Application of Mathieu Functions to Solve Wave Field Changes by Elliptic Bathymetric Forms with Gradual Depth Transitions

This paper presents and demonstrates a method to determine wave field modifications resulting from elliptic bathymetric anomalies (pit or shoal) with gradual transitions in depth. The analytic (semi-numerical) method is valid for linear waves in a uniform depth domain with an arbitrary number of concentric elliptic forms of different, but uniform, depths combined to represent either a pit or a shoal. Sections present the theory, formulation, and results in the form of contour plots of the relative amplitude in the presence of the depth anomaly. The elliptic forms in the model induce wave transformation through processes of wave refraction, wave diffraction, and wave reflection with asymmetry in the solution for oblique incident wave angles. The results investigate the effect of the incident wave angle on the resulting wave field.