The localization length of randomly scattered water waves

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Abstract
A theory for the reflection-transmission problem of linear water waves in shallow channels with large-amplitude, rapidly varying topographies is given in Nachbin & Papanicolaou (1992b). However, it is very difficult to extract quantitative information from the theory in the large-amplitude regime. In this work, theoretical parameters are evaluated numerically, through the use of a numerical Schwarz–Christoffel transformation and of a Monte Carlo simulation. This enables the theory to be applied to its full extent. As a result we calculate the localization length for any given type of random bottom topography. Additionally, the numerical conformal mapping provides further insight into depth effects arising from potential theory. Statistical results, for numerically generated reflected waves, are in very good agreement with the theory for both piecewise-linear and piecewise-constant topographies of large amplitude.

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