that of trenches having uniform/sloping seabed.