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Explicit Dirichlet–Neumann operator for water waves

Published online by Cambridge University Press:  24 October 2022

Didier Clamond Open the ORCID record for Didier Clamond [Opens in a new window]
Didier Clamond*
Affiliation:
Université Côte d'Azur, CNRS UMR 7351, Laboratoire J. A. Dieudonné, Parc Valrose, 06108 Nice CEDEX 2, France
*
†Email address for correspondence: [email protected]
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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, and subsequently extrapolated to 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.

JFM classification

Mathematical Foundations: General fluid mechanics Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 950 , 10 November 2022 , A33
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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