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arXiv · 2209.06490

Explicit Dirichlet-neumann Operator For Water Waves

Didier Clamond
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Abstract

An explicit expression for the Dirichlet-Neumann operator for surface water waves is presented. For non-overturning waves, but without assuming small amplitudes, the formula is first derived in two dimensions, subsequently extrapolated in higher dimensions and with a moving bottom. Although described here for water waves, this elementary approach could be adapted to many other problems having similar mathematical formulations.

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Didier Clamond. 2022-09-14. Explicit Dirichlet-neumann Operator For Water Waves. https://doi.org/10.1017/jfm.2022.830

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