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We derived analytical solutions for long waves on a circular island with combined topographies. The inner region is a circular island on a flat bottom and the outer region is a cylindrical island on a shoal. The solution for the circular island on a flat bottom was developed previously by Jung et al. (2010) [13]. The solution for the cylindrical island on a shoal was developed in the present study...
In this paper, several recursive formulae for calculating arbitrary order derivatives of the bottom curvature term and the slope-square term in the modified mild-slope equation (MMSE) are derived and an analytic model based on Taylor series to solve the MMSE for linear waves propagating over one-dimensional piecewise smooth topographies is proposed. By using this analytic model, wave reflections by...
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