Wave Resonance and Dissipation in Collections of Partially Reflecting Vertical Cylinders

Abstract

Plane waves scattered by a coastal feature exhibit resonance with partially standing waves forming on the windward side and wave dissipation on the leeward side. In this research, the complicated interactions of waves occurring in collections of partially reflecting vertical cylinders were studied using a novel adaptation of the analytic element method. This method organizes the separation-of-variables solution of Hankel and trigonometric functions on an element basis to separate each cylinder’s unknown coefficients from all others. A partially reflective boundary condition is adapted for each element using least squares, and its system of equations is formulated as matrix multiplications of Fourier series terms. A comprehensive solution is then obtained by iteration across all elements. The residual errors achieved demonstrate that the Robin boundary conditions are satisfied with nearly exact precision. Results illustrate the resonance and dissipation occurring within collections of regularly and randomly placed natural and engineered coastal features. This work contributes toward predicting the formation of regions with heavy seas and tranquil zones formed across variations in the wavelength, size of elements, and reflection coefficient, with related applications in acoustics, electromagnetism, and optics.