BEM solution for scattering of water waves by dual thick rigid structures over non-periodic bottom morphologies

Abstract

The combined effect of dual rigid structures over non-periodic bottom morphologies is examined through a boundary value problem to characterize the scattering phenomenon. Three different types of bottom morphologies: (a) monotonically decreasing oscillatory, (b) exponential decreasing oscillatory and (c) Gaussian oscillatory are taken into consideration. Utilizing the boundary element method (BEM), the boundary value problem coins to a system of algebraic equations that can be solved numerically to determine the physical quantities such as reflection and transmission coefficients. The reflection coefficient is compared to the results available in the literature, and a good agreement is found, indicating the validity of the current approach. Reflection is seen to increase with the decay factor, number of ripples, and width of the structures. Interestingly, a split in the Bragg peak is noted which increases with increasing gap and number of ripples but decreases with increasing in decay factor and submergence depth of both structures. Zeros in reflection are vanished due to the presence of both structures. It is found that Bragg resonance is observed for all three bottom profiles Comparison analysis between monotonically decreasing profile, Gaussian profile and exponentially decreasing profile is made which portrays that the Bragg peak is highest for monotonically decreasing oscillatory profile. This model is an attempt to create a tranquil zone utilizing breakwaters.