Abstract
We present a general method for determining the runup and the amplification explicitly for nonbreaking long waves propagating over piecewise linear topography, using the linear shallow water wave equations. We associate each constant-depth segment and each linearly-varying depth segment with (2 x 2) matrices and we calculate the transmitted wave amplitude after propagating over any number of segments explicitly. We then extend our methodology to the three dimensional topography of a conical island. Our method is applicable in the design of dikes, sea-walls and other coastal structures.
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