Explicit Dirichlet-neumann Operator For Water Waves

TL;DR

This paper derives an explicit formula for the Dirichlet-Neumann operator in water wave problems, applicable to non-overturning waves of arbitrary amplitude, and extends it to higher dimensions and moving bottoms.

Contribution

It provides a novel explicit expression for the Dirichlet-Neumann operator that does not assume small amplitudes and can be adapted to various related problems.

Findings

Explicit formula for water wave Dirichlet-Neumann operator

Applicable to non-overturning waves of arbitrary amplitude

Extensible to higher dimensions and moving bottoms

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.