Scattering of surface gravity waves over a pair of trenches

Abstract A numerical model based on boundary element method is developed to study the scattering of surface gravity waves over a pair of trenches of varied configurations under the assumption of small amplitude water wave theory. Both the cases of symmetric and asymmetric trenches are considered in the present study. The accuracy of the numerical results is validated by comparing the reflection and transmission coefficients with energy identity, and the known results associated with single trench available in the literature. The study reveals that wave reflection decreases in an oscillatory manner with an increase in trench width. Moreover, Bragg resonance in wave reflection is observed for wave number corresponding to waves in shallow and intermediate depths in the case of a pair of trenches. Further, Bragg reflection increases with an increase in the number of trenches. In the case of multiple trenches, subharmonic peaks in Bragg reflection are depicted and the number of subharmonic peaks between two harmonic peaks is found to be two less than the number of trenches. However, for triangular trenches, the occurrence of the subharmonic peak is invariant of the number of trenches and the same vanishes for larger trench depth. Irrespective of trench configurations, wave reflection follows certain uniform oscillatory pattern with an increase in the gap between the trenches in case of deep water.