Gravity wave refraction by islands

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Abstract
The refractive influence on tsunami run-up of the offshore bottom topography of islands is analyzed. Shallow water theory is used to treat problems in which the geometry resembles that of individual Hawaiian islands and in which the incident wave is plane and monochromatic.Mathematically, the differential equation for long-wave propagation is converted into an integral equation to which numerical methods are applied. Results of practical importance include the run-up on island coastal areas. The results are used in conjunction with earlier one-dimensional analyses to estimate the total tsunami run-up.

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