This paper describes the mathematical formulation and application of a linear refraction-diffraction model for steep bathymetry. The model involves two coupled governing equations derived from Green's second identity. It reduces to the extended and original mild-slope models, when the seabed slope is small. The capability of the present model to simulate flow velocity and wave amplitude over steep island bathymetry is examined. The computed results are compared with the original and extended mild-slope solutions and verified with those of a three-dimensional wave model. The present model has the same data requirements as other two-dimensional models, but provides more accurate and realistic three-dimensional results.
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