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An Analytical Solution To The Modified Mild-Slope Equation For Waves Propagating Around A Circular Conical Island, Sung-Shan Hsiao, Chun-Ming Chang, Chih-Chung Wen

Journal of Marine Science and Technology

There are many analytical solutions to the mild-slope equation that employ Hunt’s direct solution of linear dispersion [7] to solve wave-scattering problems involving varying quiescent depths. The advantage of Hunt’s direct solution of linear dispersion is that it can extend the range of applicability of the mild-slope equation from long-wave to deep-wave conditions. However, because the bottom curvature and slope-squared terms are neglected, the mild-slope equation cannot preserve mass conservation. In this investigation, we derived an analytic solution of the modified mild-slope equation for a conical island by adopting Hunt’s direct solution of linear dispersion to be applicable to intermediate …