### Abstract

Several theories for weakly damped free-surface flows have been formulated. In this Letter we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schrödinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.

Original language | English (US) |
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Pages (from-to) | 1297-1302 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 372 |

Issue number | 8 |

DOIs | |

State | Published - Feb 18 2008 |

### Keywords

- Free surface
- Navier-Stokes equations
- Potential flow
- Viscosity

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*372*(8), 1297-1302. https://doi.org/10.1016/j.physleta.2007.09.027